From 434e9634c33e6f514552ad48ac59115ccfe1cba6 Mon Sep 17 00:00:00 2001 From: Nathan Abramov Date: Tue, 7 Jul 2026 12:21:30 +0300 Subject: [PATCH] format --- .../quantum_volume/quantum_volume.ipynb | 2404 +++++------ .../fermi_hubbard_1D.ipynb | 3677 ++++++++--------- .../logical_qubits_by_alice_and_bob.ipynb | 2345 ++++++----- .../qml_with_classiq_guide.ipynb | 2277 +++++----- 4 files changed, 5276 insertions(+), 5427 deletions(-) diff --git a/applications/benchmarking/quantum_volume/quantum_volume.ipynb b/applications/benchmarking/quantum_volume/quantum_volume.ipynb index df69b3850..833a871f0 100644 --- a/applications/benchmarking/quantum_volume/quantum_volume.ipynb +++ b/applications/benchmarking/quantum_volume/quantum_volume.ipynb @@ -1,1258 +1,1152 @@ { - "cells": [ - { - "cell_type": "markdown", - "id": "0", - "metadata": {}, - "source": [ - "# Quantum Volume\n", - "\n", - "Quantum volume is a measurement of the errors characterizing a chosen quantum hardware. The quantum volume is a result of running a circuit based on principles of randomness and statistical analysis, which provides a single number to compare different hardware backends.\n", - "\n", - "The scheme of the quantum volume [[1](#circuit)]:\n", - "1. For a number of qubits $n$, a circuit is made of the $n$ quantum layer.\n", - "2. Each layer consists of a unitary operation between pairs of $n$ qubits. The pairs are chosen at random. If $n$ is odd, one of them does not have an operation.\n", - "3. The unitary operation between each pair is the Haar random matrix; i.e., an SU(4) operation containing a random complex number in such a manner that the probability of measuring a quantum state is kept with uniform distribution.\n", - "4. A single circuit of $n$ qubits is measured and the heavy output probability (i.e., the probability of measuring the states above the median value) is calculated. Due to the nature of the distribution of random complex numbers, one can evaluate that for an ideal case (no noises), the heavy output probability should be ~0.85. For an assessment of the quantum volume, the demand subsides to the following inequality: (1) $P_{\\rm heavy\\_ outputs} \\leq 2/3.$\n", - "5. For a given output, to get the quantum volume, repeat Items 1-4 for an increasing number of qubits until the inequality described in Item 4 does not hold. To ensure it, the circuits are created many times and the average and standard deviation are taken into account.\n", - "6. The quantum volume is two to the power of the number of qubits, such that they pass inequality (1) as per the procedure described in Items 1-5.\n", - "\n", - "The heavy output probability is a good measurement of the quality of the circuit, as noise reduces the probabilities of uniform distribution. While this is so, consider that there are many components to the results of the procedure - not only the hardware noises, but also the connectivity map, the quality of the transpilation, and even the quantum software that translates the circuit into basis gates for the hardware, thus contributing to the circuit depth.\n", - "\n", - "This demonstration shows the code for implementing the steps to calculate the quantum volume using the Classiq platform and an example of such calculations for several quantum simulators and hardware backends." - ] - }, - { - "cell_type": "markdown", - "id": "1", - "metadata": {}, - "source": [ - "## Step 1: Create a Haar Random Unitary Matrix\n", - "\n", - "Create a function, generating a (n,n) sized Haar random unitary matrix [[2](#unitary)]. This matrix contains a random complex number that is distributed evenly in the $2^n$ space of quantum states. The Haar distribution indicates how to weight the elements of $U(N)$ such that uniform distribution occurs in the parameter space." - ] - }, - { - "cell_type": "code", - "execution_count": 1, - "id": "2", - "metadata": {}, - "outputs": [], - "source": [ - "import numpy as np\n", - "from numpy.linalg import qr\n", - "from scipy.stats import unitary_group\n", - "\n", - "\n", - "def haar(n):\n", - " u1 = unitary_group.rvs(n)\n", - " u2 = unitary_group.rvs(n)\n", - " Z = u1 + 1j * u2\n", - "\n", - " Q, R = qr(Z)\n", - "\n", - " Lambda = np.diag([R[i, i] / np.abs(R[i, i]) for i in range(n)])\n", - "\n", - " return np.dot(Q, Lambda)" - ] - }, - { - "cell_type": "markdown", - "id": "3", - "metadata": {}, - "source": [ - "## Step 2: Create a Quantum Volume Circuit\n", - "\n", - "The `qv_model` function creates the quantum volume model for a given $N$ number of qubits. For $N$ qubits, the circuit must include $N$ quantum volume layers. The layers are built using the `qv_layer` function, which creates random pairing between the $N$ qubits. (For an odd number, a randomly chosen qubit is not operational.) Between each pair, a unitary gate operates, consisting of a Haar random unitary matrix of size 4." - ] - }, - { - "cell_type": "code", - "execution_count": 2, - "id": "4", - "metadata": {}, - "outputs": [], - "source": [ - "import math\n", - "import random\n", - "\n", - "from classiq import *\n", - "\n", - "\n", - "@qfunc\n", - "def qv_layer(N: int, target: QArray):\n", - " # Step 1: start with a shuffle of the qubits\n", - " qubit_list = list(range(N))\n", - " random.shuffle(qubit_list)\n", - "\n", - " for idx in range(math.floor(N / 2)):\n", - " # Step 2: Isolate the qubit pairs for the layers\n", - " a = qubit_list[idx]\n", - " b = qubit_list[math.floor(N / 2) + idx]\n", - "\n", - " # Step 3: Generate the random matrix (this needs to change for the random matrix when possible)\n", - " gate_matrix = haar(4).tolist()\n", - " unitary(gate_matrix, [target[a], target[b]])\n", - "\n", - "\n", - "def qv_model(N):\n", - " @qfunc\n", - " def main(target: Output[QArray]):\n", - " allocate(N, target)\n", - " repeat(N, lambda _: qv_layer(N, target))\n", - "\n", - " return main" - ] - }, - { - "cell_type": "markdown", - "id": "5", - "metadata": {}, - "source": [ - "## Step 3: Execute and Analyze\n", - "\n", - "\n", - "The execution and analysis part consists of these functions:\n", - "* `execute_qv` sends a quantum program for execution on a given quantum hardware with a specified number of shots. The function returns the results of the execution from the hardware.\n", - "* `heavy_outputs_prob` analyzes the results from execution and returns the heavy output probability; i.e., the probability for a single state in the space to be greater than the median value (median = \"middle\" of a sorted list of numbers).\n", - "\n", - "The `round_significant` function rounds a number for one significant figure." - ] - }, - { - "cell_type": "code", - "execution_count": 3, - "id": "6", - "metadata": {}, - "outputs": [], - "source": [ - "def execute_qv(qprog, num_shots, preferences):\n", - " execution_prefs = ExecutionPreferences(\n", - " num_shots=num_shots, backend_preferences=preferences\n", - " )\n", - " with ExecutionSession(qprog, execution_prefs) as es:\n", - " res = es.sample()\n", - "\n", - " return res" - ] - }, - { - "cell_type": "code", - "execution_count": 4, - "id": "7", - "metadata": {}, - "outputs": [], - "source": [ - "def heavy_outputs_prob(results):\n", - " d = list(results.counts.values())\n", - " med = np.median(d)\n", - " heavy_outputs_prob = 0\n", - " # print(med)\n", - " for count, item in enumerate(d):\n", - " if item >= med:\n", - " heavy_outputs_prob = heavy_outputs_prob + item\n", - " return heavy_outputs_prob" - ] - }, - { - "cell_type": "code", - "execution_count": 5, - "id": "8", - "metadata": {}, - "outputs": [], - "source": [ - "from math import floor, log10\n", - "\n", - "\n", - "def round_significant(x):\n", - " return round(x, -int(floor(log10(abs(x)))))" - ] - }, - { - "cell_type": "markdown", - "id": "9", - "metadata": {}, - "source": [ - "## Step 4: Find the Quantum Volume Algorithm\n", - "\n", - "Using the previously defined functions, `find_qv` finds the quantum volume value for defined parameters including hardware definitions.\n", - "The `find_qv` function sends the value of heavy output probability for each number of qubits defined (between `min_qubit` and `max_qubits`). This repeats `num_trials` times. Then, the heavy output probability is averaged, and the standard deviation is calculated. If the number of qubits chosen for the circuit is less than the number of qubits in the chosen hardware, the qubits are randomly picked to run according to the rules of the hardware provider.\n", - "\n", - "The quantum volume qubits number is defined as the larger number of qubits for which the heavy output probability, decreased by two sigma (twice the standard deviation), is greater than or equal to 2/3. The quantum volume is two to the power of the number of quantum volume qubits.\n", - "\n", - "Note that if the result given for the log2 of the quantum volume is the same as the chosen `max_qubits`, there is a possibility that the quantum volume is greater than found by the function. In this case, run the program for a greater span." - ] - }, - { - "cell_type": "code", - "execution_count": 6, - "id": "10", - "metadata": {}, - "outputs": [], - "source": [ - "from tqdm import tqdm\n", - "\n", - "# For testing, we save all qprogs generated in the notebook\n", - "qprogs = []\n", - "\n", - "\n", - "def find_qv(num_trials, num_shots, min_qubits, max_qubits, preferences):\n", - " ### initialization\n", - " qubit_num = range(min_qubits, max_qubits + 1)\n", - " heavy_list = np.zeros(max_qubits - min_qubits + 1)\n", - " std_list = np.zeros(max_qubits - min_qubits + 1)\n", - " qubit_v = 0\n", - "\n", - " ### calculate the heavy outputs for each number of qubits\n", - " for num in tqdm(qubit_num):\n", - " heavy_outputs = 0\n", - " std = 0\n", - " heavytostd = np.zeros(num_trials)\n", - " for idx in tqdm(range(num_trials)):\n", - " qprog = synthesize(qv_model(num))\n", - " qprogs.append(qprog)\n", - " results = execute_qv(qprog, num_shots, preferences)\n", - " heavy_temp = heavy_outputs_prob(results)\n", - " heavy_outputs = heavy_outputs + heavy_temp\n", - " heavytostd[idx] = heavy_temp\n", - " s = num - min_qubits\n", - " heavy_list[s] = heavy_outputs / (num_trials * num_shots)\n", - " temp_hl = heavy_outputs / (num_trials * num_shots)\n", - " std = np.std(heavytostd) / (num_trials * num_shots)\n", - " std_list[s] = std\n", - " temp_std = round_significant(std)\n", - " print(\n", - " f\"for {num} qubits the heavy outputs probability is: {temp_hl} with {temp_std} standard deviation\"\n", - " )\n", - "\n", - " ### determine the quantum volume\n", - " for num in qubit_num:\n", - " s = num - min_qubits\n", - " heavy_is = heavy_list[s] - 2 * (std_list[s])\n", - " if heavy_is >= 2 / 3:\n", - " qubit_v = num\n", - " else:\n", - " break\n", - "\n", - " qv = 2**qubit_v\n", - " print(f\"##### The quantum volume is {qv} #####\")\n", - "\n", - " return qv" - ] - }, - { - "cell_type": "markdown", - "id": "11", - "metadata": {}, - "source": [ - "## Examples\n", - "\n", - "Run the code to find the quantum volume of several quantum simulators and hardware backends." - ] - }, - { - "cell_type": "markdown", - "id": "12", - "metadata": {}, - "source": [ - "### Running with the Classiq Simulator" - ] - }, - { - "cell_type": "code", - "execution_count": 7, - "id": "13", - "metadata": {}, - "outputs": [ - { - "name": "stderr", - "output_type": "stream", - "text": [ - " 0%| | 0/4 [00:00= med:\n", + " heavy_outputs_prob = heavy_outputs_prob + item\n", + " return heavy_outputs_prob" + ], + "execution_count": 4, + "outputs": [], + "id": "7" + }, + { + "cell_type": "code", + "metadata": {}, + "source": [ + "from math import floor, log10\n", + "\n", + "\n", + "def round_significant(x):\n", + " return round(x, -int(floor(log10(abs(x)))))" + ], + "execution_count": 5, + "outputs": [], + "id": "8" + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Step 4: Find the Quantum Volume Algorithm\n", + "\n", + "Using the previously defined functions, `find_qv` finds the quantum volume value for defined parameters including hardware definitions.\n", + "The `find_qv` function sends the value of heavy output probability for each number of qubits defined (between `min_qubit` and `max_qubits`). This repeats `num_trials` times. Then, the heavy output probability is averaged, and the standard deviation is calculated. If the number of qubits chosen for the circuit is less than the number of qubits in the chosen hardware, the qubits are randomly picked to run according to the rules of the hardware provider.\n", + "\n", + "The quantum volume qubits number is defined as the larger number of qubits for which the heavy output probability, decreased by two sigma (twice the standard deviation), is greater than or equal to 2/3. The quantum volume is two to the power of the number of quantum volume qubits.\n", + "\n", + "Note that if the result given for the log2 of the quantum volume is the same as the chosen `max_qubits`, there is a possibility that the quantum volume is greater than found by the function. In this case, run the program for a greater span." + ], + "id": "9" + }, + { + "cell_type": "code", + "metadata": {}, + "source": [ + "from tqdm import tqdm\n", + "\n", + "# For testing, we save all qprogs generated in the notebook\n", + "qprogs = []\n", + "\n", + "\n", + "def find_qv(num_trials, num_shots, min_qubits, max_qubits, preferences):\n", + " ### initialization\n", + " qubit_num = range(min_qubits, max_qubits + 1)\n", + " heavy_list = np.zeros(max_qubits - min_qubits + 1)\n", + " std_list = np.zeros(max_qubits - min_qubits + 1)\n", + " qubit_v = 0\n", + "\n", + " ### calculate the heavy outputs for each number of qubits\n", + " for num in tqdm(qubit_num):\n", + " heavy_outputs = 0\n", + " std = 0\n", + " heavytostd = np.zeros(num_trials)\n", + " for idx in tqdm(range(num_trials)):\n", + " qprog = synthesize(qv_model(num))\n", + " qprogs.append(qprog)\n", + " results = execute_qv(qprog, num_shots, preferences)\n", + " heavy_temp = heavy_outputs_prob(results)\n", + " heavy_outputs = heavy_outputs + heavy_temp\n", + " heavytostd[idx] = heavy_temp\n", + " s = num - min_qubits\n", + " heavy_list[s] = heavy_outputs / (num_trials * num_shots)\n", + " temp_hl = heavy_outputs / (num_trials * num_shots)\n", + " std = np.std(heavytostd) / (num_trials * num_shots)\n", + " std_list[s] = std\n", + " temp_std = round_significant(std)\n", + " print(\n", + " f\"for {num} qubits the heavy outputs probability is: {temp_hl} with {temp_std} standard deviation\"\n", + " )\n", + "\n", + " ### determine the quantum volume\n", + " for num in qubit_num:\n", + " s = num - min_qubits\n", + " heavy_is = heavy_list[s] - 2 * (std_list[s])\n", + " if heavy_is >= 2 / 3:\n", + " qubit_v = num\n", + " else:\n", + " break\n", + "\n", + " qv = 2**qubit_v\n", + " print(f\"##### The quantum volume is {qv} #####\")\n", + "\n", + " return qv" + ], + "execution_count": 6, + "outputs": [], + "id": "10" + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Examples\n", + "\n", + "Run the code to find the quantum volume of several quantum simulators and hardware backends." + ], + "id": "11" + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Running with the Classiq Simulator" + ], + "id": "12" + }, + { + "cell_type": "code", + "metadata": {}, + "source": [ + "num_trials = 10 # number of times to run the QV circuit for each number of qubits. Best: 200 or more\n", + "num_shots = 100 # number of runs for each execution. Best: 1000 or more\n", + "preferences = ClassiqBackendPreferences(\n", + " backend_name=ClassiqSimulatorBackendNames.SIMULATOR\n", + ")\n", + "min_qubits = 3\n", + "max_qubits = 6\n", + "\n", + "qv = find_qv(num_trials, num_shots, min_qubits, max_qubits, preferences)" + ], + "execution_count": 7, + "outputs": [ + { + "output_type": "stream", + "text": [ + " 0%| | 0/4 [00:00[1] [Andrew W. Cross, Lev S. Bishop, Sarah Sheldon, Paul D. Nation, and Jay M. Gambetta (2019). Validating quantum computers using randomized model circuits.](https://arxiv.org/pdf/1811.12926.pdf)\n", + "\n", + "[2] [Maris Ozols (2009). How to generate a random unitary matrix.](http://home.lu.lv/~sd20008/papers/essays/Random%20unitary%20[paper].pdf)" + ], + "id": "21" + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.11.9" } - ], - "source": [ - "num_trials = 10 # number of times to run the QV circuit for each number of qubits. Best: 200 or more\n", - "num_shots = 100 # number of runs for each execution. Best: 1000 or more\n", - "preferences = ClassiqBackendPreferences(\n", - " backend_name=ClassiqSimulatorBackendNames.SIMULATOR\n", - ")\n", - "min_qubits = 3\n", - "max_qubits = 6\n", - "\n", - "qv = find_qv(num_trials, num_shots, min_qubits, max_qubits, preferences)" - ] - }, - { - "cell_type": "markdown", - "id": "14", - "metadata": {}, - "source": [ - "Since this is a simulator with no errors, we expect the heavy output probability for any number of qubits to be approximately 0.85." - ] - }, - { - "cell_type": "markdown", - "id": "15", - "metadata": {}, - "source": [ - "### Running with Rigetti Aspen M-3" - ] - }, - { - "cell_type": "code", - "execution_count": 8, - "id": "16", - "metadata": {}, - "outputs": [], - "source": [ - "num_trials = 10 # number of times to run the QV circuit for each number of qubits\n", - "num_shots = 3 # number of runs for each execution\n", - "preferences = AzureBackendPreferences(backend_name=\"Rigetti.Qpu.Aspen-M-3\")\n", - "min_qubits = 2\n", - "max_qubits = 3\n", - "\n", - "# qv = find_qv_trials, num_(numshots, min_qubits, max_qubits, preferences)" - ] - }, - { - "cell_type": "markdown", - "id": "17", - "metadata": {}, - "source": [ - "### Running with IBM Cloud targets\n", - "\n", - "Run on a few IBM machines: \n", - "- ibm_fez with a reported quantum volume of 8\n", - "- ibm_marrakesh with a reported quantum volume of 16\n", - "- ibm_sherbrooke with a reported quantum volume of 32 \n", - "\n", - "Refer to the [IBM website](https://quantum.cloud.ibm.com/computers)" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "18", - "metadata": {}, - "outputs": [], - "source": [ - "preferences = IBMBackendPreferences(\n", - " backend_name=\"ibm_fez\",\n", - " access_token=\"my-access-token\",\n", - " channel=\"ibm_cloud\",\n", - " instance_crn=\"instance-CRN\",\n", - ")\n", - "\n", - "num_trials = 5 # number of times to run the QV circuit for each number of qubits\n", - "num_shots = 10 # number of runs for each execution\n", - "min_qubits = 2\n", - "max_qubits = 4\n", - "\n", - "# qv = find_qv(num_trials, num_shots, min_qubits, max_qubits, preferences)" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "19", - "metadata": {}, - "outputs": [], - "source": [ - "preferences = IBMBackendPreferences(\n", - " backend_name=\"ibm_marrakesh\",\n", - " access_token=\"my-access-token\",\n", - " channel=\"ibm_cloud\",\n", - " instance_crn=\"instance-CRN\",\n", - ")\n", - "\n", - "num_trials = 1 # number of times to run the QV circuit for each number of qubits\n", - "num_shots = 10 # number of runs for each execution\n", - "min_qubits = 2\n", - "max_qubits = 3\n", - "\n", - "# qv = find_qv(num_trials, num_shots, min_qubits, max_qubits, preferences)" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "20", - "metadata": {}, - "outputs": [], - "source": [ - "preferences = IBMBackendPreferences(\n", - " backend_name=\"ibm_sherbrooke\",\n", - " access_token=\"my-access-token\",\n", - " channel=\"ibm_cloud\",\n", - " instance_crn=\"instance-CRN\",\n", - ")\n", - "\n", - "num_trials = 1 # number of times to run the QV circuit for each number of qubits\n", - "num_shots = 10 # number of runs for each execution\n", - "min_qubits = 2\n", - "max_qubits = 3\n", - "\n", - "# qv = find_qv(num_trials, num_shots, min_qubits, max_qubits, preferences)" - ] - }, - { - "cell_type": "markdown", - "id": "21", - "metadata": {}, - "source": [ - "## References\n", - "\n", - "[1] [Andrew W. Cross, Lev S. Bishop, Sarah Sheldon, Paul D. Nation, and Jay M. Gambetta (2019). Validating quantum computers using randomized model circuits.](https://arxiv.org/pdf/1811.12926.pdf)\n", - "\n", - "[2] [Maris Ozols (2009). How to generate a random unitary matrix.](http://home.lu.lv/~sd20008/papers/essays/Random%20unitary%20[paper].pdf)" - ] - } - ], - "metadata": { - "kernelspec": { - "display_name": "Python 3 (ipykernel)", - "language": "python", - "name": "python3" }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.11.9" - } - }, - "nbformat": 4, - "nbformat_minor": 9 -} + "nbformat": 4, + "nbformat_minor": 9 +} \ No newline at end of file diff --git a/applications/physical_systems/fermi_hubbard_model_1D/fermi_hubbard_1D.ipynb b/applications/physical_systems/fermi_hubbard_model_1D/fermi_hubbard_1D.ipynb index b37f7b68d..da5227a23 100644 --- a/applications/physical_systems/fermi_hubbard_model_1D/fermi_hubbard_1D.ipynb +++ b/applications/physical_systems/fermi_hubbard_model_1D/fermi_hubbard_1D.ipynb @@ -1,1851 +1,1834 @@ { - "cells": [ - { - "cell_type": "markdown", - "id": "0", - "metadata": {}, - "source": [ - "# One-Dimensional Fermi-Hubbard Model" - ] - }, - { - "cell_type": "markdown", - "id": "1", - "metadata": {}, - "source": [ - "## Overview\n", - "\n", - "This notebook implements a quantum simulation of the one-dimensional Fermi-Hubbard model using Classiq's quantum programming framework. The simulation proceeds in three stages:\n", - "\n", - "1. **Initial state preparation** - The ground state of a non-interacting Hamiltonian with a spin-dependent attractive potential is prepared as a Slater determinant via Givens rotations. This creates an initial state with localized charge and spin densities.\n", - "\n", - "2. **Time evolution** - The system is quenched to the interacting Fermi-Hubbard Hamiltonian and propagated using a first-order Trotterized circuit, where each Trotter step is decomposed into hopping and interaction layers using the Jordan-Wigner transformation.\n", - "\n", - "3. **Measurement and analysis** - Charge and spin densities are measured at each time step to observe the dynamics, testing the phenomenon of spin-charge separation at intermediate interaction strengths.\n", - "\n", - "Finally, the results are validated against exact analytical solutions in two limiting cases: the non-interacting limit ($U=0$), where the dynamics reduce to single-particle evolution, and the vanishing hopping limit ($J=0$), where the Trotter decomposition becomes exact and all densities are frozen.\n", - "\n", - "The simulation closely follows the experimental and algorithmic procedure desribed in [[1](#google_paper)]" - ] - }, - { - "cell_type": "markdown", - "id": "2", - "metadata": {}, - "source": [ - "## Introduction\n", - "The Fermi-Hubbard model is a fundamental corner step of condensed matter physics, describing the interplay between kinetic energy and repulsion interaction between electrons in a solid. Although very simple, in certain parameter regimes, the model showcases a variety strongly correlated phenomena, such as the metal-insulator transition (Mott physics), antiferromagnetism, inhomogeneous phases, and unconventional Fermi liquids.\n", - "\n", - "In order to motivate or conceptually derive the model, consider of a metalic material composed of atoms organized in a regular pattern, i.e., a lattice. We assume the temperature is sufficiently low, so the that the vibrations of the atoms can be neglected and the atoms are essentially held in a fix position in the lattice sites. Moreover, typically each atom has a handful of relevant energy levels, however, in order to simplify the problem we will consider only a single energy level at each lattice site (one energy level per atom). In the metal, valance electrons move freely between the metal atoms, leading to the expected conductive behaviour. The movement of the electrons between the sites is dictated by the overlap of the spatial wave function on different sites. Since the atomic wave-functions decay exponentially with the distance to the nuclei, we consider only the dominant contribution, giving rise to hopping of electrons only between adjacent lattice sites.\n", - "These consideration lead to the first the hopping term, constituting the kinetic energy contribution: $-J \\sum_{\\langle i,j \\rangle, \\sigma} \\left ( c_{i\\sigma}^\\dagger c_{j\\sigma} + c_{i\\sigma}^\\dagger c_{j\\sigma}\\right)$, where $c_{i\\sigma}$ is the fermionic annihilation operator on the $i$'th lattice site and $\\sigma =\n", - "\\uparrow, \\downarrow$ spin. In addition, $\\langle i,j\\rangle$ designates that the sum is only over nearest-neighbors.\n", - "\n", - "A second contribution arises from the repulsive Coulomb interaction between two electrons. Such interaction is strongest between electrons on the same atom. We consider only this dominant contribution, adding an energy penalty of $U$, for two-electrons on the same site. In addition, Pauli's exclusion principle dictates that two electrons cannot be in the same quantum state, therefore the repulsive interaction can only be between electrons with different spins: $U \\sum_{j} c_{j \\uparrow}^\\dagger c_{j \\uparrow} c_{j\\downarrow}^\\dagger c_{j\\downarrow}$.\n", - "\n", - "Overall, the Fermi-Hubbard Hamiltonian is given by: $$H_{HF} = -J \\sum_{\\langle i,j \\rangle, \\sigma} \\left ( c_{i\\sigma}^\\dagger c_{j\\sigma} + c_{i\\sigma}^\\dagger c_{j\\sigma}\\right) + U \\sum_{j} n_{j \\uparrow} n_{j\\downarrow}~~,~~~~~~ (1)$$ where $ n_{j \\sigma}= c_{j \\sigma}^\\dagger c_{j \\sigma}$ is the number operator.\n", - "\n", - "\n", - "The model constitutes a key tool in the investigation of transition metal oxides, organic conductors and cuprates, which exhibit high-temperature superconductivity and exotic quantum magnetism properties and unconventional symmetry breaking.\n", - "Despite its apparent simplicity, the model is notoriously challenging, in 1D the Fermi-Hubbard model is solvable via Bethe ansatz [[2](#LiebWu)], while the 2D and 3D cases have not exact solution (for general hopping and interaction coefficients, $J$ and $U$). However, in 3D quantum phenomena are suppressed and the model typically exhibit classical behaviour, well described by mean-field theories.\n", - "Numerical studies are also limited beyond specific doping regimes (doping modifies the fraction of electrons/lattice sites). Perturbation theory becomes invalid when strong correlations between the electron emerge, while Monte-Carlo methods are restricted by the sign problem away from half filling (at half filling the number of electrons equals the number lattice sites)." - ] - }, - { - "cell_type": "markdown", - "id": "3", - "metadata": {}, - "source": [ - "The physics of the model are conveniently analysed by measuring the evolution of the spin densities $$\\rho_j^{\\pm}(t) = \\langle n_{j,\\uparrow}\\rangle \\pm \\langle n_{j,\\downarrow} \\rangle~~.$$\n", - "\n", - "We consider a simplified model consisting of a lattice of $N=4$ sites, and study the dynamics for an intermediate interaction strength, $U/J = 3$." - ] - }, - { - "cell_type": "markdown", - "id": "4", - "metadata": {}, - "source": [ - "## Classiq Implementation\n", - "\n", - "We implement the Hamiltonian simulation in three steps, utilizing Classiq's built-in functions.\n", - "\n", - "1. Initial state-preparation: Efficiently prepare the ground state of a non-interacting FH system in the presence of an external spin dependent potential. The ground state is a Gaussian Fermionic state, creating a localized density peak, acting as a wavepacket source. \n", - "2. Time-evolution: Abruptly turn on the two-electron repulsion interaction and turn off the external potential, leading to dynamics governed by Hamiltonian (1). Utilizing a first-order Trotter expansion, the system is evolved in time.\n", - "3. Measurement: The spin densities are evaluated.\n", - "\n", - "Repetition of these three steps many times produces the evolution of expectation values of spin-density in time, $\\{\\rho^{\\pm}_{j}(t)\\}$.\n", - "\n" - ] - }, - { - "cell_type": "markdown", - "id": "5", - "metadata": {}, - "source": [ - "We begin by importing the required software packages and defining global constants" - ] - }, - { - "cell_type": "code", - "execution_count": 1, - "id": "6", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "\n", - "[optparse.groups]Usage:[/] \n", - " pip install \\[options] \\[package-index-options] ...\n", - " pip install \\[options] -r \\[package-index-options] ...\n", - " pip install \\[options] [-e] ...\n", - " pip install \\[options] [-e] ...\n", - " pip install \\[options] ...\n", - "\n", - "no such option: -u\n" - ] - } - ], - "source": [ - "!pip install -u -qq \"classiq[chemistry]\"" - ] - }, - { - "cell_type": "code", - "execution_count": 2, - "id": "7", - "metadata": {}, - "outputs": [], - "source": [ - "import numpy as np\n", - "from openfermion.circuits.slater_determinants import (\n", - " slater_determinant_preparation_circuit,\n", - ")\n", - "from openfermion.linalg.givens_rotations import (\n", - " fermionic_gaussian_decomposition,\n", - " givens_decomposition,\n", - ")\n", - "from openfermion.ops import QuadraticHamiltonian\n", - "\n", - "from classiq import *" - ] - }, - { - "cell_type": "code", - "execution_count": 3, - "id": "8", - "metadata": {}, - "outputs": [], - "source": [ - "N = 4 # number of lattice sites\n", - "a = 1 # lattice spacing\n", - "L = N * a # length of the lattice\n", - "M = 2 * N # total number of fermionic modes\n", - "NUM_ITERS = 10\n", - "J = 1 # hopping strength\n", - "tau = 0.1 / J # Trotter step time interval\n", - "T = NUM_ITERS * tau" - ] - }, - { - "cell_type": "markdown", - "id": "9", - "metadata": {}, - "source": [ - "### Initial State Preperation\n", - "\n", - "We begin by desribing a general algorithm to prepare Slater determinant states. \n", - "\n", - "Following, the algorithm is benchmarked on a simple example involving a four-by-four single particle hamiltonian. \n", - "\n", - "The state preperation algorithm is then utilized to prepare the ground state of the non-interacting Fermi-Hubbard Hamiltonian for the case of a single electron. This is then benchmarked against an analitical solution. \n", - "\n", - "Finally, we prepare on the initial state of the dynamic simulation, a ground state of the Fermi-Hubbard model for a quater-filling." - ] - }, - { - "cell_type": "markdown", - "id": "10", - "metadata": {}, - "source": [ - "#### Preparation of a Slater Determinant State\n", - "\n", - "A Slater-Determinant is the ground state of a quadratic Fermionic Hamiltonian which conserves the number of particles.\n", - "\n", - "We begin by discussing an efficient algorithm to construct the initial non-interacting state.\n", - "\n", - "As all ground states of non-interacting fermionic Hamiltonian, the ground state is a fermionic Gaussian state, which can be prepared in a worst-case circuit depth of $O(N^2)$ [[3](#fermionic_gaussian_state)]. Specifically, for a quadratic Hamiltonian which conserves the number of particles, the fermionic Gaussian state can be expressed as a Slater determinant.\n" - ] - }, - { - "cell_type": "markdown", - "id": "11", - "metadata": {}, - "source": [ - "For a general number conserving quadratic fermionic Hamiltonian $$H = \\sum_{\\mu\\nu}c_\\mu^\\dagger h_{\\mu\\nu}c_\\nu~~,~~~~(2)$$ where $h$ is known as the **one-body Hamiltonian**.\n", - "\n", - "Using the anti-commutation relations and the Heisenberg equation ($\\frac{dO(t)}{dt} = i\\left[H, O(t) \\right]$), we have \n", - "\n", - "$$\\frac{dc_\\lambda^\\dagger}{dt} = i\\left[H, c_\\lambda^\\dagger \\right]= i \\sum_{\\mu\\nu} h_{\\mu\\nu}[c_\\mu^\\dagger c_\\nu,c_\\lambda] $$\n", - "\n", - "\n", - "$$= i \\sum_{\\mu\\nu} h_{\\mu\\nu}[c_\\mu^\\dagger c_\\nu,c_\\lambda^\\dagger] = i \\sum_{\\mu\\nu} h_{\\mu\\nu}c_\\mu^\\dagger \\delta_{\\nu \\lambda} = i \\sum_{\\mu} h_{\\mu\\lambda}c_\\mu^\\dagger ~~, $$\n", - "where the the time-dependence is suppressed for concisness.\n", - "\n", - " The dynamics in the Heisenberg representation can therefore be expressed as $$\\mathbf{c}^\\dagger (t) = e^{i H t} \\mathbf{c}^\\dagger e^{-i H t} = e^{i h^T }\\mathbf{c}^\\dagger~~,$$ where $\\mathbf{c}^\\dagger = \\{c_1^\\dagger,\\dots,c_M^\\dagger\\}^T$ and $M$ is the total number of fermionic modes. Remarkably, this implies that the diagonalization of $h$, (an $M$ by $M$ matrix) provides the dynamics in the $2^M$ Hilbert space.\n", - "\n", - "\n", - "Diagonalizing the single particle Hamiltonian $M= \\bar{Q} D \\bar{Q}^\\dagger$, where $\\bar{Q}$ is and $M$-by-$M$ unitary matrix and $D = \\text{diag}(\\epsilon_1,...,\\epsilon_M)$, we obtain $H=\\sum_{k=1}^M \\epsilon_k d_k^\\dagger d_k$, where $$d_\\eta^\\dagger= \\sum_{\\mu=1}^{M} \\bar{Q}_{\\mu \\eta}c_\\mu^\\dagger~~. \\tag{3}$$\n", - "Alternatively, the basis transformation can be expressed in terms of the single-particle transformation, $U\\mathbf{c}^\\dagger = \\mathbf{d}^\\dagger~,$ where we collected the creation operators to form an operator valued vector: $\\mathbf{c}^\\dagger = \\{c_1^\\dagger,\\dots,c_M^\\dagger\\}^T$ and similarly for $\\mathbf{d}^\\dagger$.\n", - "\n", - "For a fixed particle number $N_{\\text{elec}}$ the ground state is given by\n", - "$$|\\psi_{g.s}\\rangle =\\Pi_{k} {\\cal U}c_k^\\dagger |0^M\\rangle = \\Pi_{k=1}^{N_{\\text{elec}}} d_k^\\dagger |0^M\\rangle ~~,$$\n", - "where $i$ iterates over the occupied fermionic modes and ${\\cal U} c_j^\\dagger {\\cal U}^\\dagger = U_{[j,:]} \\mathbf{d}^\\dagger = d_j^\\dagger$.\n", - "The diagonalization of $h$ scales only polynomially with the number of lattice sites, $O(L^3)$ and can be efficiently done on a classical computer.\n", - "\n", - "In order to prepare the desired ground state we focus on a part of $\\bar{Q}$ which corresponds to the occupied modes, and denote the $N_{\\text{elec}}$ by $M$ matrix describing these modes by $Q = (\\bar{Q}^T)_{[{\\text{occupied modes}},:]}$. This identification leads to an alternative form for Eq. (3), for the occupied modes we have $$d_\\eta^\\dagger= \\sum_{\\mu=1}^{M} {Q}_{\\eta \\mu}c_\\mu^\\dagger~~.$$" - ] - }, - { - "cell_type": "markdown", - "id": "12", - "metadata": {}, - "source": [ - "An efficient quantum circuit for the ground state preparation can be obtained by a modified QR decomposition of $Q$, using a product of elementary two-mode rotations, called Given rotations. Each rotation can be expressed as\n", - "$$\n", - "\\begin{pmatrix}\n", - "\\mathcal{G}c_k^\\dagger\\mathcal{G}\\\\\n", - "\\mathcal{G}c_j^\\dagger\\mathcal{G}\n", - "\\end{pmatrix}\n", - "=\n", - "G(\\theta,\\varphi)\\,\n", - "\\begin{pmatrix}\n", - "c_k\\\\\n", - "c_j\n", - "\\end{pmatrix}~~,\n", - " $$\n", - "and the form of a Given rotation is $$G_{jk}(\\theta,\\varphi) = \\begin{pmatrix}\n", - "\\cos(\\theta) & -e^{i\\varphi}\\sin(\\theta)\\\\\n", - "\\sin(\\theta) & e^{i\\varphi}\\cos(\\theta)\n", - "\\end{pmatrix}~~. $$\n", - "\n", - "To simplify the decomposition we begin by utilizing the invariance of the Slater determinant (up to a global phase) under the mapping ${Q}\\rightarrow V{Q}$, where $V$ is a unitary transformation. For the transformation of basis to be valid we require that the first $N_{\\text{elec}}$ rows of $VQ$ are equal to $U$, or alternatively $$V{Q}U^\\dagger = (I_{N_{\\text{elec}}}, \\boldsymbol{0})~~.$$ Each Given transformation operates only on two columns and it's parameters, $\\theta$ and $\\phi$ are set so to nullify elements in the upper right part of the matrix. Due to the orthogonality of the rows of $Q$, some transformations nullify more than a single matrix element. As a result, the total number of required Given transformations are $N_G = N_{\\text{elec}}(M-N_\\text{elec})$, where $N_\\text{elec}$ is the number of electrons and $M$ is the number of fermionic modes. The diagonalization procedure results in a product of Given rotations $$U = G_{N_G}\\cdots G_2 G_1~~.$$\n", - "\n", - "After the Jordan-Wigner transformation, each two-mode ($j,k$) rotations correspond to a rotation in the single particle subspace of the two qubits $j$ and $k$ ($|01\\rangle$ and $|10\\rangle$). This completely, defines the state preparation circuit in terms of a sequence two-qubit rotations.\n", - "The gate complexity is $O(N_G) = O(N_{\\text{elec}}^2)$ (worst case achieved for $N_\\text{elec}=M/2$), and parallelization leads to a circuit depth of $M-1$." - ] - }, - { - "cell_type": "markdown", - "id": "13", - "metadata": {}, - "source": [ - "#### Given Rotations Example\n", - "In order to understand the state preparation algorithm, we first show how Given rotations are utilized to diagonalize a simple one-body Hamiltonian.\n", - "\n", - "Consider a simple $4$-by-$4$ Hermitian matrix, representing a one-body Hamiltonian:\n", - "$$h =\n", - "\\begin{pmatrix}\n", - "\\varepsilon_0 & t_{01} & 0 & t_{03} \\\\\n", - "t_{01} & \\varepsilon_1 & t_{12} & 0 \\\\\n", - "0 & t_{12} & \\varepsilon_2 & t_{23} \\\\\n", - "t_{03} & 0 & t_{23} & \\varepsilon_3\n", - "\\end{pmatrix}\n", - " $$" - ] - }, - { - "cell_type": "code", - "execution_count": 4, - "id": "14", - "metadata": {}, - "outputs": [], - "source": [ - "## Defining the single-body Hamiltonian\n", - "# Onsite energies\n", - "eps0, eps1, eps2, eps3 = 0.8, -0.4, 0.3, -0.1\n", - "\n", - "# Hopping amplitudes (real for simplicity)\n", - "t01 = 0.25\n", - "t12 = -0.35\n", - "t23 = 0.20\n", - "t03 = 0.15\n", - "\n", - "# 4x4 Hermitian one-body matrix h_{pq}\n", - "h = np.array(\n", - " [\n", - " [eps0, t01, 0.0, t03],\n", - " [t01, eps1, t12, 0.0],\n", - " [0.0, t12, eps2, t23],\n", - " [t03, 0.0, t23, eps3],\n", - " ],\n", - " dtype=complex,\n", - ")" - ] - }, - { - "cell_type": "markdown", - "id": "15", - "metadata": {}, - "source": [ - "We employ the methods of OpenFermion's `QuadraticHamiltonian` class in order to extract the Given rotations.\n", - "The number conserving quadratic Hamiltonian is then diagonalized utilizing a Bogoliubov transformation, leading to the `orbital_energies` and a `transformation_matrix`." - ] - }, - { - "cell_type": "code", - "execution_count": 5, - "id": "16", - "metadata": {}, - "outputs": [], - "source": [ - "# Number-conserving quadratic Hamiltonian (no pairing term)\n", - "qh = QuadraticHamiltonian(h, constant=0.0)\n", - "orbital_energies, transformation_matrix, constant = (\n", - " qh.diagonalizing_bogoliubov_transform()\n", - ")\n", - "# Taking the number of electrons to be equal to be two\n", - "occupied_orbitals = np.where(orbital_energies < 0.0)[0]\n", - "slater_determinant_matrix = transformation_matrix[occupied_orbitals]\n", - "\n", - "E, Qbar = np.linalg.eigh(h)\n", - "\n", - "# Sanity check: the transformation matrix from the Bogoliubov transform should diagonalize the one-body Hamiltonian\n", - "assert np.allclose(transformation_matrix, Qbar.T)\n", - "assert np.allclose(orbital_energies, E)\n", - "assert np.allclose(Qbar.T @ h @ Qbar, np.diag(E))" - ] - }, - { - "cell_type": "markdown", - "id": "17", - "metadata": {}, - "source": [ - "We extract the given rotations utilizing OpenFermion's `given_decomposition`, returning a list of tuples: `[(G_1,G_2),(G_3,),...]`. Each tuple includes the Given rotations which can be operated in parallel. The Given rotations are encoded as a tuple: $G_k = (i_k,j_k,\\theta_k,\\phi_k)$, where $i_k$ and $i_k$ are the columns of $U^\\dagger$ which the Given rotation $G_k^\\dagger$ is operated on from the right (see calculation below)." - ] - }, - { - "cell_type": "code", - "execution_count": 6, - "id": "18", - "metadata": {}, - "outputs": [], - "source": [ - "rotations, V, diag = givens_decomposition(slater_determinant_matrix)" - ] - }, - { - "cell_type": "markdown", - "id": "19", - "metadata": {}, - "source": [ - "We introduce two utility functions to demonstrate the decomposition, `givens_gate` implements the two-by-two matrix and `build_U_from_rotations`, gathers all the Given rotations to create $U$." - ] - }, - { - "cell_type": "code", - "execution_count": 7, - "id": "20", - "metadata": {}, - "outputs": [], - "source": [ - "def givens_gate(theta: float, phi: float) -> np.ndarray:\n", - " \"\"\"\n", - " Givens rotation:\n", - " G(i,j,theta, phi) = [[ cos(theta), -e^{i phi} sin(theta)],\n", - " [ sin(theta), e^{i phi} cos(theta)]]\n", - " \"\"\"\n", - " c = np.cos(theta)\n", - " s = np.sin(theta)\n", - " e = np.exp(1j * phi)\n", - " return np.array([[c, -e * s], [s, e * c]], dtype=complex)\n", - "\n", - "\n", - "def build_U_from_rotations(M: int, rotations) -> np.ndarray:\n", - " \"\"\"\n", - " Reconstruct U (M x M) from OpenFermion 'givens_rotations' list.\n", - "\n", - " OpenFermion applies these to columns during decomposition; updating columns\n", - " by right-multiplying with G^\\dagger reproduces the same effect.\n", - " \"\"\"\n", - " U_dagger = np.eye(M, dtype=complex)\n", - " for parallel_ops in rotations:\n", - " for i, j, theta, phi in parallel_ops:\n", - " G = givens_gate(theta, phi)\n", - " cols = U_dagger[:, [i, j]]\n", - " U_dagger[:, [i, j]] = cols @ G.conj().T\n", - " return U_dagger.conj().T\n", - "\n", - "\n", - "def build_state_from_rotations(M: int, N: int, circuit_description: list) -> np.ndarray:\n", - " v = np.zeros((M,), dtype=complex)\n", - " v[:N] = np.ones_like(v[:N])\n", - " for parallel_ops in circuit_description:\n", - " for i, j, theta, phi in parallel_ops:\n", - " G = givens_gate(theta, phi)\n", - " v[[i, j]] = G @ v[[i, j]]\n", - " return v" - ] - }, - { - "cell_type": "markdown", - "id": "21", - "metadata": {}, - "source": [ - "Next, we decompose $U$ into Given rotations: $$U = G_{N_G},\\dots,G_1 $$ and verify that $V Q U^\\dagger = (I,\\mathbf{0})$." - ] - }, - { - "cell_type": "code", - "execution_count": 8, - "id": "22", - "metadata": {}, - "outputs": [], - "source": [ - "tol = 1e-8\n", - "Q = np.asarray(slater_determinant_matrix, dtype=complex)\n", - "n, m = Q.shape\n", - "\n", - "U = build_U_from_rotations(m, rotations)\n", - "\n", - "# Check V Q.T U^† = D where D has diag entries in first m columns and zeros elsewhere\n", - "D = np.zeros((n, m), dtype=complex)\n", - "D[np.arange(n), np.arange(n)] = diag\n", - "\n", - "A = V @ Q @ U.conj().T\n", - "\n", - "# Normalize to (I,0) by removing the diagonal unitary on the left:\n", - "# Let Dm = diag(diag) (m x m). Then Dm^† (V Q U^†) = (I,0).\n", - "# So define V' = Dm^† V.\n", - "Dm_dag = np.diag(\n", - " np.conjugate(diag)\n", - ") # Dm^† since diag entries are unit-modulus in theory\n", - "\n", - "Vprime = Dm_dag @ V\n", - "\n", - "I0 = np.zeros((n, m), dtype=complex)\n", - "I0[:, :n] = np.eye(n, dtype=complex)\n", - "\n", - "B = Vprime @ Q @ U.conj().T\n", - "assert np.allclose(A, D, atol=tol, rtol=tol)\n", - "assert np.allclose(B, I0, atol=tol, rtol=tol)" - ] - }, - { - "cell_type": "markdown", - "id": "23", - "metadata": {}, - "source": [ - "State preparation check" - ] - }, - { - "cell_type": "code", - "execution_count": 9, - "id": "24", - "metadata": {}, - "outputs": [], - "source": [ - "# State preparation check for the single excitation subspace\n", - "slater_determinant_matrix = transformation_matrix[[0]]\n", - "rotations, V, diag = givens_decomposition(slater_determinant_matrix)\n", - "circuit_description = reversed(rotations)\n", - "ground_state = build_state_from_rotations(m, n, circuit_description)\n", - "assert np.allclose(h @ Qbar[:, 0], E[0] * Qbar[:, 0], atol=tol, rtol=tol)" - ] - }, - { - "cell_type": "markdown", - "id": "25", - "metadata": {}, - "source": [ - "#### Initial State Preparation of the Fermi Hubbard Model\n", - "\n", - "The initial state is chosen to be the ground state of the non-interacting (i.e, quadratic in the fermionic creation/annihilation operators) Hamiltonian $$H_{0} =-J \\sum_{j, \\sigma} \\left ( c_{j,\\sigma}^\\dagger c_{j+1,\\sigma} + c_{j+1,\\sigma}^\\dagger c_{j,\\sigma}\\right) + \\sum_{j,\\sigma}\\epsilon_{j,\\sigma}n_{j,\\sigma} ~~,$$ where the spin-up fermions feel a Gaussian attractive potential $$\\epsilon_{j,\\uparrow} = -\\lambda \\exp \\left[ -\\frac{(j-m)^2}{2 w^2}\\right]~~,$$ where spin-down fermions feel no potential, $\\epsilon_{j,\\downarrow}$. The parameters $\\lambda$, $m$ and $w$ dictate the precise shape and strength of the potential.\n", - "Such potential creates a localized density peak of spin-up fermions and a flatter distribution for the spin-down fermions. As a result, the simulation begins with localized charge and spin densities. This state is generally not an eigenstate of the interacting Hamiltonian, constituting a highly excited (non-equilibrium) of the interacting system.\n" - ] - }, - { - "cell_type": "markdown", - "id": "26", - "metadata": {}, - "source": [ - "We begin by defining a function mapping lattice and spin degrees of freedom to qubit number, these will assist us to associate fermionic degrees of freedom to the corresponding qubits in the quantum variables." - ] - }, - { - "cell_type": "code", - "execution_count": 10, - "id": "27", - "metadata": {}, - "outputs": [], - "source": [ - "def qubit_idx(site: int, spin: int):\n", - " \"\"\"\n", - " Maps lattice site and spin to qubit indices.\n", - " Non-interleaved layout: spin-up modes occupy qubits 0..N-1,\n", - " spin-down modes occupy qubits N..2N-1.\n", - " This ensures same-spin hopping acts on adjacent JWT qubits.\n", - "\n", - " Args:\n", - " site (int): Lattice site index, the range [0,N-1]\n", - " spin (int): Spin index, either 0 or 1\n", - "\n", - " Returns:\n", - " qubit_idx (int): qubit index\n", - " \"\"\"\n", - " return site + spin * N\n", - "\n", - "\n", - "def qubit_idx_to_site_and_spin(qubit_idx: int):\n", - " \"\"\"\n", - " Maps qubit index to site and spin indices.\n", - "\n", - " Args:\n", - " qubit_idx (int): qubit index\n", - "\n", - " Returns:\n", - " site (int): site index\n", - " spin (int): spin index\n", - " \"\"\"\n", - " spin = qubit_idx // N\n", - " site = qubit_idx % N\n", - " return site, spin" - ] - }, - { - "cell_type": "markdown", - "id": "28", - "metadata": {}, - "source": [ - "The Givens rotation matrix $G(\\theta, \\varphi)$ used in [[2]](#fermionic_gaussian_state) acts on the single-particle subspace of two fermionic modes $i$ and $j$ as\n", - "\n", - "$$G(\\theta, \\varphi) = \\begin{pmatrix} \\cos\\theta & -e^{i\\varphi}\\sin\\theta \\\\ \\sin\\theta & e^{i\\varphi}\\cos\\theta \\end{pmatrix}~~,$$\n", - "\n", - "where the first (second) row/column corresponds to mode $i$ ($j$). When this $2\\times 2$ block is embedded in a two-qubit unitary, the mapping between matrix indices and qubit states depends on the qubit ordering convention of the quantum framework.\n", - "\n", - "OpenFermion's `givens_decomposition` returns rotation parameters $(i, j, \\theta, \\varphi)$ assuming the standard (little-endian) convention where the first qubit in the register is the least significant bit:\n", - "$|01\\rangle \\to$ mode $i$ occupied, $|10\\rangle \\to$ mode $j$ occupied.\n", - "\n", - "Classiq's `unitary` gate, however, uses **big-endian** ordering where the first qubit in the list is the most significant bit:\n", - "$|01\\rangle \\to$ mode $j$ occupied, $|10\\rangle \\to$ mode $i$ occupied.\n", - "\n", - "Under the big-endian convention, the $G$ matrix as written above effectively implements $G^{-1}$ (the inverse rotation) in the single-particle picture, introducing alternating sign errors $(-1)^j$ in the prepared state amplitudes. To compensate, we **swap the qubit order** in the call to `G`, passing `[qba[j], qba[i]]` instead of `[qba[i], qba[j]]`. This restores the correct mode-to-index mapping so that the circuit faithfully implements the Givens rotations from the decomposition." - ] - }, - { - "cell_type": "code", - "execution_count": 11, - "id": "29", - "metadata": {}, - "outputs": [], - "source": [ - "@qfunc\n", - "def G(theta: float, phi: float, qba: QArray[QBit, 2]):\n", - " \"\"\"\n", - " Implements a Given rotation on two qubits.\n", - " \"\"\"\n", - " c = np.cos(theta)\n", - " s = np.sin(theta)\n", - " e = np.exp(1j * phi)\n", - " U = [\n", - " [1, 0, 0, 0],\n", - " [0, c, -e * s, 0],\n", - " [0, s, e * c, 0],\n", - " [0, 0, 0, 1],\n", - " ]\n", - " unitary(U, qba)\n", - "\n", - "\n", - "@qfunc\n", - "def given_rotation(gate: list[int, int, float, float], qba: QArray[QBit, M]) -> None:\n", - " \"\"\"\n", - " Implements a Given rotation on two specific qubits, i and j, from an M-qubit quantum array, qba.\n", - " Note: the qubit order is swapped ([qba[j], qba[i]]) to account for Classiq's\n", - " big-endian qubit ordering in the unitary gate (see markdown cell above).\n", - " \"\"\"\n", - " i, j, theta, phi = gate\n", - " G(theta, phi, [qba[j], qba[i]])\n", - "\n", - "\n", - "@qfunc\n", - "def prepare_slater_det(h: list[list[float, M], M], Nelec: int, qba: QArray[QBit, M]):\n", - " \"\"\"\n", - " Prepares the ground state associated with the single electron matrix h.\n", - " The Hamiltonian satisfies H = \\sum_{\\mu,\\nu}c_{\\mu}^\\dagger h_{\\mu,\\nu} c_{\\nu}\n", - "\n", - " Args:\n", - " h (ndarray): single electron matrix\n", - " Nelec (int): number of electrons\n", - " qba (list[QBit]): list of qubits\n", - " \"\"\"\n", - " # preparing the reference state, as the state with the first Nelec qubits in state |1> and the rest in state |0>.\n", - " repeat(Nelec, lambda i: X(qba[i]))\n", - "\n", - " # diagonalizing h\n", - " D, Qbar = np.linalg.eigh(h)\n", - " Q = (Qbar.T)[:Nelec, :] # occupying the N lowest energy states\n", - " rotations, _, _ = givens_decomposition(Q)\n", - " # U = build_U_from_rotations(M, rotations)\n", - " circuit_description = list(reversed(rotations))\n", - " # ground_state = build_state_from_rotations(M, N, circuit_description)\n", - " for parallel_ops in circuit_description:\n", - " for gate in parallel_ops:\n", - " given_rotation(list(gate), qba)" - ] - }, - { - "cell_type": "markdown", - "id": "30", - "metadata": {}, - "source": [ - "The circuit can be verified by considering the single excitation subspace and comparing the compared state to the analytical result.\n", - "\n", - "The ground state of the single excitation subspace is up to a global phase just $$d_1^\\dagger | 0^M\\rangle =\\sum_\\mu Q_{1,\\mu} c^{\\dagger}_\\mu | 0^M\\rangle ~~,$$ which after the Jordan-Wigner transformation corresponds to the quibt state with amplitudes $$[Q_{1,1},Q_{1,2},\\dots, Q_{1,M}]~~.$$" - ] - }, - { - "cell_type": "markdown", - "id": "31", - "metadata": {}, - "source": [ - "In order to prepare the initial state, we begin by constructing the initial Hamiltonian. Utility functions are defined and the Hamiltonian parameters are set." - ] - }, - { - "cell_type": "code", - "execution_count": 12, - "id": "32", - "metadata": {}, - "outputs": [], - "source": [ - "def sym(A):\n", - " \"\"\"\n", - " Symmetrizes the matrix A\n", - " \"\"\"\n", - " return (A + A.T) / 2\n", - "\n", - "\n", - "def kinetic_energy(N: int, J: float) -> np.ndarray:\n", - " \"\"\"\n", - " Builds single electron matrix of nearest-neighbor hopping term,\n", - " hopping strength J, for an N-site open chain (no periodic boundary).\n", - " \"\"\"\n", - " K = np.zeros((2 * N, 2 * N), dtype=float)\n", - " for site in range(N - 1):\n", - " for spin in range(2):\n", - " mu = qubit_idx(site, spin)\n", - " nu = qubit_idx(site + 1, spin)\n", - " K[mu, nu] = -J\n", - " K = 2 * sym(K)\n", - " return K\n", - "\n", - "\n", - "def spin_potential(N: int, spin=0, parameters: tuple[float] = (1, 1, 1)) -> np.ndarray:\n", - " \"\"\"\n", - " Builds single electron matrix associated with the external potential.\n", - " Associated with an N site lattice.\n", - " \"\"\"\n", - " lam, mean, std = parameters\n", - " V = np.zeros((2 * N, 2 * N), dtype=float)\n", - " for site in range(N):\n", - " mu = qubit_idx(site, spin)\n", - " V[mu, mu] = -lam * np.exp(-((site - mean) ** 2) / (2 * std**2))\n", - " return V\n", - "\n", - "\n", - "def construct_single_electron_hamiltonian(\n", - " N: int, J: float, parameters: tuple\n", - ") -> np.ndarray:\n", - " return kinetic_energy(N, J) + spin_potential(N, spin=0, parameters=parameters)" - ] - }, - { - "cell_type": "code", - "execution_count": 13, - "id": "33", - "metadata": {}, - "outputs": [], - "source": [ - "lam = 3.0\n", - "mean = (L - 1) / 2\n", - "std = 0.5\n", - "h = construct_single_electron_hamiltonian(L, J=1, parameters=(lam, mean, std))\n", - "Nelec = 1" - ] - }, - { - "cell_type": "code", - "execution_count": 14, - "id": "34", - "metadata": {}, - "outputs": [], - "source": [ - "@qfunc\n", - "def main(qba: Output[QArray[QBit, M]]) -> None:\n", - " allocate(M, qba)\n", - " prepare_slater_det(h, Nelec, qba)\n", - "\n", - "\n", - "qprog = synthesize(main)" - ] - }, - { - "attachments": { - "gaussian_state_preperation.png": { - "image/png": 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" - } - }, - "cell_type": "markdown", - "id": "35", - "metadata": {}, - "source": [ - "The state preparation quantum circuit. The Given rotation, operating on two qubits, is decomposed into the basis gates.\n", - "\n", - "![State preparation circuit](attachment:gaussian_state_preperation.png)" - ] - }, - { - "cell_type": "markdown", - "id": "36", - "metadata": {}, - "source": [ - "#### Single State Excitation Subspace Verification" - ] - }, - { - "cell_type": "markdown", - "id": "37", - "metadata": {}, - "source": [ - "For the single excitation subspace we can easily compare the preparation of the quantum state with the exact diagonalization. To compare between the two we normalize the quantum solution so to cancel the difference in the global phase with respect to the classical result." - ] - }, - { - "cell_type": "code", - "execution_count": 15, - "id": "38", - "metadata": {}, - "outputs": [], - "source": [ - "backend_preferences = ClassiqBackendPreferences(\n", - " backend_name=ClassiqSimulatorBackendNames.SIMULATOR_STATEVECTOR\n", - ")\n", - "\n", - "\n", - "# Construct a representation of HHL model\n", - "def state_check_model(main, backend_preferences):\n", - " qmod_state_check = create_model(\n", - " main,\n", - " execution_preferences=ExecutionPreferences(\n", - " num_shots=1, backend_preferences=backend_preferences\n", - " ),\n", - " )\n", - " return qmod_state_check" - ] - }, - { - "cell_type": "code", - "execution_count": 16, - "id": "39", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Circuit depth = 13\n" - ] - } - ], - "source": [ - "# Construct the quantum program\n", - "qmod_state_check = state_check_model(main, backend_preferences)\n", - "qprog_state_check = synthesize(qmod_state_check)\n", - "\n", - "print(\"Circuit depth = \", qprog_state_check.transpiled_circuit.depth)\n", - "res_state_check = execute(qprog_state_check).result_value()" - ] - }, - { - "cell_type": "code", - "execution_count": 17, - "id": "40", - "metadata": {}, - "outputs": [], - "source": [ - "import matplotlib.pyplot as plt\n", - "\n", - "\n", - "def get_quantum_amplitudes(result):\n", - " df = result.dataframe\n", - " mask = np.abs(df[\"amplitude\"]) > 1e-12\n", - " filtered = df.loc[mask, [\"bitstring\", \"amplitude\"]].copy()\n", - " amps = filtered[\"amplitude\"].to_numpy()\n", - " bitstring = filtered[\"bitstring\"].tolist() # must be integers\n", - " # mapping the bitstrings to qubit indices in the array\n", - " qubit_index = [[i for i, b in enumerate(s[::-1]) if b == \"1\"] for s in bitstring]\n", - " qubit_index = np.array([i[0] for i in qubit_index])\n", - " idx = np.argsort(qubit_index)\n", - " qubit_index = qubit_index[idx]\n", - " amps = amps[idx]\n", - " amps = amps / np.linalg.norm(amps)\n", - "\n", - " qsol = np.zeros(M, dtype=complex)\n", - " qsol[qubit_index] = amps\n", - " return qsol" - ] - }, - { - "cell_type": "code", - "execution_count": 18, - "id": "41", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Fidelity ||^2 = 1.0000000000\n" - ] - } - ], - "source": [ - "# Compare quantum amplitudes with exact diagonalization (Nelec=1)\n", - "qsol = get_quantum_amplitudes(res_state_check)\n", - "\n", - "# Exact ground state: lowest eigenvector of h\n", - "E_exact, Qbar_exact = np.linalg.eigh(h)\n", - "exact_state = Qbar_exact[:, 0]\n", - "\n", - "# Align global phase: multiply qsol by phase so that it matches exact_state\n", - "overlap = np.dot(exact_state.conj(), qsol)\n", - "phase_global = overlap / np.abs(overlap)\n", - "qsol_aligned = qsol / phase_global\n", - "\n", - "fig, ax = plt.subplots(figsize=(6, 4))\n", - "\n", - "# Real part\n", - "ax.bar(np.arange(M) - 0.15, np.real(exact_state), width=0.3, label=\"Exact\", alpha=0.8)\n", - "ax.bar(\n", - " np.arange(M) + 0.15, np.real(qsol_aligned), width=0.3, label=\"Quantum\", alpha=0.8\n", - ")\n", - "ax.set_xlabel(\"Qubit index\", fontsize=12)\n", - "ax.set_ylabel(\"Amplitude (real)\", fontsize=12)\n", - "ax.set_title(\"Real Part\", fontsize=14)\n", - "ax.set_xticks(np.arange(M))\n", - "ax.legend()\n", - "\n", - "plt.suptitle(\"State Preparation vs Exact Ground State ($N_{elec}=1$)\", fontsize=16)\n", - "plt.tight_layout()\n", - "plt.show()\n", - "\n", - "# Fidelity check\n", - "fidelity = np.abs(np.dot(exact_state.conj(), qsol)) ** 2\n", - "print(f\"Fidelity ||^2 = {fidelity:.10f}\")\n", - "assert fidelity > 0.95, f\"Fidelity too low: {fidelity}\"" - ] - }, - { - "cell_type": "markdown", - "id": "42", - "metadata": {}, - "source": [ - "#### Initial State at Quater-Filling\n", - "At quater-filling the number of electrons $N_{\\text{elec}}$ equals to half number of lattice sites $N$ (quater of the $M=2N$ fermionic modes). The one-body potential strength $\\lambda$ is set such that the two electrons will have different spins ($N_{\\downarrow} = N_{\\uparrow}=1$)" - ] - }, - { - "cell_type": "code", - "execution_count": 19, - "id": "43", - "metadata": {}, - "outputs": [], - "source": [ - "Nelec = N // 2 # quater-filling" - ] - }, - { - "cell_type": "code", - "execution_count": 20, - "id": "44", - "metadata": {}, - "outputs": [], - "source": [ - "@qfunc\n", - "def main(qba: Output[QArray[QBit, M]]) -> None:\n", - " allocate(M, qba)\n", - " prepare_slater_det(h, Nelec, qba)\n", - "\n", - "\n", - "qprog = synthesize(main)" - ] - }, - { - "cell_type": "markdown", - "id": "45", - "metadata": {}, - "source": [ - "To image the ground state, we measure the charge and spin densities: $\\rho_j^{\\pm} = \\langle n_{j,\\uparrow}\\rangle \\pm \\langle n_{j,\\downarrow} \\rangle$. The charge density, $\\rho_j^{+}$, corresponds to the average number of electrons on the $j$'th site, while the spin density, $\\rho_j^{-}$, is the net spin on the same site.\n", - "\n", - "The number operator $n_\\mu = c^\\dagger_\\mu c_\\mu$ maps under the Jordan-Wigner transformation to $$n_\\mu \\rightarrow \\frac{I-Z_{\\mu}}{2}~~. $$\n", - "Therefore, the charge density maps to $$\\rho_j^{+} = 1 - (\\langle Z_{j,\\uparrow}\\rangle + \\langle Z_{j,\\downarrow}\\rangle)/2~~,$$ while the spin density corresponds to $$ \\rho_j^{-} = (\\langle Z_{j,\\downarrow}\\rangle - \\langle Z_{j,\\uparrow}\\rangle)/2 ~~.$$\n", - "\n", - "We introduce the functions `charge_density` and `spin_density` which allow measuring the corresponding observables." - ] - }, - { - "cell_type": "code", - "execution_count": 21, - "id": "46", - "metadata": {}, - "outputs": [], - "source": [ - "def charge_density(site: int, M: int) -> SparsePauliOp:\n", - " s = SparsePauliOp([], M)\n", - " for spin in (0, 1):\n", - " idx = qubit_idx(site=site, spin=spin)\n", - " s += (Pauli.I(idx) - Pauli.Z(idx)) * 0.5\n", - " return s\n", - "\n", - "\n", - "def spin_density(site: int, M: int) -> SparsePauliOp:\n", - " s_up, s_down = SparsePauliOp([], M), SparsePauliOp([], M)\n", - " idx_up, idx_down = qubit_idx(site=site, spin=0), qubit_idx(site=site, spin=1)\n", - " s_up += Pauli.Z(idx_up)\n", - " s_down += Pauli.Z(idx_down)\n", - " return (s_down - s_up) * 0.5" - ] - }, - { - "cell_type": "markdown", - "id": "47", - "metadata": {}, - "source": [ - "Next, we execute the quantum program and measure the spin and change densities" - ] - }, - { - "cell_type": "code", - "execution_count": 22, - "id": "48", - "metadata": {}, - "outputs": [], - "source": [ - "initial_charge_density = np.zeros(L)\n", - "initial_spin_density = np.zeros(L)\n", - "\n", - "with ExecutionSession(qprog) as es:\n", - " for site in range(L):\n", - " initial_charge_density[site] = np.real(\n", - " es.estimate(charge_density(site, M)).value\n", - " )\n", - " initial_spin_density[site] = np.real(es.estimate(spin_density(site, M)).value)" - ] - }, - { - "cell_type": "code", - "execution_count": 23, - "id": "49", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "sites = np.arange(0, L)\n", - "plt.figure()\n", - "plt.title(\"Initial Densities\", fontsize=18)\n", - "plt.plot(sites, initial_charge_density, \"o\", label=\"charge density\")\n", - "plt.plot(sites, initial_spin_density, \"+\", markersize=10, label=\"spin density\")\n", - "plt.xlabel(\"Site\", fontsize=12)\n", - "plt.ylabel(\"Density\", fontsize=12)\n", - "plt.xticks(sites)\n", - "plt.legend()\n", - "plt.show()" - ] - }, - { - "cell_type": "markdown", - "id": "50", - "metadata": {}, - "source": [ - "The attractive potential is centered around `mean` = $1.5$, therefore the initial charge and spin densities form a peak around that site." - ] - }, - { - "cell_type": "markdown", - "id": "51", - "metadata": {}, - "source": [ - "### Time-Evolution\n", - "\n", - "The propagation stage approximates the time-evolution operator $U = \\exp(-i H t)$, where\n", - "\n", - "$$ H =-J \\sum_{j, \\sigma} \\left ( c_{j,\\sigma}^\\dagger c_{j+1,\\sigma} + c_{j,\\sigma}^\\dagger c_{j+1,\\sigma}\\right) + U \\sum_{j} n_{j \\uparrow} n_{j\\downarrow} \\tag{4}$$\n", - "\n", - "is the 1D version of Eq. (1).\n", - "\n", - "The propagation of the initial state with respect to Eq. (4), simulates an effective quench of the system at initial time, abruptly changing the Hamiltonian $H_0\\rightarrow H$. As a consequence, the initial state is a highly excited state of $H$.\n", - "\n", - "In order to minimize the circuit depth of the quantum circuit it is beneficial to decompose the Hamiltonian into four sets of terms, where all the operators in a set commute with one another. The terms correspond to an even and odd edge hopping terms and even and odd site interaction terms:\n", - "$$H = H_{\\text{hop-even}} +H_{\\text{hop-odd}} +H_{\\text{int-even}}+ H_{\\text{int-odd}} ~~.$$\n", - "The odd hopping Hamiltonian term includes the hopping terms between $1\\leftrightarrow\n", - "2$ and $3\\leftrightarrow\n", - "4$ neighbouring sites ($j$ is odd in Eq. (3)), while the odd hopping term includes the odd edge pairs ($2\\leftrightarrow\n", - "3$, $4\\leftrightarrow\n", - "1$, even $j$).\n", - "\n", - "The evolution operator $U$ is approximated by a first-order Trotter expansion, where each Trotter step consists of five stages.\n", - "$$U = e^{-i H t} \\approx \\left(e^{-i H \\tau}\\right)^{t/\\tau}~~, $$ with $$e^{-i H \\tau} \\approx e^{-i H_{\\text{hop-even}}\\tau} e^{-i H_{\\text{int-even}}\\tau} e^{-i H_{\\text{int-odd}}\\tau} e^{-i H_{\\text{hop-odd}}\\tau}. $$\n", - "Each component in the Trotter step can be achieved by simultaneous application (circuit depth of one) of simple two-qubit gates.\n", - "\n", - "An additional algorithmic trick simplifying the circuit and reducing the circuit depth even further. Between the even and odd interaction terms a fermionic mode swap operation is conducted, effectively performing a cyclic shifting of the fermionic modes. Crucially, this operation swaps the logical ordering of the qubits, while preserving the fermionic parity sign (using an iSWAP gates). Alternatively, the operation modifies the mapping between physical qubits and logical fermionic. As a result, the Hamiltonian terms are interpreted relative to the new ordering, effectively swapping the odd and even edge.\n", - "The incorporation of the swap mode operation, allows parallelism, locality (only nearest neighbor gates, bypassing the need for long Jordan Wigner strings).\n", - "After the application of $\\exp(-i H_{\\text{hop-even}}\\tau)$ an inverse fermionic mode swap is needed to swap the even and odd edges back, allowing application of the consecutive Trotter step. Since the even edge hopping term commutes with the inverse fermionic mod swap, these operations are merged to a single stage.\n", - "\n", - "Overall, the time-evolution involves iteration (each iteration corresponds to a single Trotter step) of a five-step procedure:\n", - "1. Hopping operation on odd edges.\n", - "2. Interaction on odd sites\n", - "3. Fermionic mode swap\n", - "4. Interaction on even sites\n", - "5. Hopping operation on even sites + inverse fermionic mode swap\n" - ] - }, - { - "cell_type": "markdown", - "id": "52", - "metadata": {}, - "source": [ - "Setting the Hamiltonian parameters" - ] - }, - { - "cell_type": "code", - "execution_count": 24, - "id": "53", - "metadata": {}, - "outputs": [], - "source": [ - "U = 3 * J # J is set to unity in the beginning of the notebook" - ] - }, - { - "cell_type": "markdown", - "id": "54", - "metadata": {}, - "source": [ - "We begin by defining utility functions" - ] - }, - { - "cell_type": "code", - "execution_count": 25, - "id": "55", - "metadata": {}, - "outputs": [], - "source": [ - "## Elementary gates\n", - "\n", - "\n", - "# K(theta) = exp(-i*(theta/2)*(XX + YY))\n", - "@qfunc\n", - "def K(theta: float, qba: QArray[QBit, 2]):\n", - " suzuki_trotter(\n", - " pauli_operator=0.5 * (Pauli.X(0) * Pauli.X(1) + Pauli.Y(0) * Pauli.Y(1)),\n", - " evolution_coefficient=theta,\n", - " order=1,\n", - " repetitions=1,\n", - " qbv=qba,\n", - " )\n", - "\n", - "\n", - "# P(phi) = CPHASE(phi) = diag(1, 1, 1, e^{-i*phi})\n", - "# Implements exp(-i*phi * n_up * n_down) up to global phase\n", - "@qfunc\n", - "def P(phi: float, target: QArray[QBit, 2]) -> None:\n", - " phase(phi * target[0] * target[1])" - ] - }, - { - "cell_type": "markdown", - "id": "56", - "metadata": {}, - "source": [ - "To propagate the system state we transform the fermion Hamilotonian to a qubit representation utilizing the Jordan-Wigner transformation.\n", - "\n", - "A single hopping term transforms as\n", - "$$c_{\\mu}^{\\dagger} c_{\\nu} + c_{\\mu}^{\\dagger} c_{\\nu} \\xrightarrow{\\text{JW}} \\frac{1}{2} \\left( X_{\\mu}X_{\\nu} + Y_{\\mu}Y_{\\nu} \\right)~~,$$\n", - "while an interaction term gives $$n_{\\mu}n_{\\nu} \\xrightarrow{\\text{JW}} = \\frac{1}{4}\\left(I -Z_\\mu -Z_\\nu + Z_\\mu Z_\\nu \\right)~~. $$\n", - "\n", - "As a consequence, the five stages can be performed by implementation of the basic unitaries $K(\\theta)= \\exp\\left(-i \\frac{\\theta}{2}\\left(XX + YY \\right)\\right)$ and $P(\\phi) = \\exp\\left(-i \\frac{\\phi}{2}\\left(I-Z_{\\mu}-Z_{\\nu}+Z_{\\mu}Z_{\\nu} \\right)\\right)$. The functions `K` and `P` above implement the corresponding unitary transformations.\n", - "\n", - "The first stage, including odd hopping terms, is obtained by simultaneous application of $K(\\theta = -\\tau J)$ on different paris of qubits. Similarly, the second and fourth stages, involving the odd and even interactions are achieved with simultaneous application of $P(\\phi = \\tau U/2)$ on the corresponding pairs of qubits. The third stage, constituting the fermionic mode swap, is implemented by simultaneous iSWAP gates which is equivalent to $K(\\theta = -\\pi/2)$. The last stage includes a merge of even-edge hopping operation, and an inverse fermionic mode swap operation. Naturally, since these operation commute, the transformation is obtained by $K(\\theta = -\\tau J + \\pi/2)$ two-qubit gates.\n", - "\n", - "We implement the simultaneous operations on the qubit array utilizing Classiq's built-in `repeat` function within the `hop` and `interact` functions." - ] - }, - { - "cell_type": "code", - "execution_count": 26, - "id": "57", - "metadata": {}, - "outputs": [], - "source": [ - "def hop(pairs: list[tuple[int, int]], theta: float, qba: QArray[QBit, M]) -> None:\n", - " for spin in (0, 1):\n", - " for pair in pairs:\n", - " site1, site2 = pair\n", - " K(\n", - " theta,\n", - " [\n", - " qba[qubit_idx(site=site1, spin=spin)],\n", - " qba[qubit_idx(site=site2, spin=spin)],\n", - " ],\n", - " )\n", - "\n", - "\n", - "def interact(sites: list[int], phi: float, qba: QArray[QBit, M]) -> None:\n", - " for site in sites:\n", - " P(\n", - " phi,\n", - " [qba[qubit_idx(site=site, spin=0)], qba[qubit_idx(site=site, spin=1)]],\n", - " )" - ] - }, - { - "cell_type": "markdown", - "id": "58", - "metadata": {}, - "source": [ - "Defining the odd and even pairs and sites, to account for the finite chane we evaluate which sites are really swapped. " - ] - }, - { - "cell_type": "code", - "execution_count": 27, - "id": "59", - "metadata": {}, - "outputs": [], - "source": [ - "ODD_PAIRS = [(i, i + 1) for i in range(0, L - 1, 2)]\n", - "EVEN_PAIRS = [(i, i + 1) for i in range(1, L - 1, 2)]\n", - "ODD_SITES = list(range(0, L, 2))\n", - "EVEN_SITES = list(range(1, L, 2))\n", - "\n", - "# After iSWAP on EVEN_PAIRS, compute where even sites end up\n", - "_perm = list(range(L))\n", - "for i, j in EVEN_PAIRS:\n", - " _perm[i], _perm[j] = _perm[j], _perm[i]\n", - "_inv_perm = [0] * L\n", - "for pos, site in enumerate(_perm):\n", - " _inv_perm[site] = pos\n", - "SWAPPED_EVEN_SITES = sorted([_inv_perm[s] for s in EVEN_SITES])" - ] - }, - { - "cell_type": "markdown", - "id": "60", - "metadata": {}, - "source": [ - "Gathering all the stages together to form the Trotter step" - ] - }, - { - "cell_type": "code", - "execution_count": 28, - "id": "61", - "metadata": {}, - "outputs": [], - "source": [ - "def trotter_step(tau: float, J: float, U: float, qba: QArray[QBit, M]) -> None:\n", - "\n", - " # stage 1 - hopping on odd-edge pairs\n", - " hop(pairs=ODD_PAIRS, theta=-tau * J, qba=qba)\n", - "\n", - " # stage 2 - interaction on odd sites\n", - " interact(sites=ODD_SITES, phi=tau * U, qba=qba)\n", - "\n", - " # stage 3 - fermionic mode swap\n", - " hop(pairs=EVEN_PAIRS, theta=-np.pi / 2, qba=qba)\n", - " # stage 4 - interaction on even sites (at their swapped positions)\n", - " interact(sites=SWAPPED_EVEN_SITES, phi=tau * U, qba=qba)\n", - "\n", - " # stage 5 - hopping on even-edge pairs and inverse fermionic mode swap\n", - " hop(pairs=EVEN_PAIRS, theta=-tau * J + np.pi / 2, qba=qba)" - ] - }, - { - "cell_type": "markdown", - "id": "62", - "metadata": {}, - "source": [ - "### Propagation and Execution (\"Measurement\")" - ] - }, - { - "cell_type": "code", - "execution_count": 29, - "id": "63", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Quantum program link: https://platform.classiq.io/circuit/3BhmprAOCkSPptCBxO3TT71oX0i\n" - ] - } - ], - "source": [ - "@qfunc\n", - "def main(qba: Output[QArray[QBit, M]], num_iter: CInt) -> None:\n", - " allocate(M, qba)\n", - " prepare_slater_det(h, Nelec, qba)\n", - " power(num_iter, lambda: trotter_step(tau, J, U, qba))\n", - "\n", - "\n", - "qprog = synthesize(main)\n", - "show(qprog)" - ] - }, - { - "cell_type": "markdown", - "id": "64", - "metadata": {}, - "source": [ - "The physics of the model are analyzed by measuring the charge and spin densities and the spin spreads $\\kappa^{\\pm}(t)$, defined above.\n", - "The number operators map to local Pauli operators $n_{\\mu} = c^\\dagger_{\\mu}c_{\\mu} = (1-Z_\\mu)/2$, where $\\mu=(j,\\sigma)$ encodes a site, spin pair.\n" - ] - }, - { - "cell_type": "code", - "execution_count": 30, - "id": "65", - "metadata": {}, - "outputs": [], - "source": [ - "def spread(density: list, L: int) -> float:\n", - " s = 0\n", - " for site in range(L):\n", - " s += np.abs(site - (L - 1) / 2) * density[site]\n", - " return s" - ] - }, - { - "cell_type": "code", - "execution_count": 31, - "id": "66", - "metadata": {}, - "outputs": [], - "source": [ - "charge_density_mat = np.zeros((L, NUM_ITERS))\n", - "spin_density_mat = np.zeros((L, NUM_ITERS))\n", - "\n", - "\n", - "with ExecutionSession(qprog) as es:\n", - " iter_params = [{\"num_iter\": iter} for iter in range(NUM_ITERS)]\n", - "\n", - " for site in range(L):\n", - " charge_results = es.batch_estimate(charge_density(site, M), iter_params)\n", - " spin_results = es.batch_estimate(spin_density(site, M), iter_params)\n", - "\n", - " charge_density_mat[site, :] = [np.real(r.value) for r in charge_results]\n", - " spin_density_mat[site, :] = [np.real(r.value) for r in spin_results]" - ] - }, - { - "cell_type": "code", - "execution_count": 32, - "id": "67", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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- "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "sites = np.arange(0, N)\n", - "time_indices = [0, 4, 9]\n", - "time_labels = [f\"$t = {tau * i:.1f}/J$\" for i in time_indices]\n", - "\n", - "fig, axes = plt.subplots(1, 3, figsize=(14, 4), sharey=True)\n", - "for ax, t_idx, t_label in zip(axes, time_indices, time_labels):\n", - " ax.plot(sites, charge_density_mat[:, t_idx], \"o-\", label=r\"Charge $\\rho^+$\")\n", - " ax.plot(sites, spin_density_mat[:, t_idx], \"s--\", label=r\"Spin $\\rho^-$\")\n", - " ax.set_title(t_label, fontsize=14)\n", - " ax.set_xlabel(\"Site\", fontsize=12)\n", - " ax.set_xticks(sites)\n", - " ax.legend(fontsize=9)\n", - "\n", - "axes[0].set_ylabel(\"Density\", fontsize=12)\n", - "plt.suptitle(\"Charge and Spin Density Dynamics\", fontsize=16)\n", - "plt.tight_layout()\n", - "plt.show()" - ] - }, - { - "cell_type": "markdown", - "id": "68", - "metadata": {}, - "source": [ - "## Analysis - Spin-Charge Separation\n", - "\n", - "\n", - "In order to quantify the spin-charge seperation, we evaluate the spin and charge spread:\n", - "$$\\kappa^{\\pm}(t) = \\sum_{j=1}^N |j - j_c| \\rho^{\\pm}_j(t)~~, $$\n", - "where $j_c = (N+1)/2$.\n", - "Different values between the spin and charge spreads, signifies spin-charge seperation." - ] - }, - { - "cell_type": "code", - "execution_count": 33, - "id": "69", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "def spread(density: list, N: int) -> float:\n", - " s = 0\n", - " for site in range(N):\n", - " s += np.abs(site - (N + 1) / 2) * density[site]\n", - " return s\n", - "\n", - "\n", - "times = np.array([tau * i for i in range(NUM_ITERS)])\n", - "\n", - "\n", - "charge_spread_vec = np.array(\n", - " [spread(charge_density_mat[:, i], L) for i in range(NUM_ITERS)]\n", - ")\n", - "spin_spread_vec = np.array(\n", - " [spread(spin_density_mat[:, i], L) for i in range(NUM_ITERS)]\n", - ")\n", - "\n", - "plt.figure(figsize=(7, 5))\n", - "plt.plot(times * J, charge_spread_vec, \"o-\", label=r\"Charge spread $\\kappa^+$\")\n", - "plt.plot(times * J, spin_spread_vec, \"s--\", label=r\"Spin spread $\\kappa^-$\")\n", - "plt.xlabel(r\"$t \\cdot J$\", fontsize=14)\n", - "plt.ylabel(r\"Spread $\\kappa$\", fontsize=14)\n", - "plt.title(\"Charge and Spin Spread vs. Time\", fontsize=16)\n", - "plt.legend(fontsize=12)\n", - "plt.tight_layout()\n", - "plt.show()" - ] - }, - { - "cell_type": "markdown", - "id": "70", - "metadata": {}, - "source": [ - "The lack of agreement between the spin and charge spreads indicates spin-charge seperation.\n", - "\n", - "\n", - "\n" - ] - }, - { - "cell_type": "markdown", - "id": "71", - "metadata": {}, - "source": [ - "## Comparison with Analytical Results" - ] - }, - { - "cell_type": "markdown", - "id": "72", - "metadata": {}, - "source": [ - "In order to validate the results, we compare the model prediction with the analytical solutions.\n", - "\n", - "There are two natural physical limits, where the model can be solved exactly and efficiently utilizing classical methods:\n", - "1. The non-interacting limit the on-site interaction vanishes $U = 0$ (alternatively $U\\ll J$).\n", - "2. Vanishing hopping limit, $J=0$ (alternatively $U\\gg J$).\n", - "\n", - "### Non-interacting Particles\n", - "In the non-interacting limit of $U=0$, the FH Hamiltonian is a quadratic Hamiltonian. As a consequence, even in the case of site-dependent hopping or hopping between non-adjacent sites, the state dynamics can be solved classically in polynomial time in the number of fermionic modes $M$, utilizing standard matrix exponentiation methods.\n", - "In the case of the FH model on an open chain of $L$ sites, the non-interacting Hamiltonian becomes $$H^{\\text{n.i}} =\\sum_{\\mu, \\nu} c_{\\mu}^\\dagger M_{\\mu\\nu}c_{\\nu} = -J \\sum_{j=1}^{L-1} \\sum_{\\sigma} \\left ( c_{j,\\sigma}^\\dagger c_{j+1,\\sigma} + c_{j+1,\\sigma}^\\dagger c_{j,\\sigma}\\right) ~~,$$ where n.i denotes \"non-interacting\". The commutativity of the spin-up and spin-down terms allows them to be treated independently. For an open chain (no periodic boundary), the eigenstates are standing waves rather than plane waves. The single-particle eigenstates are $$\\phi_{n}(j) = \\sqrt{\\frac{2}{L+1}}\\sin\\!\\left(\\frac{\\pi n j}{L+1}\\right)~~, \\quad n=1,2,\\dots,L~~,$$ with corresponding energies $$\\omega_n = -2J\\cos\\!\\left(\\frac{\\pi n}{L+1}\\right)~~.$$ Each eigenstate is doubly degenerate (spin-up and spin-down). The ground state of an $N_{\\text{elec}}$-electron system is obtained by filling the lowest-energy single-particle states one by one." - ] - }, - { - "cell_type": "markdown", - "id": "73", - "metadata": {}, - "source": [ - "The time-dependent expectation values of the charge and spin densities, $\\langle\\rho^{\\pm}_j(t)\\rangle$, can readily obtained by employing the Heisenberg representation of quantum mechanics. In this representation, an operator's, $O(t)$, dynamics is generated by the Heisenberg equation\n", - "$$\\frac{dO(t)}{dt} = i \\left[ H^{\\text{n.i}}, O(t) \\right] ~~,$$\n", - "where $O(t) = U(t)^\\dagger O U(t)$, where $U(t) = \\exp(-i H^{\\text{n.i}} t)$.\n", - "Substituting the diagonal form of $H^{\\text{n.i}}$ and utilizing the fermionic anti-commutation relations $$\\{c^\\dagger_{\\mu}, c_\\nu\\} = \\delta_{\\mu,\\nu}~~, ~~\\{c_{\\mu}, c_\\nu\\} = \\{c_{\\mu}^\\dagger, c_\\nu^\\dagger\\} = 0~~,$$\n", - "(the Fourier fermionic operators satisfy similar commutation relations) we obtain $\\dot{c}_\\mu^\\dagger = i M_{\\nu \\mu} c_{\n", - "\\nu}^\\dagger$, therefore $\\dot{\\mathbf{c}}^\\dagger = i M^T \\mathbf{c}^\\dagger$, leading to $$\\mathbf{c}^\\dagger(t) = e^{i M^T t}\\mathbf{c}^\\dagger(0)$$\n", - "\n", - "\n", - "The dynamics can be evaluated by introducing the matrices ${\\cal U}(t) = e^{i M^T t}~~,$ and ${\\cal N}$ with elements ${\\cal N_{\n", - "\\mu \\nu}} = \\langle c_{\\mu}^\\dagger c_\\nu\\rangle$, this allows writting the dynamics of a second order correlation as\n", - "$$\\langle c_{\\mu}^\\dagger c_{\\nu} \\rangle = \\left[ {\\cal{U}} (t){\\cal{N}} {\\cal{U}}^\\dagger (t)\\right]_{\\mu \\nu}~~.$$\n", - "In the one-excitation subspace, the ground state reads $|\\psi_{\\text{g.s}} \\rangle = \\sum_{\\mu} V_{0,\\mu}c_{\\mu}^\\dagger|\\text{vacc}\\rangle$, where $\\{V_{0\\mu}\\}$ are the elements of the eigenstate of $M$, i.e. $M V_0 = \\epsilon_0 V_0$, where $\\epsilon_0$ is the ground state energy." - ] - }, - { - "cell_type": "markdown", - "id": "74", - "metadata": {}, - "source": [ - "#### Numerical Evaluation on a small model." - ] - }, - { - "cell_type": "markdown", - "id": "75", - "metadata": {}, - "source": [ - "Defining parameters" - ] - }, - { - "cell_type": "code", - "execution_count": 34, - "id": "76", - "metadata": {}, - "outputs": [], - "source": [ - "L = 4 # number of lattice sites\n", - "M = 2 * L # total number of fermionic modes\n", - "NUM_ITERS = 10\n", - "J = 1 # hopping strength\n", - "tau = 0.1 / J # smaller Trotter step for better agreement with analytical U=0 result\n", - "T = NUM_ITERS * tau\n", - "U = 0\n", - "Nelec = 1 # single electron subspace" - ] - }, - { - "cell_type": "code", - "execution_count": 35, - "id": "77", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "import matplotlib.pyplot as plt\n", - "\n", - "## Check eigenvalues vs analytical dispersion (open chain)\n", - "# For open BC, E_n = -2J cos(pi*n/(N+1)), n = 1..N\n", - "M0 = construct_single_electron_hamiltonian(L, J=J, parameters=(0.0, 0, 1))\n", - "E, V = np.linalg.eigh(M0)\n", - "\n", - "n_vals = np.arange(1, N + 1)\n", - "E_analytical = -2 * J * np.cos(np.pi * n_vals / (N + 1))\n", - "E_analytical_full = np.sort(np.tile(E_analytical, 2)) # doubly degenerate (spin)\n", - "assert np.allclose(\n", - " E, E_analytical_full\n", - "), f\"Mismatch: numerical {E} vs analytical {E_analytical_full}\"\n", - "\n", - "## Single-electron dynamics: electron starts at site 0, spin-up\n", - "psi_0 = np.zeros(2 * L)\n", - "psi_0[qubit_idx(0, 0)] = 1.0\n", - "\n", - "t_max = 4.0 / J\n", - "t_vec = np.linspace(0, t_max, 400)\n", - "\n", - "# Numerical time evolution via eigendecomposition\n", - "coeffs = V.conj().T @ psi_0\n", - "phases = np.exp(-1j * np.outer(t_vec, E))\n", - "psi_t = (phases * coeffs) @ V.conj().T\n", - "\n", - "spin_up_idx = np.array([qubit_idx(site, 0) for site in range(N)])\n", - "occ_numerical = np.abs(psi_t[:, spin_up_idx]) ** 2\n", - "\n", - "# Analytical: standing waves on the open chain\n", - "# phi_n(j) = sqrt(2/(L+1)) * sin(pi*n*j/(L+1)), j = 1..L (1-indexed)\n", - "# = sum_n phi_n(j) * phi_n(1) * e^{-i E_n t}\n", - "sites_1indexed = np.arange(1, N + 1)\n", - "phi = np.sqrt(2 / (N + 1)) * np.sin(\n", - " np.pi * np.outer(n_vals, sites_1indexed) / (N + 1)\n", - ") # (N, N): phi[n, j]\n", - "phi_at_start = phi[:, 0] # phi_n(j=1), the starting site\n", - "phases_analytical = np.exp(-1j * np.outer(t_vec, E_analytical))\n", - "psi_analytical = (phases_analytical * phi_at_start) @ phi\n", - "occ_analytical = np.abs(psi_analytical) ** 2\n", - "\n", - "# Plot\n", - "fig, axes = plt.subplots(2, 2, figsize=(8, 5), sharey=True)\n", - "for site in range(L):\n", - " ax = axes[site // 2, site % 2]\n", - " ax.plot(t_vec, occ_numerical[:, site], label=\"Numerical\")\n", - " ax.plot(t_vec, occ_analytical[:, site], \"--\", label=\"Analytical\")\n", - " ax.set_title(f\"Site {site}\")\n", - " ax.set_xlabel(\"$t$\")\n", - " if site % 2 == 0:\n", - " ax.set_ylabel(\"Occupation\")\n", - " ax.legend(fontsize=7)\n", - "plt.suptitle(\n", - " r\"Single electron dynamics (open chain): $|\\psi(0)\\rangle = |j{=}0,\\uparrow\\rangle$\"\n", - ")\n", - "plt.tight_layout()\n", - "plt.show()" - ] - }, - { - "cell_type": "code", - "execution_count": 37, - "id": "78", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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", 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" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "NUM_ITERS = 10 # more steps for better resolution of Trotter dynamics\n", - "tau_trotter = 0.1 / J # time step for Trotter evolution\n", - "n_steps_list = list(range(0, NUM_ITERS + 1, 1))\n", - "t_trotter = np.array(n_steps_list) * tau_trotter\n", - "t_max = t_trotter[-1]\n", - "t_vec = np.linspace(0, t_max, 400)\n", - "\n", - "# Numerical time evolution via eigendecomposition\n", - "coeffs = V.conj().T @ psi_0\n", - "phases = np.exp(-1j * np.outer(t_vec, E))\n", - "psi_t = (phases * coeffs) @ V.conj().T\n", - "\n", - "spin_up_idx = np.array([qubit_idx(site, 0) for site in range(N)])\n", - "occ_numerical = np.abs(psi_t[:, spin_up_idx]) ** 2\n", - "\n", - "\n", - "## Trotter dynamics via Classiq\n", - "# Initial state: single electron at site 0, spin-up\n", - "h_loc = np.zeros((2 * N, 2 * N))\n", - "h_loc[qubit_idx(0, 0), qubit_idx(0, 0)] = -1.0\n", - "\n", - "\n", - "@qfunc\n", - "def main(qba: Output[QArray[QBit, M]], num_iter: CInt) -> None:\n", - " allocate(M, qba)\n", - " prepare_slater_det(h_loc, Nelec, qba)\n", - " power(num_iter, lambda: trotter_step(tau_trotter, J, 0, qba))\n", - "\n", - "\n", - "qprog = synthesize(main)\n", - "\n", - "occ_trotter = np.zeros((len(n_steps_list), N))\n", - "\n", - "\n", - "def spin_up_occ(site: int, M: int) -> SparsePauliOp:\n", - " s = SparsePauliOp([], M)\n", - " idx = qubit_idx(site=site, spin=0)\n", - " s += (Pauli.I(idx) - Pauli.Z(idx)) * 0.5\n", - " return s\n", - "\n", - "\n", - "with ExecutionSession(qprog) as es:\n", - " step_params = [{\"num_iter\": n_step} for n_step in n_steps_list]\n", - "\n", - " for site in range(L):\n", - " results = es.batch_estimate(spin_up_occ(site, M), step_params)\n", - " occ_trotter[:, site] = [np.real(r.value) for r in results]\n", - "\n", - "## Plot: exact vs Trotter\n", - "fig, axes = plt.subplots(2, 2, figsize=(8, 5), sharey=True)\n", - "for site in range(L):\n", - " ax = axes[site // 2, site % 2]\n", - " ax.plot(t_vec, occ_numerical[:, site], label=\"Exact\")\n", - " ax.plot(\n", - " t_trotter,\n", - " occ_trotter[:, site],\n", - " \"o--\",\n", - " ms=3,\n", - " label=f\"Trotter ($\\\\tau={tau_trotter:.2f}$)\",\n", - " )\n", - " ax.set_title(f\"Site {site}\")\n", - " ax.set_xlabel(\"$t$\")\n", - " if site % 2 == 0:\n", - " ax.set_ylabel(\"Occupation\")\n", - " ax.legend(fontsize=7)\n", - "plt.suptitle(\n", - " r\"Exact vs Trotter ($U=0$, open chain): $|\\psi(0)\\rangle = |j{=}0,\\uparrow\\rangle$\"\n", - ")\n", - "plt.tight_layout()\n", - "plt.show()" - ] - }, - { - "cell_type": "markdown", - "id": "79", - "metadata": {}, - "source": [ - "\n", - "**Why the quantum and analytical results don't match exactly:** The quantum circuit uses a first-order Trotter decomposition of the time evolution. Even for $U=0$, the odd- and even-edge hopping terms do not commute, so each step approximates $\\exp(-i H \\tau)$ and Trotter error accumulates (roughly $\\propto \\tau^2$ per step). For a closer match, use a smaller Trotter step, while keeping the total propagation time." - ] - }, - { - "cell_type": "markdown", - "id": "80", - "metadata": {}, - "source": [ - "### Vanishing hopping limit\n", - "The other extreme is obtained when the onsite interactions is much larger than the hopping constant. In this regime interaction dominate the physics and supress hopping between adjacent sites, allowing us to take $J=0$.\n", - "The FH Hamiltonian then becomes a sum of local commuting terms, diagonal in the Fock basis (eigenstates of the number operators $\\{n_{\\mu}\\}$).\n", - "The Hamiltonian reduces to $$ H^{\\text{n.h}} = U \\sum_{j} n_{j \\uparrow} n_{j\\downarrow}~~,$$ where n.h denotes \"no hopping\".\n", - "As a consequence the local number operators are a constant of motion $\\langle n_{j} (t)\\rangle = \\langle n_{j} (0)\\rangle$, and we expect the charges to freeze in time.\n", - "\n", - "Since all terms in $H^{\\text{n.h}}$ commute with one another, i.e., $[n_{i\\uparrow}n_{i\\downarrow},\\, n_{j\\uparrow}n_{j\\downarrow}] = 0$ for all $i,j$, the first-order Trotter decomposition is **exact**:\n", - "$$e^{-i H^{\\text{n.h}} \\tau} = \\prod_j e^{-i U \\tau\\, n_{j\\uparrow}n_{j\\downarrow}}~~.$$\n", - "This means the Trotter circuit reproduces the exact time evolution with no approximation error, regardless of the step size $\\tau$.\n", - "\n", - "To verify this, we prepare an initial state that is **not** an eigenstate of $H^{\\text{n.h}}$ - specifically, the ground state of the non-interacting Hamiltonian with an attractive potential (a Slater determinant with non-uniform charge distribution). We then compare the Trotter dynamics with the exact analytical prediction: frozen charge and spin densities." - ] - }, - { - "cell_type": "markdown", - "id": "81", - "metadata": {}, - "source": [ - "#### Numerical Evaluation" - ] - }, - { - "cell_type": "code", - "execution_count": 38, - "id": "82", - "metadata": {}, - "outputs": [], - "source": [ - "# Parameters\n", - "N = 4 # number of lattice sites\n", - "L = N * a # length of the lattice\n", - "M = 2 * N # total number of fermionic modes\n", - "J = 0 # vanishing hopping\n", - "U = 2.0 # on-site interaction strength\n", - "Nelec_vh = N # half-filling\n", - "NUM_ITERS_vh = 10\n", - "tau_vh = 0.3 # deliberately large Trotter step — still exact since terms commute\n", - "T = NUM_ITERS_vh * tau_vh\n", - "\n", - "# Initial state: ground state of the non-interacting Hamiltonian with attractive potential\n", - "# This is NOT an eigenstate of H^{n.h.}, making the test non-trivial\n", - "lam = 10.0\n", - "mean = (L - 1) / 2\n", - "std = L / 6\n", - "h_vh = construct_single_electron_hamiltonian(N, J=1, parameters=(lam, mean, std))\n", - "\n", - "\n", - "@qfunc\n", - "def main(qba: Output[QArray[QBit, M]], num_iter: CInt) -> None:\n", - " allocate(M, qba)\n", - " prepare_slater_det(h_vh, Nelec_vh, qba)\n", - " power(num_iter, lambda: trotter_step(tau=tau_vh, J=J, U=U, qba=qba))\n", - "\n", - "\n", - "qprog_vh = synthesize(main)" - ] - }, - { - "cell_type": "code", - "execution_count": 39, - "id": "83", - "metadata": {}, - "outputs": [], - "source": [ - "# Measure initial charge and spin densities (at num_iter=0),\n", - "# then measure at each Trotter step\n", - "n_steps_vh = list(range(0, NUM_ITERS_vh + 1))\n", - "t_trotter_vh = np.array(n_steps_vh) * tau_vh\n", - "\n", - "charge_density_vh = np.zeros((N, len(n_steps_vh)))\n", - "spin_density_vh = np.zeros((N, len(n_steps_vh)))\n", - "\n", - "with ExecutionSession(qprog_vh) as es:\n", - " step_params = [{\"num_iter\": n_step} for n_step in n_steps_vh]\n", - "\n", - " for site in range(N):\n", - " charge_results = es.batch_estimate(charge_density(site, M), step_params)\n", - " spin_results = es.batch_estimate(spin_density(site, M), step_params)\n", - "\n", - " charge_density_vh[site, :] = [np.real(r.value) for r in charge_results]\n", - " spin_density_vh[site, :] = [np.real(r.value) for r in spin_results]" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "84", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Max charge density deviation from exact: 4.25e-02\n", - "Max spin density deviation from exact: 3.32e-02\n" - ] + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# One-Dimensional Fermi-Hubbard Model" + ], + "id": "0" + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Overview\n", + "\n", + "This notebook implements a quantum simulation of the one-dimensional Fermi-Hubbard model using Classiq's quantum programming framework. The simulation proceeds in three stages:\n", + "\n", + "1. **Initial state preparation** - The ground state of a non-interacting Hamiltonian with a spin-dependent attractive potential is prepared as a Slater determinant via Givens rotations. This creates an initial state with localized charge and spin densities.\n", + "\n", + "2. **Time evolution** - The system is quenched to the interacting Fermi-Hubbard Hamiltonian and propagated using a first-order Trotterized circuit, where each Trotter step is decomposed into hopping and interaction layers using the Jordan-Wigner transformation.\n", + "\n", + "3. **Measurement and analysis** - Charge and spin densities are measured at each time step to observe the dynamics, testing the phenomenon of spin-charge separation at intermediate interaction strengths.\n", + "\n", + "Finally, the results are validated against exact analytical solutions in two limiting cases: the non-interacting limit ($U=0$), where the dynamics reduce to single-particle evolution, and the vanishing hopping limit ($J=0$), where the Trotter decomposition becomes exact and all densities are frozen.\n", + "\n", + "The simulation closely follows the experimental and algorithmic procedure desribed in [[1](#google_paper)]" + ], + "id": "1" + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Introduction\n", + "The Fermi-Hubbard model is a fundamental corner step of condensed matter physics, describing the interplay between kinetic energy and repulsion interaction between electrons in a solid. Although very simple, in certain parameter regimes, the model showcases a variety strongly correlated phenomena, such as the metal-insulator transition (Mott physics), antiferromagnetism, inhomogeneous phases, and unconventional Fermi liquids.\n", + "\n", + "In order to motivate or conceptually derive the model, consider of a metalic material composed of atoms organized in a regular pattern, i.e., a lattice. We assume the temperature is sufficiently low, so the that the vibrations of the atoms can be neglected and the atoms are essentially held in a fix position in the lattice sites. Moreover, typically each atom has a handful of relevant energy levels, however, in order to simplify the problem we will consider only a single energy level at each lattice site (one energy level per atom). In the metal, valance electrons move freely between the metal atoms, leading to the expected conductive behaviour. The movement of the electrons between the sites is dictated by the overlap of the spatial wave function on different sites. Since the atomic wave-functions decay exponentially with the distance to the nuclei, we consider only the dominant contribution, giving rise to hopping of electrons only between adjacent lattice sites.\n", + "These consideration lead to the first the hopping term, constituting the kinetic energy contribution: $-J \\sum_{\\langle i,j \\rangle, \\sigma} \\left ( c_{i\\sigma}^\\dagger c_{j\\sigma} + c_{i\\sigma}^\\dagger c_{j\\sigma}\\right)$, where $c_{i\\sigma}$ is the fermionic annihilation operator on the $i$'th lattice site and $\\sigma =\n", + "\\uparrow, \\downarrow$ spin. In addition, $\\langle i,j\\rangle$ designates that the sum is only over nearest-neighbors.\n", + "\n", + "A second contribution arises from the repulsive Coulomb interaction between two electrons. Such interaction is strongest between electrons on the same atom. We consider only this dominant contribution, adding an energy penalty of $U$, for two-electrons on the same site. In addition, Pauli's exclusion principle dictates that two electrons cannot be in the same quantum state, therefore the repulsive interaction can only be between electrons with different spins: $U \\sum_{j} c_{j \\uparrow}^\\dagger c_{j \\uparrow} c_{j\\downarrow}^\\dagger c_{j\\downarrow}$.\n", + "\n", + "Overall, the Fermi-Hubbard Hamiltonian is given by: $$H_{HF} = -J \\sum_{\\langle i,j \\rangle, \\sigma} \\left ( c_{i\\sigma}^\\dagger c_{j\\sigma} + c_{i\\sigma}^\\dagger c_{j\\sigma}\\right) + U \\sum_{j} n_{j \\uparrow} n_{j\\downarrow}~~,~~~~~~ (1)$$ where $ n_{j \\sigma}= c_{j \\sigma}^\\dagger c_{j \\sigma}$ is the number operator.\n", + "\n", + "\n", + "The model constitutes a key tool in the investigation of transition metal oxides, organic conductors and cuprates, which exhibit high-temperature superconductivity and exotic quantum magnetism properties and unconventional symmetry breaking.\n", + "Despite its apparent simplicity, the model is notoriously challenging, in 1D the Fermi-Hubbard model is solvable via Bethe ansatz [[2](#LiebWu)], while the 2D and 3D cases have not exact solution (for general hopping and interaction coefficients, $J$ and $U$). However, in 3D quantum phenomena are suppressed and the model typically exhibit classical behaviour, well described by mean-field theories.\n", + "Numerical studies are also limited beyond specific doping regimes (doping modifies the fraction of electrons/lattice sites). Perturbation theory becomes invalid when strong correlations between the electron emerge, while Monte-Carlo methods are restricted by the sign problem away from half filling (at half filling the number of electrons equals the number lattice sites)." + ], + "id": "2" + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The physics of the model are conveniently analysed by measuring the evolution of the spin densities $$\\rho_j^{\\pm}(t) = \\langle n_{j,\\uparrow}\\rangle \\pm \\langle n_{j,\\downarrow} \\rangle~~.$$\n", + "\n", + "We consider a simplified model consisting of a lattice of $N=4$ sites, and study the dynamics for an intermediate interaction strength, $U/J = 3$." + ], + "id": "3" + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Classiq Implementation\n", + "\n", + "We implement the Hamiltonian simulation in three steps, utilizing Classiq's built-in functions.\n", + "\n", + "1. Initial state-preparation: Efficiently prepare the ground state of a non-interacting FH system in the presence of an external spin dependent potential. The ground state is a Gaussian Fermionic state, creating a localized density peak, acting as a wavepacket source. \n", + "2. Time-evolution: Abruptly turn on the two-electron repulsion interaction and turn off the external potential, leading to dynamics governed by Hamiltonian (1). Utilizing a first-order Trotter expansion, the system is evolved in time.\n", + "3. Measurement: The spin densities are evaluated.\n", + "\n", + "Repetition of these three steps many times produces the evolution of expectation values of spin-density in time, $\\{\\rho^{\\pm}_{j}(t)\\}$.\n", + "\n" + ], + "id": "4" + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We begin by importing the required software packages and defining global constants" + ], + "id": "5" + }, + { + "cell_type": "code", + "metadata": {}, + "source": [ + "!pip install -u -qq \"classiq[chemistry]\"" + ], + "execution_count": 1, + "outputs": [ + { + "output_type": "stream", + "text": [ + "\n", + "[optparse.groups]Usage:[/] \n", + " pip install \\[options] \\[package-index-options] ...\n", + " pip install \\[options] -r \\[package-index-options] ...\n", + " pip install \\[options] [-e] ...\n", + " pip install \\[options] [-e] ...\n", + " pip install \\[options] ...\n", + "\n", + "no such option: -u\n" + ] + } + ], + "id": "6" + }, + { + "cell_type": "code", + "metadata": {}, + "source": [ + "import numpy as np\n", + "from openfermion.circuits.slater_determinants import (\n", + " slater_determinant_preparation_circuit,\n", + ")\n", + "from openfermion.linalg.givens_rotations import (\n", + " fermionic_gaussian_decomposition,\n", + " givens_decomposition,\n", + ")\n", + "from openfermion.ops import QuadraticHamiltonian\n", + "\n", + "from classiq import *" + ], + "execution_count": 2, + "outputs": [], + "id": "7" + }, + { + "cell_type": "code", + "metadata": {}, + "source": [ + "N = 4 # number of lattice sites\n", + "a = 1 # lattice spacing\n", + "L = N * a # length of the lattice\n", + "M = 2 * N # total number of fermionic modes\n", + "NUM_ITERS = 10\n", + "J = 1 # hopping strength\n", + "tau = 0.1 / J # Trotter step time interval\n", + "T = NUM_ITERS * tau" + ], + "execution_count": 3, + "outputs": [], + "id": "8" + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Initial State Preperation\n", + "\n", + "We begin by desribing a general algorithm to prepare Slater determinant states. \n", + "\n", + "Following, the algorithm is benchmarked on a simple example involving a four-by-four single particle hamiltonian. \n", + "\n", + "The state preperation algorithm is then utilized to prepare the ground state of the non-interacting Fermi-Hubbard Hamiltonian for the case of a single electron. This is then benchmarked against an analitical solution. \n", + "\n", + "Finally, we prepare on the initial state of the dynamic simulation, a ground state of the Fermi-Hubbard model for a quater-filling." + ], + "id": "9" + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### Preparation of a Slater Determinant State\n", + "\n", + "A Slater-Determinant is the ground state of a quadratic Fermionic Hamiltonian which conserves the number of particles.\n", + "\n", + "We begin by discussing an efficient algorithm to construct the initial non-interacting state.\n", + "\n", + "As all ground states of non-interacting fermionic Hamiltonian, the ground state is a fermionic Gaussian state, which can be prepared in a worst-case circuit depth of $O(N^2)$ [[3](#fermionic_gaussian_state)]. Specifically, for a quadratic Hamiltonian which conserves the number of particles, the fermionic Gaussian state can be expressed as a Slater determinant.\n" + ], + "id": "10" + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "For a general number conserving quadratic fermionic Hamiltonian $$H = \\sum_{\\mu\\nu}c_\\mu^\\dagger h_{\\mu\\nu}c_\\nu~~,~~~~(2)$$ where $h$ is known as the **one-body Hamiltonian**.\n", + "\n", + "Using the anti-commutation relations and the Heisenberg equation ($\\frac{dO(t)}{dt} = i\\left[H, O(t) \\right]$), we have \n", + "\n", + "$$\\frac{dc_\\lambda^\\dagger}{dt} = i\\left[H, c_\\lambda^\\dagger \\right]= i \\sum_{\\mu\\nu} h_{\\mu\\nu}[c_\\mu^\\dagger c_\\nu,c_\\lambda] $$\n", + "\n", + "\n", + "$$= i \\sum_{\\mu\\nu} h_{\\mu\\nu}[c_\\mu^\\dagger c_\\nu,c_\\lambda^\\dagger] = i \\sum_{\\mu\\nu} h_{\\mu\\nu}c_\\mu^\\dagger \\delta_{\\nu \\lambda} = i \\sum_{\\mu} h_{\\mu\\lambda}c_\\mu^\\dagger ~~, $$\n", + "where the the time-dependence is suppressed for concisness.\n", + "\n", + " The dynamics in the Heisenberg representation can therefore be expressed as $$\\mathbf{c}^\\dagger (t) = e^{i H t} \\mathbf{c}^\\dagger e^{-i H t} = e^{i h^T }\\mathbf{c}^\\dagger~~,$$ where $\\mathbf{c}^\\dagger = \\{c_1^\\dagger,\\dots,c_M^\\dagger\\}^T$ and $M$ is the total number of fermionic modes. Remarkably, this implies that the diagonalization of $h$, (an $M$ by $M$ matrix) provides the dynamics in the $2^M$ Hilbert space.\n", + "\n", + "\n", + "Diagonalizing the single particle Hamiltonian $M= \\bar{Q} D \\bar{Q}^\\dagger$, where $\\bar{Q}$ is and $M$-by-$M$ unitary matrix and $D = \\text{diag}(\\epsilon_1,...,\\epsilon_M)$, we obtain $H=\\sum_{k=1}^M \\epsilon_k d_k^\\dagger d_k$, where $$d_\\eta^\\dagger= \\sum_{\\mu=1}^{M} \\bar{Q}_{\\mu \\eta}c_\\mu^\\dagger~~. \\tag{3}$$\n", + "Alternatively, the basis transformation can be expressed in terms of the single-particle transformation, $U\\mathbf{c}^\\dagger = \\mathbf{d}^\\dagger~,$ where we collected the creation operators to form an operator valued vector: $\\mathbf{c}^\\dagger = \\{c_1^\\dagger,\\dots,c_M^\\dagger\\}^T$ and similarly for $\\mathbf{d}^\\dagger$.\n", + "\n", + "For a fixed particle number $N_{\\text{elec}}$ the ground state is given by\n", + "$$|\\psi_{g.s}\\rangle =\\Pi_{k} {\\cal U}c_k^\\dagger |0^M\\rangle = \\Pi_{k=1}^{N_{\\text{elec}}} d_k^\\dagger |0^M\\rangle ~~,$$\n", + "where $i$ iterates over the occupied fermionic modes and ${\\cal U} c_j^\\dagger {\\cal U}^\\dagger = U_{[j,:]} \\mathbf{d}^\\dagger = d_j^\\dagger$.\n", + "The diagonalization of $h$ scales only polynomially with the number of lattice sites, $O(L^3)$ and can be efficiently done on a classical computer.\n", + "\n", + "In order to prepare the desired ground state we focus on a part of $\\bar{Q}$ which corresponds to the occupied modes, and denote the $N_{\\text{elec}}$ by $M$ matrix describing these modes by $Q = (\\bar{Q}^T)_{[{\\text{occupied modes}},:]}$. This identification leads to an alternative form for Eq. (3), for the occupied modes we have $$d_\\eta^\\dagger= \\sum_{\\mu=1}^{M} {Q}_{\\eta \\mu}c_\\mu^\\dagger~~.$$" + ], + "id": "11" + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "An efficient quantum circuit for the ground state preparation can be obtained by a modified QR decomposition of $Q$, using a product of elementary two-mode rotations, called Given rotations. Each rotation can be expressed as\n", + "$$\n", + "\\begin{pmatrix}\n", + "\\mathcal{G}c_k^\\dagger\\mathcal{G}\\\\\n", + "\\mathcal{G}c_j^\\dagger\\mathcal{G}\n", + "\\end{pmatrix}\n", + "=\n", + "G(\\theta,\\varphi)\\,\n", + "\\begin{pmatrix}\n", + "c_k\\\\\n", + "c_j\n", + "\\end{pmatrix}~~,\n", + " $$\n", + "and the form of a Given rotation is $$G_{jk}(\\theta,\\varphi) = \\begin{pmatrix}\n", + "\\cos(\\theta) & -e^{i\\varphi}\\sin(\\theta)\\\\\n", + "\\sin(\\theta) & e^{i\\varphi}\\cos(\\theta)\n", + "\\end{pmatrix}~~. $$\n", + "\n", + "To simplify the decomposition we begin by utilizing the invariance of the Slater determinant (up to a global phase) under the mapping ${Q}\\rightarrow V{Q}$, where $V$ is a unitary transformation. For the transformation of basis to be valid we require that the first $N_{\\text{elec}}$ rows of $VQ$ are equal to $U$, or alternatively $$V{Q}U^\\dagger = (I_{N_{\\text{elec}}}, \\boldsymbol{0})~~.$$ Each Given transformation operates only on two columns and it's parameters, $\\theta$ and $\\phi$ are set so to nullify elements in the upper right part of the matrix. Due to the orthogonality of the rows of $Q$, some transformations nullify more than a single matrix element. As a result, the total number of required Given transformations are $N_G = N_{\\text{elec}}(M-N_\\text{elec})$, where $N_\\text{elec}$ is the number of electrons and $M$ is the number of fermionic modes. The diagonalization procedure results in a product of Given rotations $$U = G_{N_G}\\cdots G_2 G_1~~.$$\n", + "\n", + "After the Jordan-Wigner transformation, each two-mode ($j,k$) rotations correspond to a rotation in the single particle subspace of the two qubits $j$ and $k$ ($|01\\rangle$ and $|10\\rangle$). This completely, defines the state preparation circuit in terms of a sequence two-qubit rotations.\n", + "The gate complexity is $O(N_G) = O(N_{\\text{elec}}^2)$ (worst case achieved for $N_\\text{elec}=M/2$), and parallelization leads to a circuit depth of $M-1$." + ], + "id": "12" + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### Given Rotations Example\n", + "In order to understand the state preparation algorithm, we first show how Given rotations are utilized to diagonalize a simple one-body Hamiltonian.\n", + "\n", + "Consider a simple $4$-by-$4$ Hermitian matrix, representing a one-body Hamiltonian:\n", + "$$h =\n", + "\\begin{pmatrix}\n", + "\\varepsilon_0 & t_{01} & 0 & t_{03} \\\\\n", + "t_{01} & \\varepsilon_1 & t_{12} & 0 \\\\\n", + "0 & t_{12} & \\varepsilon_2 & t_{23} \\\\\n", + "t_{03} & 0 & t_{23} & \\varepsilon_3\n", + "\\end{pmatrix}\n", + " $$" + ], + "id": "13" + }, + { + "cell_type": "code", + "metadata": {}, + "source": [ + "## Defining the single-body Hamiltonian\n", + "# Onsite energies\n", + "eps0, eps1, eps2, eps3 = 0.8, -0.4, 0.3, -0.1\n", + "\n", + "# Hopping amplitudes (real for simplicity)\n", + "t01 = 0.25\n", + "t12 = -0.35\n", + "t23 = 0.20\n", + "t03 = 0.15\n", + "\n", + "# 4x4 Hermitian one-body matrix h_{pq}\n", + "h = np.array(\n", + " [\n", + " [eps0, t01, 0.0, t03],\n", + " [t01, eps1, t12, 0.0],\n", + " [0.0, t12, eps2, t23],\n", + " [t03, 0.0, t23, eps3],\n", + " ],\n", + " dtype=complex,\n", + ")" + ], + "execution_count": 4, + "outputs": [], + "id": "14" + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We employ the methods of OpenFermion's `QuadraticHamiltonian` class in order to extract the Given rotations.\n", + "The number conserving quadratic Hamiltonian is then diagonalized utilizing a Bogoliubov transformation, leading to the `orbital_energies` and a `transformation_matrix`." + ], + "id": "15" + }, + { + "cell_type": "code", + "metadata": {}, + "source": [ + "# Number-conserving quadratic Hamiltonian (no pairing term)\n", + "qh = QuadraticHamiltonian(h, constant=0.0)\n", + "orbital_energies, transformation_matrix, constant = (\n", + " qh.diagonalizing_bogoliubov_transform()\n", + ")\n", + "# Taking the number of electrons to be equal to be two\n", + "occupied_orbitals = np.where(orbital_energies < 0.0)[0]\n", + "slater_determinant_matrix = transformation_matrix[occupied_orbitals]\n", + "\n", + "E, Qbar = np.linalg.eigh(h)\n", + "\n", + "# Sanity check: the transformation matrix from the Bogoliubov transform should diagonalize the one-body Hamiltonian\n", + "assert np.allclose(transformation_matrix, Qbar.T)\n", + "assert np.allclose(orbital_energies, E)\n", + "assert np.allclose(Qbar.T @ h @ Qbar, np.diag(E))" + ], + "execution_count": 5, + "outputs": [], + "id": "16" + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We extract the given rotations utilizing OpenFermion's `given_decomposition`, returning a list of tuples: `[(G_1,G_2),(G_3,),...]`. Each tuple includes the Given rotations which can be operated in parallel. The Given rotations are encoded as a tuple: $G_k = (i_k,j_k,\\theta_k,\\phi_k)$, where $i_k$ and $i_k$ are the columns of $U^\\dagger$ which the Given rotation $G_k^\\dagger$ is operated on from the right (see calculation below)." + ], + "id": "17" + }, + { + "cell_type": "code", + "metadata": {}, + "source": [ + "rotations, V, diag = givens_decomposition(slater_determinant_matrix)" + ], + "execution_count": 6, + "outputs": [], + "id": "18" + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We introduce two utility functions to demonstrate the decomposition, `givens_gate` implements the two-by-two matrix and `build_U_from_rotations`, gathers all the Given rotations to create $U$." + ], + "id": "19" + }, + { + "cell_type": "code", + "metadata": {}, + "source": [ + "def givens_gate(theta: float, phi: float) -> np.ndarray:\n", + " \"\"\"\n", + " Givens rotation:\n", + " G(i,j,theta, phi) = [[ cos(theta), -e^{i phi} sin(theta)],\n", + " [ sin(theta), e^{i phi} cos(theta)]]\n", + " \"\"\"\n", + " c = np.cos(theta)\n", + " s = np.sin(theta)\n", + " e = np.exp(1j * phi)\n", + " return np.array([[c, -e * s], [s, e * c]], dtype=complex)\n", + "\n", + "\n", + "def build_U_from_rotations(M: int, rotations) -> np.ndarray:\n", + " \"\"\"\n", + " Reconstruct U (M x M) from OpenFermion 'givens_rotations' list.\n", + "\n", + " OpenFermion applies these to columns during decomposition; updating columns\n", + " by right-multiplying with G^\\dagger reproduces the same effect.\n", + " \"\"\"\n", + " U_dagger = np.eye(M, dtype=complex)\n", + " for parallel_ops in rotations:\n", + " for i, j, theta, phi in parallel_ops:\n", + " G = givens_gate(theta, phi)\n", + " cols = U_dagger[:, [i, j]]\n", + " U_dagger[:, [i, j]] = cols @ G.conj().T\n", + " return U_dagger.conj().T\n", + "\n", + "\n", + "def build_state_from_rotations(M: int, N: int, circuit_description: list) -> np.ndarray:\n", + " v = np.zeros((M,), dtype=complex)\n", + " v[:N] = np.ones_like(v[:N])\n", + " for parallel_ops in circuit_description:\n", + " for i, j, theta, phi in parallel_ops:\n", + " G = givens_gate(theta, phi)\n", + " v[[i, j]] = G @ v[[i, j]]\n", + " return v" + ], + "execution_count": 7, + "outputs": [], + "id": "20" + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Next, we decompose $U$ into Given rotations: $$U = G_{N_G},\\dots,G_1 $$ and verify that $V Q U^\\dagger = (I,\\mathbf{0})$." + ], + "id": "21" + }, + { + "cell_type": "code", + "metadata": {}, + "source": [ + "tol = 1e-8\n", + "Q = np.asarray(slater_determinant_matrix, dtype=complex)\n", + "n, m = Q.shape\n", + "\n", + "U = build_U_from_rotations(m, rotations)\n", + "\n", + "# Check V Q.T U^† = D where D has diag entries in first m columns and zeros elsewhere\n", + "D = np.zeros((n, m), dtype=complex)\n", + "D[np.arange(n), np.arange(n)] = diag\n", + "\n", + "A = V @ Q @ U.conj().T\n", + "\n", + "# Normalize to (I,0) by removing the diagonal unitary on the left:\n", + "# Let Dm = diag(diag) (m x m). Then Dm^† (V Q U^†) = (I,0).\n", + "# So define V' = Dm^† V.\n", + "Dm_dag = np.diag(\n", + " np.conjugate(diag)\n", + ") # Dm^† since diag entries are unit-modulus in theory\n", + "\n", + "Vprime = Dm_dag @ V\n", + "\n", + "I0 = np.zeros((n, m), dtype=complex)\n", + "I0[:, :n] = np.eye(n, dtype=complex)\n", + "\n", + "B = Vprime @ Q @ U.conj().T\n", + "assert np.allclose(A, D, atol=tol, rtol=tol)\n", + "assert np.allclose(B, I0, atol=tol, rtol=tol)" + ], + "execution_count": 8, + "outputs": [], + "id": "22" + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "State preparation check" + ], + "id": "23" + }, + { + "cell_type": "code", + "metadata": {}, + "source": [ + "# State preparation check for the single excitation subspace\n", + "slater_determinant_matrix = transformation_matrix[[0]]\n", + "rotations, V, diag = givens_decomposition(slater_determinant_matrix)\n", + "circuit_description = reversed(rotations)\n", + "ground_state = build_state_from_rotations(m, n, circuit_description)\n", + "assert np.allclose(h @ Qbar[:, 0], E[0] * Qbar[:, 0], atol=tol, rtol=tol)" + ], + "execution_count": 9, + "outputs": [], + "id": "24" + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### Initial State Preparation of the Fermi Hubbard Model\n", + "\n", + "The initial state is chosen to be the ground state of the non-interacting (i.e, quadratic in the fermionic creation/annihilation operators) Hamiltonian $$H_{0} =-J \\sum_{j, \\sigma} \\left ( c_{j,\\sigma}^\\dagger c_{j+1,\\sigma} + c_{j+1,\\sigma}^\\dagger c_{j,\\sigma}\\right) + \\sum_{j,\\sigma}\\epsilon_{j,\\sigma}n_{j,\\sigma} ~~,$$ where the spin-up fermions feel a Gaussian attractive potential $$\\epsilon_{j,\\uparrow} = -\\lambda \\exp \\left[ -\\frac{(j-m)^2}{2 w^2}\\right]~~,$$ where spin-down fermions feel no potential, $\\epsilon_{j,\\downarrow}$. The parameters $\\lambda$, $m$ and $w$ dictate the precise shape and strength of the potential.\n", + "Such potential creates a localized density peak of spin-up fermions and a flatter distribution for the spin-down fermions. As a result, the simulation begins with localized charge and spin densities. This state is generally not an eigenstate of the interacting Hamiltonian, constituting a highly excited (non-equilibrium) of the interacting system.\n" + ], + "id": "25" + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We begin by defining a function mapping lattice and spin degrees of freedom to qubit number, these will assist us to associate fermionic degrees of freedom to the corresponding qubits in the quantum variables." + ], + "id": "26" + }, + { + "cell_type": "code", + "metadata": {}, + "source": [ + "def qubit_idx(site: int, spin: int):\n", + " \"\"\"\n", + " Maps lattice site and spin to qubit indices.\n", + " Non-interleaved layout: spin-up modes occupy qubits 0..N-1,\n", + " spin-down modes occupy qubits N..2N-1.\n", + " This ensures same-spin hopping acts on adjacent JWT qubits.\n", + "\n", + " Args:\n", + " site (int): Lattice site index, the range [0,N-1]\n", + " spin (int): Spin index, either 0 or 1\n", + "\n", + " Returns:\n", + " qubit_idx (int): qubit index\n", + " \"\"\"\n", + " return site + spin * N\n", + "\n", + "\n", + "def qubit_idx_to_site_and_spin(qubit_idx: int):\n", + " \"\"\"\n", + " Maps qubit index to site and spin indices.\n", + "\n", + " Args:\n", + " qubit_idx (int): qubit index\n", + "\n", + " Returns:\n", + " site (int): site index\n", + " spin (int): spin index\n", + " \"\"\"\n", + " spin = qubit_idx // N\n", + " site = qubit_idx % N\n", + " return site, spin" + ], + "execution_count": 10, + "outputs": [], + "id": "27" + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The Givens rotation matrix $G(\\theta, \\varphi)$ used in [[2]](#fermionic_gaussian_state) acts on the single-particle subspace of two fermionic modes $i$ and $j$ as\n", + "\n", + "$$G(\\theta, \\varphi) = \\begin{pmatrix} \\cos\\theta & -e^{i\\varphi}\\sin\\theta \\\\ \\sin\\theta & e^{i\\varphi}\\cos\\theta \\end{pmatrix}~~,$$\n", + "\n", + "where the first (second) row/column corresponds to mode $i$ ($j$). When this $2\\times 2$ block is embedded in a two-qubit unitary, the mapping between matrix indices and qubit states depends on the qubit ordering convention of the quantum framework.\n", + "\n", + "OpenFermion's `givens_decomposition` returns rotation parameters $(i, j, \\theta, \\varphi)$ assuming the standard (little-endian) convention where the first qubit in the register is the least significant bit:\n", + "$|01\\rangle \\to$ mode $i$ occupied, $|10\\rangle \\to$ mode $j$ occupied.\n", + "\n", + "Classiq's `unitary` gate, however, uses **big-endian** ordering where the first qubit in the list is the most significant bit:\n", + "$|01\\rangle \\to$ mode $j$ occupied, $|10\\rangle \\to$ mode $i$ occupied.\n", + "\n", + "Under the big-endian convention, the $G$ matrix as written above effectively implements $G^{-1}$ (the inverse rotation) in the single-particle picture, introducing alternating sign errors $(-1)^j$ in the prepared state amplitudes. To compensate, we **swap the qubit order** in the call to `G`, passing `[qba[j], qba[i]]` instead of `[qba[i], qba[j]]`. This restores the correct mode-to-index mapping so that the circuit faithfully implements the Givens rotations from the decomposition." + ], + "id": "28" + }, + { + "cell_type": "code", + "metadata": {}, + "source": [ + "@qfunc\n", + "def G(theta: float, phi: float, qba: QArray[QBit, 2]):\n", + " \"\"\"\n", + " Implements a Given rotation on two qubits.\n", + " \"\"\"\n", + " c = np.cos(theta)\n", + " s = np.sin(theta)\n", + " e = np.exp(1j * phi)\n", + " U = [\n", + " [1, 0, 0, 0],\n", + " [0, c, -e * s, 0],\n", + " [0, s, e * c, 0],\n", + " [0, 0, 0, 1],\n", + " ]\n", + " unitary(U, qba)\n", + "\n", + "\n", + "@qfunc\n", + "def given_rotation(gate: list[int, int, float, float], qba: QArray[QBit, M]) -> None:\n", + " \"\"\"\n", + " Implements a Given rotation on two specific qubits, i and j, from an M-qubit quantum array, qba.\n", + " Note: the qubit order is swapped ([qba[j], qba[i]]) to account for Classiq's\n", + " big-endian qubit ordering in the unitary gate (see markdown cell above).\n", + " \"\"\"\n", + " i, j, theta, phi = gate\n", + " G(theta, phi, [qba[j], qba[i]])\n", + "\n", + "\n", + "@qfunc\n", + "def prepare_slater_det(h: list[list[float, M], M], Nelec: int, qba: QArray[QBit, M]):\n", + " \"\"\"\n", + " Prepares the ground state associated with the single electron matrix h.\n", + " The Hamiltonian satisfies H = \\sum_{\\mu,\\nu}c_{\\mu}^\\dagger h_{\\mu,\\nu} c_{\\nu}\n", + "\n", + " Args:\n", + " h (ndarray): single electron matrix\n", + " Nelec (int): number of electrons\n", + " qba (list[QBit]): list of qubits\n", + " \"\"\"\n", + " # preparing the reference state, as the state with the first Nelec qubits in state |1> and the rest in state |0>.\n", + " repeat(Nelec, lambda i: X(qba[i]))\n", + "\n", + " # diagonalizing h\n", + " D, Qbar = np.linalg.eigh(h)\n", + " Q = (Qbar.T)[:Nelec, :] # occupying the N lowest energy states\n", + " rotations, _, _ = givens_decomposition(Q)\n", + " # U = build_U_from_rotations(M, rotations)\n", + " circuit_description = list(reversed(rotations))\n", + " # ground_state = build_state_from_rotations(M, N, circuit_description)\n", + " for parallel_ops in circuit_description:\n", + " for gate in parallel_ops:\n", + " given_rotation(list(gate), qba)" + ], + "execution_count": 11, + "outputs": [], + "id": "29" + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The circuit can be verified by considering the single excitation subspace and comparing the compared state to the analytical result.\n", + "\n", + "The ground state of the single excitation subspace is up to a global phase just $$d_1^\\dagger | 0^M\\rangle =\\sum_\\mu Q_{1,\\mu} c^{\\dagger}_\\mu | 0^M\\rangle ~~,$$ which after the Jordan-Wigner transformation corresponds to the quibt state with amplitudes $$[Q_{1,1},Q_{1,2},\\dots, Q_{1,M}]~~.$$" + ], + "id": "30" + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In order to prepare the initial state, we begin by constructing the initial Hamiltonian. Utility functions are defined and the Hamiltonian parameters are set." + ], + "id": "31" + }, + { + "cell_type": "code", + "metadata": {}, + "source": [ + "def sym(A):\n", + " \"\"\"\n", + " Symmetrizes the matrix A\n", + " \"\"\"\n", + " return (A + A.T) / 2\n", + "\n", + "\n", + "def kinetic_energy(N: int, J: float) -> np.ndarray:\n", + " \"\"\"\n", + " Builds single electron matrix of nearest-neighbor hopping term,\n", + " hopping strength J, for an N-site open chain (no periodic boundary).\n", + " \"\"\"\n", + " K = np.zeros((2 * N, 2 * N), dtype=float)\n", + " for site in range(N - 1):\n", + " for spin in range(2):\n", + " mu = qubit_idx(site, spin)\n", + " nu = qubit_idx(site + 1, spin)\n", + " K[mu, nu] = -J\n", + " K = 2 * sym(K)\n", + " return K\n", + "\n", + "\n", + "def spin_potential(N: int, spin=0, parameters: tuple[float] = (1, 1, 1)) -> np.ndarray:\n", + " \"\"\"\n", + " Builds single electron matrix associated with the external potential.\n", + " Associated with an N site lattice.\n", + " \"\"\"\n", + " lam, mean, std = parameters\n", + " V = np.zeros((2 * N, 2 * N), dtype=float)\n", + " for site in range(N):\n", + " mu = qubit_idx(site, spin)\n", + " V[mu, mu] = -lam * np.exp(-((site - mean) ** 2) / (2 * std**2))\n", + " return V\n", + "\n", + "\n", + "def construct_single_electron_hamiltonian(\n", + " N: int, J: float, parameters: tuple\n", + ") -> np.ndarray:\n", + " return kinetic_energy(N, J) + spin_potential(N, spin=0, parameters=parameters)" + ], + "execution_count": 12, + "outputs": [], + "id": "32" + }, + { + "cell_type": "code", + "metadata": {}, + "source": [ + "lam = 3.0\n", + "mean = (L - 1) / 2\n", + "std = 0.5\n", + "h = construct_single_electron_hamiltonian(L, J=1, parameters=(lam, mean, std))\n", + "Nelec = 1" + ], + "execution_count": 13, + "outputs": [], + "id": "33" + }, + { + "cell_type": "code", + "metadata": {}, + "source": [ + "@qfunc\n", + "def main(qba: Output[QArray[QBit, M]]) -> None:\n", + " allocate(M, qba)\n", + " prepare_slater_det(h, Nelec, qba)\n", + "\n", + "\n", + "qprog = synthesize(main)" + ], + "execution_count": 14, + "outputs": [], + "id": "34" + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The state preparation quantum circuit. The Given rotation, operating on two qubits, is decomposed into the basis gates.\n", + "\n", + "![State preparation circuit](attachment:gaussian_state_preperation.png)" + ], + "id": "35" + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### Single State Excitation Subspace Verification" + ], + "id": "36" + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "For the single excitation subspace we can easily compare the preparation of the quantum state with the exact diagonalization. To compare between the two we normalize the quantum solution so to cancel the difference in the global phase with respect to the classical result." + ], + "id": "37" + }, + { + "cell_type": "code", + "metadata": {}, + "source": [ + "backend_preferences = ClassiqBackendPreferences(\n", + " backend_name=ClassiqSimulatorBackendNames.SIMULATOR_STATEVECTOR\n", + ")\n", + "\n", + "\n", + "# Construct a representation of HHL model\n", + "def state_check_model(main, backend_preferences):\n", + " qmod_state_check = create_model(\n", + " main,\n", + " execution_preferences=ExecutionPreferences(\n", + " num_shots=1, backend_preferences=backend_preferences\n", + " ),\n", + " )\n", + " return qmod_state_check" + ], + "execution_count": 15, + "outputs": [], + "id": "38" + }, + { + "cell_type": "code", + "metadata": {}, + "source": [ + "# Construct the quantum program\n", + "qmod_state_check = state_check_model(main, backend_preferences)\n", + "qprog_state_check = synthesize(qmod_state_check)\n", + "\n", + "print(\"Circuit depth = \", qprog_state_check.transpiled_circuit.depth)\n", + "res_state_check = execute(qprog_state_check).result_value()" + ], + "execution_count": 16, + "outputs": [ + { + "output_type": "stream", + "text": [ + "Circuit depth = 13\n" + ] + } + ], + "id": "39" + }, + { + "cell_type": "code", + "metadata": {}, + "source": [ + "import matplotlib.pyplot as plt\n", + "\n", + "\n", + "def get_quantum_amplitudes(result):\n", + " df = result.dataframe\n", + " mask = np.abs(df[\"amplitude\"]) > 1e-12\n", + " filtered = df.loc[mask, [\"bitstring\", \"amplitude\"]].copy()\n", + " amps = filtered[\"amplitude\"].to_numpy()\n", + " bitstring = filtered[\"bitstring\"].tolist() # must be integers\n", + " # mapping the bitstrings to qubit indices in the array\n", + " qubit_index = [[i for i, b in enumerate(s[::-1]) if b == \"1\"] for s in bitstring]\n", + " qubit_index = np.array([i[0] for i in qubit_index])\n", + " idx = np.argsort(qubit_index)\n", + " qubit_index = qubit_index[idx]\n", + " amps = amps[idx]\n", + " amps = amps / np.linalg.norm(amps)\n", + "\n", + " qsol = np.zeros(M, dtype=complex)\n", + " qsol[qubit_index] = amps\n", + " return qsol" + ], + "execution_count": 17, + "outputs": [], + "id": "40" + }, + { + "cell_type": "code", + "metadata": {}, + "source": [ + "# Compare quantum amplitudes with exact diagonalization (Nelec=1)\n", + "qsol = get_quantum_amplitudes(res_state_check)\n", + "\n", + "# Exact ground state: lowest eigenvector of h\n", + "E_exact, Qbar_exact = np.linalg.eigh(h)\n", + "exact_state = Qbar_exact[:, 0]\n", + "\n", + "# Align global phase: multiply qsol by phase so that it matches exact_state\n", + "overlap = np.dot(exact_state.conj(), qsol)\n", + "phase_global = overlap / np.abs(overlap)\n", + "qsol_aligned = qsol / phase_global\n", + "\n", + "fig, ax = plt.subplots(figsize=(6, 4))\n", + "\n", + "# Real part\n", + "ax.bar(np.arange(M) - 0.15, np.real(exact_state), width=0.3, label=\"Exact\", alpha=0.8)\n", + "ax.bar(\n", + " np.arange(M) + 0.15, np.real(qsol_aligned), width=0.3, label=\"Quantum\", alpha=0.8\n", + ")\n", + "ax.set_xlabel(\"Qubit index\", fontsize=12)\n", + "ax.set_ylabel(\"Amplitude (real)\", fontsize=12)\n", + "ax.set_title(\"Real Part\", fontsize=14)\n", + "ax.set_xticks(np.arange(M))\n", + "ax.legend()\n", + "\n", + "plt.suptitle(\"State Preparation vs Exact Ground State ($N_{elec}=1$)\", fontsize=16)\n", + "plt.tight_layout()\n", + "plt.show()\n", + "\n", + "# Fidelity check\n", + "fidelity = np.abs(np.dot(exact_state.conj(), qsol)) ** 2\n", + "print(f\"Fidelity ||^2 = {fidelity:.10f}\")\n", + "assert fidelity > 0.95, f\"Fidelity too low: {fidelity}\"" + ], + "execution_count": 18, + "outputs": [ + { + "output_type": "display_data", + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + } + }, + { + "output_type": "stream", + "text": [ + "Fidelity ||^2 = 1.0000000000\n" + ] + } + ], + "id": "41" + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### Initial State at Quater-Filling\n", + "At quater-filling the number of electrons $N_{\\text{elec}}$ equals to half number of lattice sites $N$ (quater of the $M=2N$ fermionic modes). The one-body potential strength $\\lambda$ is set such that the two electrons will have different spins ($N_{\\downarrow} = N_{\\uparrow}=1$)" + ], + "id": "42" + }, + { + "cell_type": "code", + "metadata": {}, + "source": [ + "Nelec = N // 2 # quater-filling" + ], + "execution_count": 19, + "outputs": [], + "id": "43" + }, + { + "cell_type": "code", + "metadata": {}, + "source": [ + "@qfunc\n", + "def main(qba: Output[QArray[QBit, M]]) -> None:\n", + " allocate(M, qba)\n", + " prepare_slater_det(h, Nelec, qba)\n", + "\n", + "\n", + "qprog = synthesize(main)" + ], + "execution_count": 20, + "outputs": [], + "id": "44" + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "To image the ground state, we measure the charge and spin densities: $\\rho_j^{\\pm} = \\langle n_{j,\\uparrow}\\rangle \\pm \\langle n_{j,\\downarrow} \\rangle$. The charge density, $\\rho_j^{+}$, corresponds to the average number of electrons on the $j$'th site, while the spin density, $\\rho_j^{-}$, is the net spin on the same site.\n", + "\n", + "The number operator $n_\\mu = c^\\dagger_\\mu c_\\mu$ maps under the Jordan-Wigner transformation to $$n_\\mu \\rightarrow \\frac{I-Z_{\\mu}}{2}~~. $$\n", + "Therefore, the charge density maps to $$\\rho_j^{+} = 1 - (\\langle Z_{j,\\uparrow}\\rangle + \\langle Z_{j,\\downarrow}\\rangle)/2~~,$$ while the spin density corresponds to $$ \\rho_j^{-} = (\\langle Z_{j,\\downarrow}\\rangle - \\langle Z_{j,\\uparrow}\\rangle)/2 ~~.$$\n", + "\n", + "We introduce the functions `charge_density` and `spin_density` which allow measuring the corresponding observables." + ], + "id": "45" + }, + { + "cell_type": "code", + "metadata": {}, + "source": [ + "def charge_density(site: int, M: int) -> SparsePauliOp:\n", + " s = SparsePauliOp([], M)\n", + " for spin in (0, 1):\n", + " idx = qubit_idx(site=site, spin=spin)\n", + " s += (Pauli.I(idx) - Pauli.Z(idx)) * 0.5\n", + " return s\n", + "\n", + "\n", + "def spin_density(site: int, M: int) -> SparsePauliOp:\n", + " s_up, s_down = SparsePauliOp([], M), SparsePauliOp([], M)\n", + " idx_up, idx_down = qubit_idx(site=site, spin=0), qubit_idx(site=site, spin=1)\n", + " s_up += Pauli.Z(idx_up)\n", + " s_down += Pauli.Z(idx_down)\n", + " return (s_down - s_up) * 0.5" + ], + "execution_count": 21, + "outputs": [], + "id": "46" + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Next, we execute the quantum program and measure the spin and change densities" + ], + "id": "47" + }, + { + "cell_type": "code", + "metadata": {}, + "source": [ + "initial_charge_density = np.zeros(L)\n", + "initial_spin_density = np.zeros(L)\n", + "\n", + "with ExecutionSession(qprog) as es:\n", + " for site in range(L):\n", + " initial_charge_density[site] = np.real(\n", + " es.estimate(charge_density(site, M)).value\n", + " )\n", + " initial_spin_density[site] = np.real(es.estimate(spin_density(site, M)).value)" + ], + "execution_count": 22, + "outputs": [], + "id": "48" + }, + { + "cell_type": "code", + "metadata": {}, + "source": [ + "sites = np.arange(0, L)\n", + "plt.figure()\n", + "plt.title(\"Initial Densities\", fontsize=18)\n", + "plt.plot(sites, initial_charge_density, \"o\", label=\"charge density\")\n", + "plt.plot(sites, initial_spin_density, \"+\", markersize=10, label=\"spin density\")\n", + "plt.xlabel(\"Site\", fontsize=12)\n", + "plt.ylabel(\"Density\", fontsize=12)\n", + "plt.xticks(sites)\n", + "plt.legend()\n", + "plt.show()" + ], + "execution_count": 23, + "outputs": [ + { + "output_type": "display_data", + "data": { + "image/png": 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848aNk+joaNdF+/kAgU7n0Zna+TpTwXGnt3U78+wgpxjlh1ASUM1YObV8+XIZO3asvPbaa6aPz7Zt2+SJJ56QUaNGydChQz0eM2jQINMvyEkrOwQeBAMNNDdXj2EGZfh8lF985St51xHUAibslCxZUiIiIuTgwYNptuvtmJgYj8dooHnwwQflkUceMbdr1aolp06dkh49esjgwYNNM1h6BQoUMBcgGGlTFV888AZG+SGUBEwzVmRkpNSvX1+WLl3q2paammpux8fHezzm9OnTGQKNBiblcDDBGgBkhlF+CCUBU9lR2rzUtWtXadCggTRq1MgMPddKjXN0VpcuXaR8+fKm343q0KGDGcFVr149VzOWVnt0uzP0AAAyYpQfQklAhZ2OHTvK4cOHZdiwYaZTct26dSUxMdHVaXnPnj1pKjlDhgwxc+ro9b59+6RUqVIm6IwZM8aPrwIAgmeUn66tpqP63GvhjPKDbcIcId7eox2UdVRWUlKSFCtWzN+nAwA+xTw7CIXv74Cq7AAAfItRfggFhB0ACHGM8oPtAmY0FgAAQF4g7AAAAKsRdgAAgNUIOwAAwGqEHQAAYDXCDgAAsBphBwAAWI2wAwAArEbYAQAAViPsAAAAqxF2AACA1Qg7AADAaoQdAABgNcIOAACwGmEHAABYjbADAACsRtgBAABWI+wAAACrEXYAAIDVCDsAAMBqhB0AAGA1wg4AALAaYQcAAFiNsAMAAKxG2AEAAFYj7AAAAKsRdgAAgNUIOwAAwGqEHQAAYDXCDgAAsBphBwAAWI2wAwAArEbYAQAAViPsAAAAqxF2AACA1Qg7AADAaoQdAABgNcIOAACwGmEHAABYjbADAACsRtgBAABWI+wAAACrEXYAAIDVCDsAAMBqhB0AAGA1wg4AALAaYQcAAFiNsAMAAKxG2AEAAFYj7AAAAKsRdgAAgNUIOwAAwGqEHQAAYDXCDgAAsBphBwAAWI2wAwAArEbYAQAAViPsAAAAqxF2AACA1Qg7AADAagEXdqZMmSJxcXESFRUljRs3ltWrV2e5//Hjx6V3795StmxZKVCggFxzzTWycOFCn50vAAAIbPkkgMyZM0f69+8v06ZNM0Fn0qRJ0rZtW9m6dauULl06w/7nz5+Xm2++2dz34YcfSvny5WX37t1SvHhxv5w/AAAIPGEOh8MhAUIDTsOGDWXy5MnmdmpqqsTGxkrfvn1l4MCBGfbXUDRx4kTZsmWL5M+f/7KeMzk5WaKjoyUpKUmKFSuW69cAAADyXk6+vwOmGUurNGvWrJHWrVu7toWHh5vbK1eu9HjM/PnzJT4+3jRjlSlTRmrWrCljx46VlJQUH545AAAIZAHTjHXkyBETUjS0uNPbWrnxZMeOHfLll1/KAw88YPrpbNu2TXr16iUXLlyQhIQEj8ecO3fOXNyTIQAAsFfAVHYuhzZzaX+d6dOnS/369aVjx44yePBg07yVmXHjxpmyl/OizWQAAMBeARN2SpYsKREREXLw4ME02/V2TEyMx2N0BJaOvtLjnKpVqyYHDhwwzWKeDBo0yLTvOS979+718isBAACBJGDCTmRkpKnOLF26NE3lRm9rvxxPmjZtapqudD+nX3/91YQgfTxPdHi6dmRyvwAAAHsFTNhROux8xowZ8s4778gvv/wiPXv2lFOnTkm3bt3M/V26dDGVGSe9/88//5QnnnjChJwFCxaYDsraYRkAACCgOigr7XNz+PBhGTZsmGmKqlu3riQmJro6Le/Zs8eM0HLS/jaLFi2Sp556SmrXrm3m2dHgM2DAAD++CgAAEEgCap4df2CeHQAAgk9QzrMDAACQFwg7AADAaoQdAABgNcIOAACwGmEHAABYjbADAACsRtgBAABWI+wAAACrEXYAAIDVCDsAAMBqhB0AAGA1wg4AALAaYQcAAFiNsAMAAKxG2AEAAFYj7AAAAKsRdgAAgNUIOwAAwGqEHQAAYDXCDgAAsBphBwAAWI2wAwAArEbYAQAAViPsAAAAqxF2AACA1Qg7AADAaoQdAABgNcIOAACwGmEHAABYjbADAACsRtgBAABWI+wAAACrEXYAAIDVCDsAAMBqhB0AAGA1wg4AALAaYQcAAFiNsAMAAKxG2AEAAFYj7AAAAKsRdgAAgNUIOwAAwGqEHQAAYDXCDgAAsBphBwAAWI2wAwAArEbYAQAAViPsAAAAqxF2AACA1Qg7AADAaoQdAABgNcIOAACwGmEHAABYjbADAACsRtgBAABWI+wAAACr5SrstGvXTmbNmiVnzpzx3hkBAAAEStjZsWOHdO7cWcqUKSNdu3aVL774QhwOh/fODgAAwJ9hZ+vWrbJq1Srp1q2bLF68WNq2bSsVKlSQZ599VtatW5fbcwMAAMi1MIeXSjGpqamyZMkSee+99+STTz6RU6dOSbVq1aRLly5y//33mxAUiJKTkyU6OlqSkpKkWLFi/j4dAADg5e9vr4Udd8ePH5fHHntMPvjgA3M7PDxcWrZsKU899ZS0b99eAglhBwCA4JOT72+vjsb69ttv5fHHH5cqVaqYoFOzZk2ZMGGCvPjii3L48GG57bbbZNiwYd58SgAAgLyt7GzevNk0Xb3//vuyZ88eKV26tGm2evDBB6Vu3bpp9u3Ro4d89NFHcvToUQkUVHYAAAg+PqvsaJipVauWTJo0SZo0aSKfffaZ7Nu3z1Ry0gcd1apVKzl27NglH3fKlCkSFxcnUVFR0rhxY1m9enW2zmf27NkSFhYmd9xxx2W9HgAAYJ98uTm4ePHiMn36dLnnnnuy1bn39ttvl507d2a5z5w5c6R///4ybdo0E3Q0SOkoLx35pVWjzOzatUueeeYZadas2WW9FgAAYKdcNWNps1WpUqWkYMGCHu/XyQa1r85VV12V7cfUgNOwYUOZPHmya5RXbGys9O3bVwYOHOjxmJSUFGnevLk8/PDD8s0335gO0vPmzcvW89GMBQBA8PFZM1alSpVk7ty5md4/f/58s092nT9/XtasWSOtW7f++wTDw83tlStXZnrcyJEjTdWne/fuOTh7AAAQCnLVjHWpotCFCxdMWMmuI0eOmCqNzsjsTm9v2bIl0xFgb775ZrYnMTx37py5uCdDAABgrxyHHQ0H2kzkpCOrtDkrPd1HOwyXLVtW8sqJEyfMqK8ZM2ZIyZIls3XMuHHjZMSIEXl2TgAAIMjDzssvv2yajZSOfHryySfNJbPKz+jRo7P92BpYIiIi5ODBg2m26+2YmJgM+2/fvt10TO7QoYNrm/bxUfny5TOdmitXrpzmmEGDBpkO0O7hTfsEAQAAO+U47LRp00aKFCligsy///1v6dSpk1x33XVp9tEQVLhwYalfv740aNAg248dGRlpjlm6dKlr+LiGF73dp0+fDPtfe+21smHDhjTbhgwZYio+r7zyiscQU6BAAXMBAAChIcdhJz4+3lyUrn911113mbl2vEWrLrqCuoakRo0amaHn+jy62KjStbbKly9vmqN0Hh6dpTn9cHiVfjsAAAhNueqgnJCQIN7WsWNHM1xdl5U4cOCAmZwwMTHR1WlZ+wflpNMzAAAIbTmaZ0f76mgT1eDBg03gcPbdyfIJwsJk6NChEqiYZwcAgOCTZ6uea8DR8KKTBWr/muxUWHR/HU4eqAg7AAAEn5x8f+eoGcs50imz2wAAAIGGzi8AAMBqueqg7Mnp06fNZII6S/Gtt94qFStW9PZTAAAA+Cbs6FpUq1atko0bN7rWtmrSpInrtralffnll1KvXr3cPA0AAIB/mrGWLVtm5tlxmjVrlgk6//3vf821znrM0gwAACBow47OgxMXF+e6PW/ePDMZoM6qXL16dXn00UdN5QcAACAow44uCeFcFPTixYuyfPlyadu2rev+okWLmiFhAAAAQdlnR9fE0hXHW7VqJfPnzzdrUrkvyqkLdTpnPgYAAAi6sDNmzBhTydGmK52b8O677zbrWTnNnTtXmjZt6o3zBAAA8H3Y0ZCzZcsWWbFihVmAs0WLFq77tHmrV69eabYBAAD4Wo6Wi7ARy0UAABB88my5iMxoX53du3fLsWPHTHNWes2bN/fG0wAAAORYrsLO0aNHpU+fPvLRRx95XOxTg0+gLwQKAADslquwo/PofPrpp9KvXz9p1qyZXHHFFd47MwAAAH+HncWLF8tTTz0lEyZM8Ma5AAAABNakgoUKFUozgzIAAIBVYadz585mLh0AAAArm7F0EsGvvvpKbrnlFunRo4fExsZKRESEx5mWAQAAgm6enfDwvwtDOuoqGEdjMc8OAADBx2fz7MycOTM3hwMAAOS5XIWdrl27eu9MAAAAAq2Dsrv9+/fL+vXr5dSpU956SAAAAP+HnU8++USuvfZaqVChgumIvGrVKrP9yJEjUq9ePUZrAQCA4A07OnvyXXfdJSVLlpSEhIQ062LptvLly8vbb7/tjfMEAADwfdgZOXKkWeTz22+/ld69e2e4Pz4+Xn766afcPAUAAID/ws7GjRvl3nvvzfT+MmXKyKFDh3LzFAAAAP5dLiKrDsk7duyQK6+8MjdPAQAA4L+w06pVK3nnnXfk4sWLGe47cOCAzJgxQ9q0aZObpwAAAPBf2BkzZoz8/vvv0rBhQ3n99dfNbMmLFi2SIUOGSK1atUyHZe24DAAAEJTLRahNmzbJE088IcuWLUszGqtly5YyZcoUqVatmgQylosAACD4+Gy5CFWjRg354osv5NixY7Jt2zZJTU2Vf/zjH1KqVKncPjQAAECuXXbYOXfunLz33nuyePFi2b59u5w4cUKKFi0qVapUMaug33///RIZGZn7MwQAAPB1M9aGDRvk9ttvl927d5umKy0jFSlSRE6ePGnKSdp3R6s78+fPpxkLAAD4tRkrxx2UNdDcdtttcvDgQdNBee/evaYJy/169OjR8scff0iHDh1YKwsAAPhVjsPOzJkzZc+ePbJgwQIZOHCgWRLCnd4eNGiQWUpi586dLBcBAACCqxlL++NoM9Xnn3+erX1VYmKiBCpGYwEAEHzytBlL++vosPLsuPHGG83+AAAA/pLjsPPnn39KTExMtvbVtbF0fwAAgKAJOzrkPH/+/NnaN1++fHL+/PnLOS8AAAD/zbOza9cuWbt27SX30w7KAAAAQdVBOTw83HRQzg59aN03JSVFAhUdlAEACD55ulyEDj0HAAAIFjkOO127ds2bMwEAAAiEDsoAAADBhLADAACsRtgBAABWI+wAAACrEXYAAIDVCDsAAMBqhB0AAGA1wg4AALAaYQcAAFiNsAMAAKxG2AEAAFYj7AAAAKsRdgAAgNUIOwAAwGqEHQAAYDXCDgAAsBphBwAAWI2wAwAArEbYAQAAVgvIsDNlyhSJi4uTqKgoady4saxevTrTfWfMmCHNmjWTK664wlxat26d5f4AACC0BFzYmTNnjvTv318SEhJk7dq1UqdOHWnbtq0cOnTI4/7Lly+XTp06ybJly2TlypUSGxsrbdq0kX379vn83AEAwN9SUh2ycvtR+WTdPnOtt/0hzOFw+OeZM6GVnIYNG8rkyZPN7dTUVBNg+vbtKwMHDrzk8SkpKabCo8d36dLlkvsnJydLdHS0JCUlSbFixbzyGsx5pDpk9c4/5dCJs1K6aJQ0qlRCIsLDvPb4AAAEssSN+2XEp5tlf9JZ17ay0VGS0KG63FKzbK4fPyff3/kkgJw/f17WrFkjgwYNcm0LDw83TVNatcmO06dPy4ULF6REiRJi6wcMAEAgS9y4X3q+t1bSV1MOJJ0126d2vs6n34cB1Yx15MgRU5kpU6ZMmu16+8CBA9l6jAEDBki5cuVMQPLk3LlzJg26X/LiA3YPOu4fsN4PAICtUlId5g9+T81Gzm16vy+btAIq7OTW888/L7Nnz5a5c+eazs2ejBs3zpS9nBdtIrP5AwYAwJe0C0f6P/jd6Teg3q/7hWTYKVmypERERMjBgwfTbNfbMTExWR77wgsvmLCzePFiqV27dqb7aROZtu85L3v37rX6AwYAwJe0r6o397Mu7ERGRkr9+vVl6dKlrm3aQVlvx8fHZ3rchAkTZNSoUZKYmCgNGjTI8jkKFChgOjK5X2z+gAEA8CUdlOPN/bwhoDooKx123rVrVxNaGjVqJJMmTZJTp05Jt27dzP06wqp8+fKmOUqNHz9ehg0bJrNmzTJz8zj79hQpUsRcQv0DBgDAl3T0sQ7K0b6qnjpt6LjkmOi/RimHZGVHdezY0TRJaYCpW7eurFu3zlRsnJ2W9+zZI/v3/93Jd+rUqWYU19133y1ly5Z1XfQx/PUBZzbAXLeX9fEHDACAL+k0Kzr6WKX/PnTe1vt9OR1LwM2z42venmfHORpLub+xzo/U18PtAAAI9Xl2CDt5MKkg8+wAACB5OsEuYSeP3qycYAZlAADyTtDOoGwTTa7xla/092kAABDyAq6DMgAAgDcRdgAAgNUIOwAAwGqEHQAAYDXCDgAAsBphBwAAWI2wAwAArEbYAQAAViPsAAAAqxF2AACA1Qg7AADAaoQdAABgNcIOAACwGmEHAABYjbADAACsRtgBAABWI+wAAACrEXYAAIDVCDsAAMBqhB0AAGA1wg4AALAaYQcAAFiNsAMAAKxG2AEAAFYj7AAAAKsRdgAAgNUIOwAAkRMHRJaN++sasAxhBwDwV8j56nnCDqxE2AEAAFYj7AAAAKsRdgAAgNUIOwAAwGr5/H0CAAAfd0T2NOJq//q01+kVjfnrAgQhwg4QbPSL6seZIg268eWDnNPfHR11lZlP+3ne3mKgSKtBvOMISoQdIFiHCFdtR9hBzmlI1t+d9LSio0Gnw6siZetkvJ+qDoIYYQcAQsmlmqM06JSr68szAvIcHZQBAIDVCDsAAMBqhB0AAGA1+uwAgYohwgDgFYQdIFAxRBi+pJ2WdXg5o65goTCHw+GQEJacnCzR0dGSlJQkxYoV8/fpANmr7FxqiDBfWAAsl5yD728qO0CgYogwAHgFHZQBAIDVCDsAAMBqhB0AAGA1wg4AALAaYQcINgwRBoAcYTQWEIxhp9Ugf58FAAQNKjsAAMBqhB0AAGA1wg4AALAaYQcAAFiNsAMAAKxG2AEAAFYj7AAAAKsRdgAAgNUIOwAAwGqEHQAAYDXCDgAAsFpAhp0pU6ZIXFycREVFSePGjWX16tVZ7v/BBx/Itddea/avVauWLFy40GfnCgAAAlvAhZ05c+ZI//79JSEhQdauXSt16tSRtm3byqFDhzzuv2LFCunUqZN0795dfvrpJ7njjjvMZePGjT4/dwAAEHjCHA6HQwKIVnIaNmwokydPNrdTU1MlNjZW+vbtKwMHDsywf8eOHeXUqVPy2WefubY1adJE6tatK9OmTbvk8yUnJ0t0dLQkJSVJsWLFvPxqAABAXsjJ93dAVXbOnz8va9askdatW7u2hYeHm9srV670eIxud99faSUos/3PnTtn3iD3CwAAsFc+CSBHjhyRlJQUKVOmTJrtenvLli0ejzlw4IDH/XW7J+PGjZMRI0Z48awB39OKp/5xAHhT/vz5JSIigjcV1gmosOMLgwYNMn2CnLSyo81kQLDQkLNz504TeABvK168uMTExEhYWBhvLqwRUGGnZMmS5q+KgwcPptmut/Ufnye6PSf7FyhQwFyAYKRd7Pbv32/+nWhI12ZewFu/W6dPn3YNBilbtixvLKwRUGEnMjJS6tevL0uXLjUjqpT+9aq3+/Tp4/GY+Ph4c/+TTz7p2rZkyRKzHbDNxYsXzRdSuXLlpFChQv4+HVimYMGC5loDT+nSpWnSgjUCKuwobWLq2rWrNGjQQBo1aiSTJk0yo626detm7u/SpYuUL1/e9L1RTzzxhLRo0UJefPFFad++vcyePVt+/PFHmT59up9fCeB92qfN+YcBkBecIfrChQuEHVgj4MKODiU/fPiwDBs2zHQy1iHkiYmJrk7Ie/bsSVO6v/7662XWrFkyZMgQee655+Tqq6+WefPmSc2aNf34KoC8RX8K8LsFBPE8O77GPDsIJmfPnjWdkytVqmRmDLfBrl27zOvRSUH1j5tgNXz4cPOH1rp163zyfMuXL5dWrVrJsWPHTKdib7Hxdwx2Ctp5dgD4RkqqQ1ZuPyqfrNtnrvU2gotWtbWzuv5nr95++22vhh7AJgHXjAUgbyVu3C8jPt0s+5POuraVjY6ShA7V5ZaaZa0aom9z3yZ9bZmNOgWQFpUdIMSCTs/31qYJOupA0lmzXe/PCzqqcsKECVKlShUz9cNVV10lY8aMSbPPjh07TLOMdpDVNfHcZ0E/evSoWQNPByfo/brg7/vvv5/m+JYtW5pRmzoyU6ex0JnU1fz5801fPm2S0cd/5513TJ+n48ePu4799ttvpVmzZmY0kg7p79evnxkYkZXnn3/e9CUsWrSoWZtPm3/Se+ONN6RatWrmuXWx4tdeey1N852ex8cff5zp6969e7d06NBBrrjiCilcuLDUqFHDtdCxNmM5X4f+rIM4tJyv2/SizWojR4702H9RmwuHDh2a5esDbELYAUKENlVpRcdTg5Vzm96fF01aOpmnhgP9gt28ebMZVJB+5vPBgwfLM888Y/q8XHPNNSbc6FB7pUFCp6VYsGCBWeS3R48e8uCDD8rq1avTPIYGGa14fPfdd2ZtPO17cvfdd5upLNavXy+PPfaYeR5327dvl1tuuUX+9a9/yc8//2wWI9bwk9l0F+p///ufCRNjx441oz91Thr3IKP++9//moEWGup++eUXs6++fj3H7L7u3r17myVuvv76a9mwYYOMHz9eihQp4rFJS0euar8FbdrSiz7mww8/bJ77hx9+cO2rfaP0dTpHuAIhwRHikpKS9H92cw0EujNnzjg2b95srnNqxbYjjooDPrvkRffzpuTkZEeBAgUcM2bM8Hj/zp07zb/BN954w7Vt06ZNZtsvv/yS6eO2b9/e8fTTT7tut2jRwlGvXr00+wwYMMBRs2bNNNsGDx5sHvvYsWPmdvfu3R09evRIs88333zjCA8Pz/R9jo+Pd/Tq1SvNtsaNGzvq1Knjul25cmXHrFmz0uwzatQoc2x2X3etWrUcw4cP93gOy5YtS/M6Zs6c6YiOjs6wX7t27Rw9e/Z03e7bt6+jZcuWjrz4HQMC9fubyg4QIg6dOOvV/bJLKwtanbjpppuy3K927dqun52z9zpn89X5hUaNGmWar0qUKGGqG4sWLTJTUbjT6o+7rVu3SsOGDdNs0/m73GnFRzv36mM6L9oEpk1vWhnK7DU1btw4zTb3iUy1CUwrRtq85f64o0ePNtuz+7q1OU2Padq0qSQkJJiKTE49+uijpslPq2Paj0mralrxAUIJHZSBEFG6aJRX98vprLzZWYQy/TxCzvW/Jk6cKK+88oppqtHAo/1XtG9O+sVQdXtOnTx50jRvabBIT/sWXQ59TDVjxowMoSj9QptZve5HHnnEBC9tvlu8eLGZTFUnUO3bt2+2z0X7/Gg/qblz55omPp0sUJv2gFBCZQcIEY0qlTCjrjJb3lG36/26nzdp52ANPLqsy+XSPji33367dO7c2XTi/cc//iG//vrrJY+rWrWq6VPjzr3/irruuutMPyLtPJ3+ktloLu10vGrVqjTbvv/+e9fP2h9Jl/TQTtfpH1Pnr8kJ7TD9+OOPm47MTz/9tAlQnui5OmfYdpcvXz4zK/3MmTPN5b777st2AAVsQWUHCBER4WFmeLmOutJg494N2RmA9H7dz5t0JNKAAQPk3//+t/lC1iYZnSV906ZNppknu4Hpww8/lBUrVpiRSS+99JJZ8Ld69epZHqcVG91Xn1+fSzsBa5OVexVF72vSpInpkKyVFK0OafjRNfYmT57s8XF1mZqHHnrILGujr0c7I+vr0RDmNGLECFMt0nlwtAO0NuVp8NJJAHVZnOzQ6lW7du1Mx2U9btmyZSZoeRIXF2cqShoqNRDq6C7n0g/6upzHaXAEQg2VHSCE6Dw6UztfJzHRaZuq9LZuz6t5dnQUklYldHSSfunqsjDOfinZocvBaAVGm3R0iLnOL+NcLDgrWkXRkKRVEe0bM3XqVNdoLG3aUbr9q6++MpUiHX5er149c55amcmMnr++Jg1w2k9Ih4j37NkzzT4aMHTouVZTtOlN1/DToJWTyo5WanRElr5nGpg09KQf9eU+IksrQHpupUqVMkP93cOi3q/D39M3qwGhgOUicjDdNOBv3prKX4eXr975p+mMrH10tOnK2xWdQKVDwXVY+t69eyVU6KpAGnh69ep1yaoSy0XAxu9vmrGAEKTBJr7ylRIKtBKiI7KuvPJK04SjnZ2zmkPHNtpkOHv2bLOwMnPrIFQRdgBY7bfffjPDt//8808zukqb03SSw1BRunRpM6P09OnTTX8nIBQRdgBY7eWXXzaXUKVNWECoo4MyAACwGmEHAABYjbADAACsRtgBAABWI+wAAACrEXaAUHXigMiycX9dA4DFCDtAqNKQ89XzQRF2dIkIXScqWB43M8OHD5e6dev67PmAgHDC/39YMc8OgICna1vlz59fgt0zzzwjffv2dd3WxUSPHz8u8+bN8+t5AT75w6pqO5GiMeIPhB0AAa9EiRJigyJFipgLAN+iGcvy0h0QCHTlcV35u2DBgmaNqtatW8upU6dc1Q1dwXzEiBFmtW5d0E9X7z5//nymzU1xcXEyduxYefjhh6Vo0aJmGQhdDiEr+nxdunQxYaNs2bLy4osvZtjn3LlzpvpSvnx5KVy4sFkhfPny5a77ddXy4sWLy6JFi8xK5PpYuhr5/v37Xfvo/o0aNTLH675NmzY1q6Knb8bSn9955x355JNPJCwszFz02BtvvDHD2l26vlVkZKQsXbr0Mt59AISdvBREfSKAvKJBoFOnTiaY/PLLL+YL/a677kqzjIF+iTvve//9902zlYafrGhYadCggfz0009mNe+ePXvK1q1bM93/2Wefla+++sqEi8WLF5vnWrt2bZp9NGSsXLnSLJz5888/yz333GPCjK6v5XT69Gl54YUX5N1335Wvv/5a9uzZYwKSunjxogluLVq0MMfrY/Xo0cMEmfT0mHvvvdcVlvRy/fXXyyOPPCKzZs0ywcvpvffeMwFMgxCAnKMZC7Cdhm1PgXv/+rTX6Wnbuhfa1/VLXEOABpyKFSuabVrlcadVi7feeksKFSokNWrUkJEjR5pwMmrUKAkP9/w32a233mpCjhowYIBZ/2rZsmVStWrVDPuePHlS3nzzTRMabrrpJrNNqyoVKlRw7aOhZebMmea6XLlyrkCSmJhotmslSV24cEGmTZsmlStXdgUkPV+VnJwsSUlJ8s9//tN1v1aAPNGqkFa6NNTExPz9Puv7pI+poUzDkLOipBUwT6EJwKURdgDb/TjzrwpjZj7t53l7i4EirXK/OnidOnVMwNCA07ZtW2nTpo3cfffdaVbg1n006DjFx8ebgLJ3715XQEqvdu3arp81BGhgOHTokMd9t2/fbprFtFnKvR+QezDasGGDpKSkyDXXXJPmWA0j2vTmpOfpDDJKm8Scz6uPqaFEX+fNN99smus0sOg+2RUVFSUPPvigCX96rFafNm7cKPPnz8/2YwCh+IdVVgg7gO0adPtrFER6+h+PBp0Or4qUrZPxfi/95xMRESFLliyRFStWmOaj//znPzJ48GBZtWqVVKpU6bIfN/3oLA08qampl/14Gq70XNesWWOu3bl3Kvb0vO5NcloF6tevn6kIzZkzR4YMGWJef5MmTbJ9LtqUpX17fv/9d/N42nyVWegDAsaP/v3DKiuEHcB2l/qrSYNOubyd+0UDgXbU1cuwYcPMF/fcuXOlf//+5v7169fLmTNnTLOO+v77703AiI2N9crzayVGQ4oGLO3MrI4dOya//vqr6V+j6tWrZyo7WqVp1qxZrp5PH0svgwYNMlUq7YPjKexo850+Z3paBdP+SDNmzDDHTp48OVfnA4TCH1ZZIexYXroD/E0DhnZA1uar0qVLm9s6usi9L4s2MXXv3t1UQXbt2iUJCQmm30pm/XVySoOTPr72A9ImKT0PrS65P742Xz3wwANmxJZ2ftawouep565NZu3bt7/k8+zcudOMCrvttttMvx/tMK2dm/UxPdFRZTqyS/fT84qOjnZVjrS6o++Bjuq68847vfI+ALb/YZUZwo7lpTvA33QouY5amjRpkunAq1UdDRPt2v39F6D26bn66qulefPmpo+Mjt7SodneNHHiRNNU1aFDBzNc/emnnzadid1pk9Ho0aPNffv27ZOSJUuaiox2OM4O7c+zZcsW0/n56NGjpq9O79695bHHHvO4/6OPPmpGhWkVR89NO1jrMHul74EOt9dr7ccD4PKFOdwbm0OQ/uerf03pf3r6n7LXKzuXKt1R2UEOnD171lQPtK9Lrr8A/1gnMr2FSI+v/PbXlmIWYc+0wqXNbz/88INcd911wfk7BuTh/zU5+f6msmN56Q5AcNGh7VoV0iY9rSr5MugAtmJSQSBUaUDXplSqiwHlu+++M81fWtHR+XwA5B6VHSBUacgJgD5jOmEe/qZ9dkK8dwFsU9T/f1gRdgAAgNV/WNGMBQAArEbYsbx0BzvRzAF+t4DsoxnL8tId7OJcxkAn4XPONgx4k67q7mlZDCCYEXaAIJIvXz4zcZ3O7KtfRt6aYRjQaqEGHV0uo3jx4hnWBwOCGWEHCCK6xpQOS9ZJ33bv3u3v04GFNOjoCvKATQg7QJDRxSN1aQVtygK8SauFVHRgI8IOEIS0+Yqp/AEge2jwBwAAViPsAAAAqxF2AACA1UK+z45zcjZdKh4AAAQH5/d2diZZDfmwc+LECfNGxMbG5vkHAwAAvP89Hh0dneU+YY4Qn3c+NTVV/vjjDylatKiZw8TbqVND1N69e6VYsWJefWyELn6vwO8VgklyHn0XanzRoFOuXLlLTrAa8pUdfYMqVKggeUk/XMIO+L1CMOD/KwTT79alKjpOdFAGAABWI+wAAACrEXbyUIECBSQhIcFcA/xeIZDx/xVs/t0K+Q7KAADAblR2AACA1Qg7AADAaoQdAABgNcIOAACwGmEnj0yZMkXi4uIkKipKGjduLKtXr86rp0KI+Prrr6VDhw5mtlCd7XvevHn+PiVYYNy4cdKwYUMzi3zp0qXljjvukK1bt/r7tBDkpk6dKrVr13ZNJBgfHy+ff/65386HsJMH5syZI/379zdD7dauXSt16tSRtm3byqFDh/Li6RAiTp06ZX6XNEgD3vLVV19J79695fvvv5clS5bIhQsXpE2bNub3DbhcujLB888/L2vWrJEff/xRbrzxRrn99ttl06ZN4g8MPc8DWsnRv5QmT57sWn9L1wXp27evDBw4MC+eEiFGKztz5841f4UD3nT48GFT4dEQ1Lx5c95ceE2JEiVk4sSJ0r17d/E1Kjtedv78eZNkW7du/febHB5ubq9cudLbTwcAXpWUlOT6YgK8ISUlRWbPnm2qhdqc5Q8hvxCotx05csR8sGXKlEmzXW9v2bLF688HAN6iVegnn3xSmjZtKjVr1uSNRa5s2LDBhJuzZ89KkSJFTDW6evXq4g+EHQCAoX13Nm7cKN9++y3vCHKtatWqsm7dOlMt/PDDD6Vr166medQfgYew42UlS5aUiIgIOXjwYJrtejsmJsbbTwcAXtGnTx/57LPPzKg/7VwK5FZkZKRUqVLF/Fy/fn354Ycf5JVXXpHXX39dfI0+O3nw4eqHunTp0jSlYb3tr7ZKAMiMw+EwQUebGL788kupVKkSbxbyhH4Xnjt3TvyByk4e0GHnWq5r0KCBNGrUSCZNmmQ6ZnXr1i0vng4h4uTJk7Jt2zbX7Z07d5oSsXYkveqqq/x6bgjupqtZs2bJJ598YubaOXDggNkeHR0tBQsW9PfpIUgNGjRI2rVrZ/5vOnHihPkdW758uSxatMgv58PQ8zyiw851iJ3+x1G3bl159dVXzZB04HLpfxStWrXKsF2D9dtvv80bi8uexsCTmTNnykMPPcS7isuiw8u1RWP//v0mOOsEgwMGDJCbb75Z/IGwAwAArEafHQAAYDXCDgAAsBphBwAAWI2wAwAArEbYAQAAViPsAAAAqxF2AACA1Qg7AKwRFxfHRHgAMiDsAAgKGzZskLvvvlsqVqwoUVFRUr58eTMb63/+859Mj9m8ebMMHz5cdu3a5dNzBRBYmEEZQMBbsWKFWSpD19nR5TFiYmJk79698v3338v27dtda4bpIoPh4eGSP39+c/vDDz+Ue+65R5YtWyYtW7b086sA4C8sBAog4I0ZM8asr/PDDz9I8eLF09x36NAh188FChTww9kBCHQ0YwEIeFq9qVGjRoago0qXLu2xz44ujqpVHaVVIV3wUi+6oKrT559/Ls2aNZPChQubFb/bt28vmzZt8slrAuA7hB0AAU/76axZs0Y2btyY7WOaN28u/fr1Mz8/99xz8u6775pLtWrVzDb9WcNNkSJFZPz48TJ06FDTx+eGG26gjw9gGfrsAAh4S5YskXbt2pmfGzVqZKoxN910k6nYOPvnOCs72jdHqzpZ9dk5efKkxMbGmvumT5/u2n7w4EGpWrWq3HvvvWm2AwhuVHYABDwddbVy5Uq57bbbZP369TJhwgRp27atGZE1f/78ywpPx48fl06dOsmRI0dcl4iICGncuLEJRwDsQQdlAEGhYcOG8vHHH8v58+dN4Jk7d668/PLLZjj6unXrpHr16tl+rN9++81c33jjjR7vL1asmNfOG4D/EXYABJXIyEgTfPRyzTXXSLdu3eSDDz6QhISEbD9Gamqqq9+ODmNPL18+/msEbMK/aABBq0GDBuZ6//79Hu/X0VeeVK5c2TWSq3Xr1nl4hgACAX12AAQ87UPjcDgybF+4cKG51k7FnuiQcqX9c9xpfx9tqho7dqxcuHAhw3GHDx/20pkDCARUdgAEvL59+8rp06flzjvvlGuvvdb029FZlefMmWNGYGlTlid169Y1nY51aHlSUpKZdFD76WhFZ+rUqfLggw/KddddJ/fdd5+UKlVK9uzZIwsWLJCmTZvK5MmTff46AeQNhp4DCHiJiYmmX44GnN9//92EHV06QoejDxkyxDWxYPqh5+qNN96QcePGye7duyUlJSXNMHSdYPD55583y07oUhM6ukuHtffp00fq16/vt9cLwLsIOwAAwGr02QEAAFYj7AAAAKsRdgAAgNUIOwAAwGqEHQAAYDXCDgAAsBphBwAAWI2wAwAArEbYAQAAViPsAAAAqxF2AACA1Qg7AADAaoQdAAAgNvt/xuUt51R289EAAAAASUVORK5CYII=", + "text/plain": [ + "
" + ] + } + } + ], + "id": "49" + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The attractive potential is centered around `mean` = $1.5$, therefore the initial charge and spin densities form a peak around that site." + ], + "id": "50" + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Time-Evolution\n", + "\n", + "The propagation stage approximates the time-evolution operator $U = \\exp(-i H t)$, where\n", + "\n", + "$$ H =-J \\sum_{j, \\sigma} \\left ( c_{j,\\sigma}^\\dagger c_{j+1,\\sigma} + c_{j,\\sigma}^\\dagger c_{j+1,\\sigma}\\right) + U \\sum_{j} n_{j \\uparrow} n_{j\\downarrow} \\tag{4}$$\n", + "\n", + "is the 1D version of Eq. (1).\n", + "\n", + "The propagation of the initial state with respect to Eq. (4), simulates an effective quench of the system at initial time, abruptly changing the Hamiltonian $H_0\\rightarrow H$. As a consequence, the initial state is a highly excited state of $H$.\n", + "\n", + "In order to minimize the circuit depth of the quantum circuit it is beneficial to decompose the Hamiltonian into four sets of terms, where all the operators in a set commute with one another. The terms correspond to an even and odd edge hopping terms and even and odd site interaction terms:\n", + "$$H = H_{\\text{hop-even}} +H_{\\text{hop-odd}} +H_{\\text{int-even}}+ H_{\\text{int-odd}} ~~.$$\n", + "The odd hopping Hamiltonian term includes the hopping terms between $1\\leftrightarrow\n", + "2$ and $3\\leftrightarrow\n", + "4$ neighbouring sites ($j$ is odd in Eq. (3)), while the odd hopping term includes the odd edge pairs ($2\\leftrightarrow\n", + "3$, $4\\leftrightarrow\n", + "1$, even $j$).\n", + "\n", + "The evolution operator $U$ is approximated by a first-order Trotter expansion, where each Trotter step consists of five stages.\n", + "$$U = e^{-i H t} \\approx \\left(e^{-i H \\tau}\\right)^{t/\\tau}~~, $$ with $$e^{-i H \\tau} \\approx e^{-i H_{\\text{hop-even}}\\tau} e^{-i H_{\\text{int-even}}\\tau} e^{-i H_{\\text{int-odd}}\\tau} e^{-i H_{\\text{hop-odd}}\\tau}. $$\n", + "Each component in the Trotter step can be achieved by simultaneous application (circuit depth of one) of simple two-qubit gates.\n", + "\n", + "An additional algorithmic trick simplifying the circuit and reducing the circuit depth even further. Between the even and odd interaction terms a fermionic mode swap operation is conducted, effectively performing a cyclic shifting of the fermionic modes. Crucially, this operation swaps the logical ordering of the qubits, while preserving the fermionic parity sign (using an iSWAP gates). Alternatively, the operation modifies the mapping between physical qubits and logical fermionic. As a result, the Hamiltonian terms are interpreted relative to the new ordering, effectively swapping the odd and even edge.\n", + "The incorporation of the swap mode operation, allows parallelism, locality (only nearest neighbor gates, bypassing the need for long Jordan Wigner strings).\n", + "After the application of $\\exp(-i H_{\\text{hop-even}}\\tau)$ an inverse fermionic mode swap is needed to swap the even and odd edges back, allowing application of the consecutive Trotter step. Since the even edge hopping term commutes with the inverse fermionic mod swap, these operations are merged to a single stage.\n", + "\n", + "Overall, the time-evolution involves iteration (each iteration corresponds to a single Trotter step) of a five-step procedure:\n", + "1. Hopping operation on odd edges.\n", + "2. Interaction on odd sites\n", + "3. Fermionic mode swap\n", + "4. Interaction on even sites\n", + "5. Hopping operation on even sites + inverse fermionic mode swap\n" + ], + "id": "51" + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Setting the Hamiltonian parameters" + ], + "id": "52" + }, + { + "cell_type": "code", + "metadata": {}, + "source": [ + "U = 3 * J # J is set to unity in the beginning of the notebook" + ], + "execution_count": 24, + "outputs": [], + "id": "53" + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We begin by defining utility functions" + ], + "id": "54" + }, + { + "cell_type": "code", + "metadata": {}, + "source": [ + "## Elementary gates\n", + "\n", + "\n", + "# K(theta) = exp(-i*(theta/2)*(XX + YY))\n", + "@qfunc\n", + "def K(theta: float, qba: QArray[QBit, 2]):\n", + " suzuki_trotter(\n", + " pauli_operator=0.5 * (Pauli.X(0) * Pauli.X(1) + Pauli.Y(0) * Pauli.Y(1)),\n", + " evolution_coefficient=theta,\n", + " order=1,\n", + " repetitions=1,\n", + " qbv=qba,\n", + " )\n", + "\n", + "\n", + "# P(phi) = CPHASE(phi) = diag(1, 1, 1, e^{-i*phi})\n", + "# Implements exp(-i*phi * n_up * n_down) up to global phase\n", + "@qfunc\n", + "def P(phi: float, target: QArray[QBit, 2]) -> None:\n", + " phase(phi * target[0] * target[1])" + ], + "execution_count": 25, + "outputs": [], + "id": "55" + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "To propagate the system state we transform the fermion Hamilotonian to a qubit representation utilizing the Jordan-Wigner transformation.\n", + "\n", + "A single hopping term transforms as\n", + "$$c_{\\mu}^{\\dagger} c_{\\nu} + c_{\\mu}^{\\dagger} c_{\\nu} \\xrightarrow{\\text{JW}} \\frac{1}{2} \\left( X_{\\mu}X_{\\nu} + Y_{\\mu}Y_{\\nu} \\right)~~,$$\n", + "while an interaction term gives $$n_{\\mu}n_{\\nu} \\xrightarrow{\\text{JW}} = \\frac{1}{4}\\left(I -Z_\\mu -Z_\\nu + Z_\\mu Z_\\nu \\right)~~. $$\n", + "\n", + "As a consequence, the five stages can be performed by implementation of the basic unitaries $K(\\theta)= \\exp\\left(-i \\frac{\\theta}{2}\\left(XX + YY \\right)\\right)$ and $P(\\phi) = \\exp\\left(-i \\frac{\\phi}{2}\\left(I-Z_{\\mu}-Z_{\\nu}+Z_{\\mu}Z_{\\nu} \\right)\\right)$. The functions `K` and `P` above implement the corresponding unitary transformations.\n", + "\n", + "The first stage, including odd hopping terms, is obtained by simultaneous application of $K(\\theta = -\\tau J)$ on different paris of qubits. Similarly, the second and fourth stages, involving the odd and even interactions are achieved with simultaneous application of $P(\\phi = \\tau U/2)$ on the corresponding pairs of qubits. The third stage, constituting the fermionic mode swap, is implemented by simultaneous iSWAP gates which is equivalent to $K(\\theta = -\\pi/2)$. The last stage includes a merge of even-edge hopping operation, and an inverse fermionic mode swap operation. Naturally, since these operation commute, the transformation is obtained by $K(\\theta = -\\tau J + \\pi/2)$ two-qubit gates.\n", + "\n", + "We implement the simultaneous operations on the qubit array utilizing Classiq's built-in `repeat` function within the `hop` and `interact` functions." + ], + "id": "56" + }, + { + "cell_type": "code", + "metadata": {}, + "source": [ + "def hop(pairs: list[tuple[int, int]], theta: float, qba: QArray[QBit, M]) -> None:\n", + " for spin in (0, 1):\n", + " for pair in pairs:\n", + " site1, site2 = pair\n", + " K(\n", + " theta,\n", + " [\n", + " qba[qubit_idx(site=site1, spin=spin)],\n", + " qba[qubit_idx(site=site2, spin=spin)],\n", + " ],\n", + " )\n", + "\n", + "\n", + "def interact(sites: list[int], phi: float, qba: QArray[QBit, M]) -> None:\n", + " for site in sites:\n", + " P(\n", + " phi,\n", + " [qba[qubit_idx(site=site, spin=0)], qba[qubit_idx(site=site, spin=1)]],\n", + " )" + ], + "execution_count": 26, + "outputs": [], + "id": "57" + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Defining the odd and even pairs and sites, to account for the finite chane we evaluate which sites are really swapped. " + ], + "id": "58" + }, + { + "cell_type": "code", + "metadata": {}, + "source": [ + "ODD_PAIRS = [(i, i + 1) for i in range(0, L - 1, 2)]\n", + "EVEN_PAIRS = [(i, i + 1) for i in range(1, L - 1, 2)]\n", + "ODD_SITES = list(range(0, L, 2))\n", + "EVEN_SITES = list(range(1, L, 2))\n", + "\n", + "# After iSWAP on EVEN_PAIRS, compute where even sites end up\n", + "_perm = list(range(L))\n", + "for i, j in EVEN_PAIRS:\n", + " _perm[i], _perm[j] = _perm[j], _perm[i]\n", + "_inv_perm = [0] * L\n", + "for pos, site in enumerate(_perm):\n", + " _inv_perm[site] = pos\n", + "SWAPPED_EVEN_SITES = sorted([_inv_perm[s] for s in EVEN_SITES])" + ], + "execution_count": 27, + "outputs": [], + "id": "59" + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Gathering all the stages together to form the Trotter step" + ], + "id": "60" + }, + { + "cell_type": "code", + "metadata": {}, + "source": [ + "def trotter_step(tau: float, J: float, U: float, qba: QArray[QBit, M]) -> None:\n", + "\n", + " # stage 1 - hopping on odd-edge pairs\n", + " hop(pairs=ODD_PAIRS, theta=-tau * J, qba=qba)\n", + "\n", + " # stage 2 - interaction on odd sites\n", + " interact(sites=ODD_SITES, phi=tau * U, qba=qba)\n", + "\n", + " # stage 3 - fermionic mode swap\n", + " hop(pairs=EVEN_PAIRS, theta=-np.pi / 2, qba=qba)\n", + " # stage 4 - interaction on even sites (at their swapped positions)\n", + " interact(sites=SWAPPED_EVEN_SITES, phi=tau * U, qba=qba)\n", + "\n", + " # stage 5 - hopping on even-edge pairs and inverse fermionic mode swap\n", + " hop(pairs=EVEN_PAIRS, theta=-tau * J + np.pi / 2, qba=qba)" + ], + "execution_count": 28, + "outputs": [], + "id": "61" + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Propagation and Execution (\"Measurement\")" + ], + "id": "62" + }, + { + "cell_type": "code", + "metadata": {}, + "source": [ + "@qfunc\n", + "def main(qba: Output[QArray[QBit, M]], num_iter: CInt) -> None:\n", + " allocate(M, qba)\n", + " prepare_slater_det(h, Nelec, qba)\n", + " power(num_iter, lambda: trotter_step(tau, J, U, qba))\n", + "\n", + "\n", + "qprog = synthesize(main)\n", + "show(qprog)" + ], + "execution_count": 29, + "outputs": [ + { + "output_type": "stream", + "text": [ + "Quantum program link: https://platform.classiq.io/circuit/3BhmprAOCkSPptCBxO3TT71oX0i\n" + ] + } + ], + "id": "63" + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The physics of the model are analyzed by measuring the charge and spin densities and the spin spreads $\\kappa^{\\pm}(t)$, defined above.\n", + "The number operators map to local Pauli operators $n_{\\mu} = c^\\dagger_{\\mu}c_{\\mu} = (1-Z_\\mu)/2$, where $\\mu=(j,\\sigma)$ encodes a site, spin pair.\n" + ], + "id": "64" + }, + { + "cell_type": "code", + "metadata": {}, + "source": [ + "def spread(density: list, L: int) -> float:\n", + " s = 0\n", + " for site in range(L):\n", + " s += np.abs(site - (L - 1) / 2) * density[site]\n", + " return s" + ], + "execution_count": 30, + "outputs": [], + "id": "65" + }, + { + "cell_type": "code", + "metadata": {}, + "source": [ + "charge_density_mat = np.zeros((L, NUM_ITERS))\n", + "spin_density_mat = np.zeros((L, NUM_ITERS))\n", + "\n", + "\n", + "with ExecutionSession(qprog) as es:\n", + " iter_params = [{\"num_iter\": iter} for iter in range(NUM_ITERS)]\n", + "\n", + " for site in range(L):\n", + " charge_results = es.batch_estimate(charge_density(site, M), iter_params)\n", + " spin_results = es.batch_estimate(spin_density(site, M), iter_params)\n", + "\n", + " charge_density_mat[site, :] = [np.real(r.value) for r in charge_results]\n", + " spin_density_mat[site, :] = [np.real(r.value) for r in spin_results]" + ], + "execution_count": 31, + "outputs": [], + "id": "66" + }, + { + "cell_type": "code", + "metadata": {}, + "source": [ + "sites = np.arange(0, N)\n", + "time_indices = [0, 4, 9]\n", + "time_labels = [f\"$t = {tau * i:.1f}/J$\" for i in time_indices]\n", + "\n", + "fig, axes = plt.subplots(1, 3, figsize=(14, 4), sharey=True)\n", + "for ax, t_idx, t_label in zip(axes, time_indices, time_labels):\n", + " ax.plot(sites, charge_density_mat[:, t_idx], \"o-\", label=r\"Charge $\\rho^+$\")\n", + " ax.plot(sites, spin_density_mat[:, t_idx], \"s--\", label=r\"Spin $\\rho^-$\")\n", + " ax.set_title(t_label, fontsize=14)\n", + " ax.set_xlabel(\"Site\", fontsize=12)\n", + " ax.set_xticks(sites)\n", + " ax.legend(fontsize=9)\n", + "\n", + "axes[0].set_ylabel(\"Density\", fontsize=12)\n", + "plt.suptitle(\"Charge and Spin Density Dynamics\", fontsize=16)\n", + "plt.tight_layout()\n", + "plt.show()" + ], + "execution_count": 32, + "outputs": [ + { + "output_type": "display_data", + "data": { + "image/png": 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" + ] + } + } + ], + "id": "67" + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Analysis - Spin-Charge Separation\n", + "\n", + "\n", + "In order to quantify the spin-charge seperation, we evaluate the spin and charge spread:\n", + "$$\\kappa^{\\pm}(t) = \\sum_{j=1}^N |j - j_c| \\rho^{\\pm}_j(t)~~, $$\n", + "where $j_c = (N+1)/2$.\n", + "Different values between the spin and charge spreads, signifies spin-charge seperation." + ], + "id": "68" + }, + { + "cell_type": "code", + "metadata": {}, + "source": [ + "def spread(density: list, N: int) -> float:\n", + " s = 0\n", + " for site in range(N):\n", + " s += np.abs(site - (N + 1) / 2) * density[site]\n", + " return s\n", + "\n", + "\n", + "times = np.array([tau * i for i in range(NUM_ITERS)])\n", + "\n", + "\n", + "charge_spread_vec = np.array(\n", + " [spread(charge_density_mat[:, i], L) for i in range(NUM_ITERS)]\n", + ")\n", + "spin_spread_vec = np.array(\n", + " [spread(spin_density_mat[:, i], L) for i in range(NUM_ITERS)]\n", + ")\n", + "\n", + "plt.figure(figsize=(7, 5))\n", + "plt.plot(times * J, charge_spread_vec, \"o-\", label=r\"Charge spread $\\kappa^+$\")\n", + "plt.plot(times * J, spin_spread_vec, \"s--\", label=r\"Spin spread $\\kappa^-$\")\n", + "plt.xlabel(r\"$t \\cdot J$\", fontsize=14)\n", + "plt.ylabel(r\"Spread $\\kappa$\", fontsize=14)\n", + "plt.title(\"Charge and Spin Spread vs. Time\", fontsize=16)\n", + "plt.legend(fontsize=12)\n", + "plt.tight_layout()\n", + "plt.show()" + ], + "execution_count": 33, + "outputs": [ + { + "output_type": "display_data", + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + } + } + ], + "id": "69" + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The lack of agreement between the spin and charge spreads indicates spin-charge seperation.\n", + "\n", + "\n", + "\n" + ], + "id": "70" + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Comparison with Analytical Results" + ], + "id": "71" + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In order to validate the results, we compare the model prediction with the analytical solutions.\n", + "\n", + "There are two natural physical limits, where the model can be solved exactly and efficiently utilizing classical methods:\n", + "1. The non-interacting limit the on-site interaction vanishes $U = 0$ (alternatively $U\\ll J$).\n", + "2. Vanishing hopping limit, $J=0$ (alternatively $U\\gg J$).\n", + "\n", + "### Non-interacting Particles\n", + "In the non-interacting limit of $U=0$, the FH Hamiltonian is a quadratic Hamiltonian. As a consequence, even in the case of site-dependent hopping or hopping between non-adjacent sites, the state dynamics can be solved classically in polynomial time in the number of fermionic modes $M$, utilizing standard matrix exponentiation methods.\n", + "In the case of the FH model on an open chain of $L$ sites, the non-interacting Hamiltonian becomes $$H^{\\text{n.i}} =\\sum_{\\mu, \\nu} c_{\\mu}^\\dagger M_{\\mu\\nu}c_{\\nu} = -J \\sum_{j=1}^{L-1} \\sum_{\\sigma} \\left ( c_{j,\\sigma}^\\dagger c_{j+1,\\sigma} + c_{j+1,\\sigma}^\\dagger c_{j,\\sigma}\\right) ~~,$$ where n.i denotes \"non-interacting\". The commutativity of the spin-up and spin-down terms allows them to be treated independently. For an open chain (no periodic boundary), the eigenstates are standing waves rather than plane waves. The single-particle eigenstates are $$\\phi_{n}(j) = \\sqrt{\\frac{2}{L+1}}\\sin\\!\\left(\\frac{\\pi n j}{L+1}\\right)~~, \\quad n=1,2,\\dots,L~~,$$ with corresponding energies $$\\omega_n = -2J\\cos\\!\\left(\\frac{\\pi n}{L+1}\\right)~~.$$ Each eigenstate is doubly degenerate (spin-up and spin-down). The ground state of an $N_{\\text{elec}}$-electron system is obtained by filling the lowest-energy single-particle states one by one." + ], + "id": "72" + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The time-dependent expectation values of the charge and spin densities, $\\langle\\rho^{\\pm}_j(t)\\rangle$, can readily obtained by employing the Heisenberg representation of quantum mechanics. In this representation, an operator's, $O(t)$, dynamics is generated by the Heisenberg equation\n", + "$$\\frac{dO(t)}{dt} = i \\left[ H^{\\text{n.i}}, O(t) \\right] ~~,$$\n", + "where $O(t) = U(t)^\\dagger O U(t)$, where $U(t) = \\exp(-i H^{\\text{n.i}} t)$.\n", + "Substituting the diagonal form of $H^{\\text{n.i}}$ and utilizing the fermionic anti-commutation relations $$\\{c^\\dagger_{\\mu}, c_\\nu\\} = \\delta_{\\mu,\\nu}~~, ~~\\{c_{\\mu}, c_\\nu\\} = \\{c_{\\mu}^\\dagger, c_\\nu^\\dagger\\} = 0~~,$$\n", + "(the Fourier fermionic operators satisfy similar commutation relations) we obtain $\\dot{c}_\\mu^\\dagger = i M_{\\nu \\mu} c_{\n", + "\\nu}^\\dagger$, therefore $\\dot{\\mathbf{c}}^\\dagger = i M^T \\mathbf{c}^\\dagger$, leading to $$\\mathbf{c}^\\dagger(t) = e^{i M^T t}\\mathbf{c}^\\dagger(0)$$\n", + "\n", + "\n", + "The dynamics can be evaluated by introducing the matrices ${\\cal U}(t) = e^{i M^T t}~~,$ and ${\\cal N}$ with elements ${\\cal N_{\n", + "\\mu \\nu}} = \\langle c_{\\mu}^\\dagger c_\\nu\\rangle$, this allows writting the dynamics of a second order correlation as\n", + "$$\\langle c_{\\mu}^\\dagger c_{\\nu} \\rangle = \\left[ {\\cal{U}} (t){\\cal{N}} {\\cal{U}}^\\dagger (t)\\right]_{\\mu \\nu}~~.$$\n", + "In the one-excitation subspace, the ground state reads $|\\psi_{\\text{g.s}} \\rangle = \\sum_{\\mu} V_{0,\\mu}c_{\\mu}^\\dagger|\\text{vacc}\\rangle$, where $\\{V_{0\\mu}\\}$ are the elements of the eigenstate of $M$, i.e. $M V_0 = \\epsilon_0 V_0$, where $\\epsilon_0$ is the ground state energy." + ], + "id": "73" + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### Numerical Evaluation on a small model." + ], + "id": "74" + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Defining parameters" + ], + "id": "75" + }, + { + "cell_type": "code", + "metadata": {}, + "source": [ + "L = 4 # number of lattice sites\n", + "M = 2 * L # total number of fermionic modes\n", + "NUM_ITERS = 10\n", + "J = 1 # hopping strength\n", + "tau = 0.1 / J # smaller Trotter step for better agreement with analytical U=0 result\n", + "T = NUM_ITERS * tau\n", + "U = 0\n", + "Nelec = 1 # single electron subspace" + ], + "execution_count": 34, + "outputs": [], + "id": "76" + }, + { + "cell_type": "code", + "metadata": {}, + "source": [ + "import matplotlib.pyplot as plt\n", + "\n", + "## Check eigenvalues vs analytical dispersion (open chain)\n", + "# For open BC, E_n = -2J cos(pi*n/(N+1)), n = 1..N\n", + "M0 = construct_single_electron_hamiltonian(L, J=J, parameters=(0.0, 0, 1))\n", + "E, V = np.linalg.eigh(M0)\n", + "\n", + "n_vals = np.arange(1, N + 1)\n", + "E_analytical = -2 * J * np.cos(np.pi * n_vals / (N + 1))\n", + "E_analytical_full = np.sort(np.tile(E_analytical, 2)) # doubly degenerate (spin)\n", + "assert np.allclose(\n", + " E, E_analytical_full\n", + "), f\"Mismatch: numerical {E} vs analytical {E_analytical_full}\"\n", + "\n", + "## Single-electron dynamics: electron starts at site 0, spin-up\n", + "psi_0 = np.zeros(2 * L)\n", + "psi_0[qubit_idx(0, 0)] = 1.0\n", + "\n", + "t_max = 4.0 / J\n", + "t_vec = np.linspace(0, t_max, 400)\n", + "\n", + "# Numerical time evolution via eigendecomposition\n", + "coeffs = V.conj().T @ psi_0\n", + "phases = np.exp(-1j * np.outer(t_vec, E))\n", + "psi_t = (phases * coeffs) @ V.conj().T\n", + "\n", + "spin_up_idx = np.array([qubit_idx(site, 0) for site in range(N)])\n", + "occ_numerical = np.abs(psi_t[:, spin_up_idx]) ** 2\n", + "\n", + "# Analytical: standing waves on the open chain\n", + "# phi_n(j) = sqrt(2/(L+1)) * sin(pi*n*j/(L+1)), j = 1..L (1-indexed)\n", + "# = sum_n phi_n(j) * phi_n(1) * e^{-i E_n t}\n", + "sites_1indexed = np.arange(1, N + 1)\n", + "phi = np.sqrt(2 / (N + 1)) * np.sin(\n", + " np.pi * np.outer(n_vals, sites_1indexed) / (N + 1)\n", + ") # (N, N): phi[n, j]\n", + "phi_at_start = phi[:, 0] # phi_n(j=1), the starting site\n", + "phases_analytical = np.exp(-1j * np.outer(t_vec, E_analytical))\n", + "psi_analytical = (phases_analytical * phi_at_start) @ phi\n", + "occ_analytical = np.abs(psi_analytical) ** 2\n", + "\n", + "# Plot\n", + "fig, axes = plt.subplots(2, 2, figsize=(8, 5), sharey=True)\n", + "for site in range(L):\n", + " ax = axes[site // 2, site % 2]\n", + " ax.plot(t_vec, occ_numerical[:, site], label=\"Numerical\")\n", + " ax.plot(t_vec, occ_analytical[:, site], \"--\", label=\"Analytical\")\n", + " ax.set_title(f\"Site {site}\")\n", + " ax.set_xlabel(\"$t$\")\n", + " if site % 2 == 0:\n", + " ax.set_ylabel(\"Occupation\")\n", + " ax.legend(fontsize=7)\n", + "plt.suptitle(\n", + " r\"Single electron dynamics (open chain): $|\\psi(0)\\rangle = |j{=}0,\\uparrow\\rangle$\"\n", + ")\n", + "plt.tight_layout()\n", + "plt.show()" + ], + "execution_count": 35, + "outputs": [ + { + "output_type": "display_data", + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + } + } + ], + "id": "77" + }, + { + "cell_type": "code", + "metadata": {}, + "source": [ + "NUM_ITERS = 10 # more steps for better resolution of Trotter dynamics\n", + "tau_trotter = 0.1 / J # time step for Trotter evolution\n", + "n_steps_list = list(range(0, NUM_ITERS + 1, 1))\n", + "t_trotter = np.array(n_steps_list) * tau_trotter\n", + "t_max = t_trotter[-1]\n", + "t_vec = np.linspace(0, t_max, 400)\n", + "\n", + "# Numerical time evolution via eigendecomposition\n", + "coeffs = V.conj().T @ psi_0\n", + "phases = np.exp(-1j * np.outer(t_vec, E))\n", + "psi_t = (phases * coeffs) @ V.conj().T\n", + "\n", + "spin_up_idx = np.array([qubit_idx(site, 0) for site in range(N)])\n", + "occ_numerical = np.abs(psi_t[:, spin_up_idx]) ** 2\n", + "\n", + "\n", + "## Trotter dynamics via Classiq\n", + "# Initial state: single electron at site 0, spin-up\n", + "h_loc = np.zeros((2 * N, 2 * N))\n", + "h_loc[qubit_idx(0, 0), qubit_idx(0, 0)] = -1.0\n", + "\n", + "\n", + "@qfunc\n", + "def main(qba: Output[QArray[QBit, M]], num_iter: CInt) -> None:\n", + " allocate(M, qba)\n", + " prepare_slater_det(h_loc, Nelec, qba)\n", + " power(num_iter, lambda: trotter_step(tau_trotter, J, 0, qba))\n", + "\n", + "\n", + "qprog = synthesize(main)\n", + "\n", + "occ_trotter = np.zeros((len(n_steps_list), N))\n", + "\n", + "\n", + "def spin_up_occ(site: int, M: int) -> SparsePauliOp:\n", + " s = SparsePauliOp([], M)\n", + " idx = qubit_idx(site=site, spin=0)\n", + " s += (Pauli.I(idx) - Pauli.Z(idx)) * 0.5\n", + " return s\n", + "\n", + "\n", + "with ExecutionSession(qprog) as es:\n", + " step_params = [{\"num_iter\": n_step} for n_step in n_steps_list]\n", + "\n", + " for site in range(L):\n", + " results = es.batch_estimate(spin_up_occ(site, M), step_params)\n", + " occ_trotter[:, site] = [np.real(r.value) for r in results]\n", + "\n", + "## Plot: exact vs Trotter\n", + "fig, axes = plt.subplots(2, 2, figsize=(8, 5), sharey=True)\n", + "for site in range(L):\n", + " ax = axes[site // 2, site % 2]\n", + " ax.plot(t_vec, occ_numerical[:, site], label=\"Exact\")\n", + " ax.plot(\n", + " t_trotter,\n", + " occ_trotter[:, site],\n", + " \"o--\",\n", + " ms=3,\n", + " label=f\"Trotter ($\\\\tau={tau_trotter:.2f}$)\",\n", + " )\n", + " ax.set_title(f\"Site {site}\")\n", + " ax.set_xlabel(\"$t$\")\n", + " if site % 2 == 0:\n", + " ax.set_ylabel(\"Occupation\")\n", + " ax.legend(fontsize=7)\n", + "plt.suptitle(\n", + " r\"Exact vs Trotter ($U=0$, open chain): $|\\psi(0)\\rangle = |j{=}0,\\uparrow\\rangle$\"\n", + ")\n", + "plt.tight_layout()\n", + "plt.show()" + ], + "execution_count": 37, + "outputs": [ + { + "output_type": "display_data", + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + } + } + ], + "id": "78" + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "**Why the quantum and analytical results don't match exactly:** The quantum circuit uses a first-order Trotter decomposition of the time evolution. Even for $U=0$, the odd- and even-edge hopping terms do not commute, so each step approximates $\\exp(-i H \\tau)$ and Trotter error accumulates (roughly $\\propto \\tau^2$ per step). For a closer match, use a smaller Trotter step, while keeping the total propagation time." + ], + "id": "79" + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Vanishing hopping limit\n", + "The other extreme is obtained when the onsite interactions is much larger than the hopping constant. In this regime interaction dominate the physics and supress hopping between adjacent sites, allowing us to take $J=0$.\n", + "The FH Hamiltonian then becomes a sum of local commuting terms, diagonal in the Fock basis (eigenstates of the number operators $\\{n_{\\mu}\\}$).\n", + "The Hamiltonian reduces to $$ H^{\\text{n.h}} = U \\sum_{j} n_{j \\uparrow} n_{j\\downarrow}~~,$$ where n.h denotes \"no hopping\".\n", + "As a consequence the local number operators are a constant of motion $\\langle n_{j} (t)\\rangle = \\langle n_{j} (0)\\rangle$, and we expect the charges to freeze in time.\n", + "\n", + "Since all terms in $H^{\\text{n.h}}$ commute with one another, i.e., $[n_{i\\uparrow}n_{i\\downarrow},\\, n_{j\\uparrow}n_{j\\downarrow}] = 0$ for all $i,j$, the first-order Trotter decomposition is **exact**:\n", + "$$e^{-i H^{\\text{n.h}} \\tau} = \\prod_j e^{-i U \\tau\\, n_{j\\uparrow}n_{j\\downarrow}}~~.$$\n", + "This means the Trotter circuit reproduces the exact time evolution with no approximation error, regardless of the step size $\\tau$.\n", + "\n", + "To verify this, we prepare an initial state that is **not** an eigenstate of $H^{\\text{n.h}}$ - specifically, the ground state of the non-interacting Hamiltonian with an attractive potential (a Slater determinant with non-uniform charge distribution). We then compare the Trotter dynamics with the exact analytical prediction: frozen charge and spin densities." + ], + "id": "80" + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### Numerical Evaluation" + ], + "id": "81" + }, + { + "cell_type": "code", + "metadata": {}, + "source": [ + "# Parameters\n", + "N = 4 # number of lattice sites\n", + "L = N * a # length of the lattice\n", + "M = 2 * N # total number of fermionic modes\n", + "J = 0 # vanishing hopping\n", + "U = 2.0 # on-site interaction strength\n", + "Nelec_vh = N # half-filling\n", + "NUM_ITERS_vh = 10\n", + "tau_vh = 0.3 # deliberately large Trotter step — still exact since terms commute\n", + "T = NUM_ITERS_vh * tau_vh\n", + "\n", + "# Initial state: ground state of the non-interacting Hamiltonian with attractive potential\n", + "# This is NOT an eigenstate of H^{n.h.}, making the test non-trivial\n", + "lam = 10.0\n", + "mean = (L - 1) / 2\n", + "std = L / 6\n", + "h_vh = construct_single_electron_hamiltonian(N, J=1, parameters=(lam, mean, std))\n", + "\n", + "\n", + "@qfunc\n", + "def main(qba: Output[QArray[QBit, M]], num_iter: CInt) -> None:\n", + " allocate(M, qba)\n", + " prepare_slater_det(h_vh, Nelec_vh, qba)\n", + " power(num_iter, lambda: trotter_step(tau=tau_vh, J=J, U=U, qba=qba))\n", + "\n", + "\n", + "qprog_vh = synthesize(main)" + ], + "execution_count": 38, + "outputs": [], + "id": "82" + }, + { + "cell_type": "code", + "metadata": {}, + "source": [ + "# Measure initial charge and spin densities (at num_iter=0),\n", + "# then measure at each Trotter step\n", + "n_steps_vh = list(range(0, NUM_ITERS_vh + 1))\n", + "t_trotter_vh = np.array(n_steps_vh) * tau_vh\n", + "\n", + "charge_density_vh = np.zeros((N, len(n_steps_vh)))\n", + "spin_density_vh = np.zeros((N, len(n_steps_vh)))\n", + "\n", + "with ExecutionSession(qprog_vh) as es:\n", + " step_params = [{\"num_iter\": n_step} for n_step in n_steps_vh]\n", + "\n", + " for site in range(N):\n", + " charge_results = es.batch_estimate(charge_density(site, M), step_params)\n", + " spin_results = es.batch_estimate(spin_density(site, M), step_params)\n", + "\n", + " charge_density_vh[site, :] = [np.real(r.value) for r in charge_results]\n", + " spin_density_vh[site, :] = [np.real(r.value) for r in spin_results]" + ], + "execution_count": 39, + "outputs": [], + "id": "83" + }, + { + "cell_type": "code", + "metadata": {}, + "source": [ + "# Exact analytical result: charge and spin densities are constants of motion\n", + "# for J=0, so the exact values at all times equal the initial (t=0) values.\n", + "initial_charge_vh = charge_density_vh[:, 0]\n", + "initial_spin_vh = spin_density_vh[:, 0]\n", + "\n", + "# Verify Trotter matches exact solution.\n", + "# Note: es.estimate() uses finite-shot sampling, so we allow for statistical noise.\n", + "charge_error = np.max(np.abs(charge_density_vh - initial_charge_vh[:, None]))\n", + "spin_error = np.max(np.abs(spin_density_vh - initial_spin_vh[:, None]))\n", + "print(f\"Max charge density deviation from exact: {charge_error:.2e}\")\n", + "print(f\"Max spin density deviation from exact: {spin_error:.2e}\")\n", + "assert charge_error < 0.2, f\"Charge density deviation too large: {charge_error}\"\n", + "assert spin_error < 0.2, f\"Spin density deviation too large: {spin_error}\"" + ], + "execution_count": null, + "outputs": [ + { + "output_type": "stream", + "text": [ + "Max charge density deviation from exact: 4.25e-02\n", + "Max spin density deviation from exact: 3.32e-02\n" + ] + } + ], + "id": "84" + }, + { + "cell_type": "code", + "metadata": {}, + "source": [ + "fig, axes = plt.subplots(1, 2, figsize=(12, 4))\n", + "sites = np.arange(N)\n", + "\n", + "# Charge density: final Trotter step vs exact (initial = frozen)\n", + "ax = axes[0]\n", + "ax.plot(\n", + " sites,\n", + " charge_density_vh[:, -1],\n", + " \"o\",\n", + " label=f\"Trotter ($t = {t_trotter_vh[-1]:.1f}$)\",\n", + ")\n", + "ax.plot(sites, initial_charge_vh, \"x\", ms=10, label=\"Exact (frozen)\")\n", + "ax.set_title(\"Charge Density ($J=0$)\", fontsize=14)\n", + "ax.set_xlabel(\"Site\", fontsize=12)\n", + "ax.set_ylabel(\"$\\\\rho^+_j$\", fontsize=12)\n", + "ax.set_xticks(sites)\n", + "ax.legend()\n", + "\n", + "# Spin density: final Trotter step vs exact (initial = frozen)\n", + "ax = axes[1]\n", + "ax.plot(\n", + " sites, spin_density_vh[:, -1], \"o\", label=f\"Trotter ($t = {t_trotter_vh[-1]:.1f}$)\"\n", + ")\n", + "ax.plot(sites, initial_spin_vh, \"x\", ms=10, label=\"Exact (frozen)\")\n", + "ax.set_title(\"Spin Density ($J=0$)\", fontsize=14)\n", + "ax.set_xlabel(\"Site\", fontsize=12)\n", + "ax.set_ylabel(\"$\\\\rho^-_j$\", fontsize=12)\n", + "ax.set_xticks(sites)\n", + "ax.legend()\n", + "\n", + "plt.suptitle(\n", + " \"Vanishing hopping limit: Trotter vs Exact at final time\\n\"\n", + " \"Trotter is exact since all terms commute\",\n", + " fontsize=12,\n", + ")\n", + "plt.tight_layout()\n", + "plt.show()" + ], + "execution_count": 41, + "outputs": [ + { + "output_type": "display_data", + "data": { + "image/png": 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" + ] + } + } + ], + "id": "85" + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## References\n", + "\n", + "[1] [Arute, F., Arya, K., Babbush, R., Bacon, D., Bardin, J. C., Barends, R., ... & Zanker, S. (2020). Observation of separated dynamics of charge and spin in the Fermi-Hubbard model. arXiv:2010.07965](https://arxiv.org/abs/2010.07965).\n", + "\n", + "[2] [Lieb, E. H., & Wu, F. Y. (2003). The one-dimensional Hubbard model: a reminiscence. Physica A: statistical mechanics and its applications, 321(1-2), 1-27. arXiv:0207529](https://arxiv.org/abs/cond-mat/0207529)\n", + "\n", + "\n", + " [3] [Jiang, Z., Sung, K. J., Kechedzhi, K., Smelyanskiy, V. N., & Boixo, S. (2018). Quantum algorithms to simulate many-body physics of correlated fermions. Physical Review Applied, 9(4), 044036](https://arxiv.org/abs/1711.05395)." + ], + "id": "86" } - ], - "source": [ - "# Exact analytical result: charge and spin densities are constants of motion\n", - "# for J=0, so the exact values at all times equal the initial (t=0) values.\n", - "initial_charge_vh = charge_density_vh[:, 0]\n", - "initial_spin_vh = spin_density_vh[:, 0]\n", - "\n", - "# Verify Trotter matches exact solution.\n", - "# Note: es.estimate() uses finite-shot sampling, so we allow for statistical noise.\n", - "charge_error = np.max(np.abs(charge_density_vh - initial_charge_vh[:, None]))\n", - "spin_error = np.max(np.abs(spin_density_vh - initial_spin_vh[:, None]))\n", - "print(f\"Max charge density deviation from exact: {charge_error:.2e}\")\n", - "print(f\"Max spin density deviation from exact: {spin_error:.2e}\")\n", - "assert charge_error < 0.2, f\"Charge density deviation too large: {charge_error}\"\n", - "assert spin_error < 0.2, f\"Spin density deviation too large: {spin_error}\"" - ] - }, - { - "cell_type": "code", - "execution_count": 41, - "id": "85", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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- "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" + ], + "metadata": { + "kernelspec": { + "display_name": ".venv (3.11.7)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.11.7" } - ], - "source": [ - "fig, axes = plt.subplots(1, 2, figsize=(12, 4))\n", - "sites = np.arange(N)\n", - "\n", - "# Charge density: final Trotter step vs exact (initial = frozen)\n", - "ax = axes[0]\n", - "ax.plot(\n", - " sites,\n", - " charge_density_vh[:, -1],\n", - " \"o\",\n", - " label=f\"Trotter ($t = {t_trotter_vh[-1]:.1f}$)\",\n", - ")\n", - "ax.plot(sites, initial_charge_vh, \"x\", ms=10, label=\"Exact (frozen)\")\n", - "ax.set_title(\"Charge Density ($J=0$)\", fontsize=14)\n", - "ax.set_xlabel(\"Site\", fontsize=12)\n", - "ax.set_ylabel(\"$\\\\rho^+_j$\", fontsize=12)\n", - "ax.set_xticks(sites)\n", - "ax.legend()\n", - "\n", - "# Spin density: final Trotter step vs exact (initial = frozen)\n", - "ax = axes[1]\n", - "ax.plot(\n", - " sites, spin_density_vh[:, -1], \"o\", label=f\"Trotter ($t = {t_trotter_vh[-1]:.1f}$)\"\n", - ")\n", - "ax.plot(sites, initial_spin_vh, \"x\", ms=10, label=\"Exact (frozen)\")\n", - "ax.set_title(\"Spin Density ($J=0$)\", fontsize=14)\n", - "ax.set_xlabel(\"Site\", fontsize=12)\n", - "ax.set_ylabel(\"$\\\\rho^-_j$\", fontsize=12)\n", - "ax.set_xticks(sites)\n", - "ax.legend()\n", - "\n", - "plt.suptitle(\n", - " \"Vanishing hopping limit: Trotter vs Exact at final time\\n\"\n", - " \"Trotter is exact since all terms commute\",\n", - " fontsize=12,\n", - ")\n", - "plt.tight_layout()\n", - "plt.show()" - ] - }, - { - "cell_type": "markdown", - "id": "86", - "metadata": {}, - "source": [ - "## References\n", - "\n", - "[1] [Arute, F., Arya, K., Babbush, R., Bacon, D., Bardin, J. C., Barends, R., ... & Zanker, S. (2020). Observation of separated dynamics of charge and spin in the Fermi-Hubbard model. arXiv:2010.07965](https://arxiv.org/abs/2010.07965).\n", - "\n", - "[2] [Lieb, E. H., & Wu, F. Y. (2003). The one-dimensional Hubbard model: a reminiscence. Physica A: statistical mechanics and its applications, 321(1-2), 1-27. arXiv:0207529](https://arxiv.org/abs/cond-mat/0207529)\n", - "\n", - "\n", - " [3] [Jiang, Z., Sung, K. J., Kechedzhi, K., Smelyanskiy, V. N., & Boixo, S. (2018). Quantum algorithms to simulate many-body physics of correlated fermions. Physical Review Applied, 9(4), 044036](https://arxiv.org/abs/1711.05395)." - ] - } - ], - "metadata": { - "kernelspec": { - "display_name": ".venv (3.11.7)", - "language": "python", - "name": "python3" }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.11.7" - } - }, - "nbformat": 4, - "nbformat_minor": 9 -} + "nbformat": 4, + "nbformat_minor": 9 +} \ No newline at end of file diff --git a/community/basic_examples/logical_qubits/logical_qubits_by_alice_and_bob.ipynb b/community/basic_examples/logical_qubits/logical_qubits_by_alice_and_bob.ipynb index d84c95b8b..958fbe1ee 100644 --- a/community/basic_examples/logical_qubits/logical_qubits_by_alice_and_bob.ipynb +++ b/community/basic_examples/logical_qubits/logical_qubits_by_alice_and_bob.ipynb @@ -1,1203 +1,1184 @@ { - "cells": [ - { - "cell_type": "markdown", - "id": "0", - "metadata": {}, - "source": [ - "# Working with Classiq and logical qubits" - ] - }, - { - "cell_type": "markdown", - "id": "1", - "metadata": {}, - "source": [ - "As explained by Professor John Preskill (https://www.youtube.com/watch?v=uwBv6piN-9s), the quantum computing community increasingly recognizes it needs fault-tolerant quantum computers, implementing quantum error correction. This will give birth to a new type of qubit: logical qubits.\n", - "\n", - "Logical qubits are error-corrected qubits, made out of several physical qubits working together to fix each other's errors. As an algorithm designer, it should matter little to you how these logical qubits are built (although you can learn more about it at https://journals.aps.org/prx/abstract/10.1103/PhysRevX.9.041053 for example). You will however care about how they behave and you will need to adapt your algorithms accordingly. This notebook offers you a glimpse at what this experience will look like.\n", - "\n", - "Two main things in particular will require your attention:\n", - "* Transpilation, because logical qubits use a specific, discrete gate set\n", - "* Error rates, because logical qubits aren't error-free\n", - "\n", - "The first part of this notebook will show you how to study the impact of transpilation to logical qubits in terms of circuit depth and accuracy, and how to find optimal transpilation parameters.\n", - "\n", - "The second part of this notebook will show you how to study the impact of noise on the quality of your algorithm's results, and how it depends on the logical qubit's parameters.\n", - "\n", - "In this notebook, we'll be using Alice & Bob's logical qubit emulator. While some parameters are specific to Alice & Bob's cat qubits, most of the principles we'll use also apply to other architectures." - ] - }, - { - "cell_type": "markdown", - "id": "2", - "metadata": {}, - "source": [ - "### Helpers" - ] - }, - { - "cell_type": "code", - "execution_count": 1, - "id": "3", - "metadata": { - "colab": { - "base_uri": "https://localhost:8080/", - "height": 400 + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Working with Classiq and logical qubits" + ], + "id": "0" }, - "outputId": "67b5b3f3-59be-44c7-9860-2d443000365f" - }, - "outputs": [], - "source": [ - "import time\n", - "\n", - "import matplotlib.pyplot as plt\n", - "import numpy as np\n", - "from matplotlib.colors import LinearSegmentedColormap\n", - "\n", - "from classiq import *\n", - "from classiq.execution import *\n", - "from classiq.interface.backend.quantum_backend_providers import (\n", - " AliceBobBackendNames,\n", - " ProviderVendor,\n", - ")\n", - "from classiq.synthesis import set_preferences" - ] - }, - { - "cell_type": "markdown", - "id": "4", - "metadata": {}, - "source": [ - "## First Part: Targeting the Logical Qubits' Gate Set" - ] - }, - { - "cell_type": "markdown", - "id": "5", - "metadata": {}, - "source": [ - "The native gates for a logical architecture are discrete, i.e. they do not take parameters like a rotation angle. Most architectures rely on the \"Clifford + T\" gate set, i.e. gates generating the [Clifford group](https://en.wikipedia.org/wiki/Clifford_group) and the [T gate](https://en.wikipedia.org/wiki/Quantum_logic_gate#Phase_shift_gates).\n", - "\n", - "This gate set is said to be \"universal\", meaning that any gate can be approximated with arbitrary precision using a series of these gates, with the number of gates growing as the logarithm of the desired precision.\n", - "\n", - "This means that if the algorithm you want to run contains rotations for example, these rotations will have to be approximated by a series of discrete gates.\n", - "\n", - "Let us see a first example, using a simple 1-qubit rotation:" - ] - }, - { - "cell_type": "code", - "execution_count": 2, - "id": "6", - "metadata": {}, - "outputs": [ { - "name": "stdout", - "output_type": "stream", - "text": [ - "Circuit depth: 1\n", - "\n", - "Opening: https://platform.classiq.io/circuit/2v4opr6xzmMgEnHrNKNAwAoZaJF?login=True&version=0.73.0\n" - ] - } - ], - "source": [ - "@qfunc\n", - "def main(q: Output[QBit]):\n", - " allocate(1, q)\n", - " RX(0.1, q)\n", - "\n", - "\n", - "qmod = create_model(main)\n", - "qmod = set_execution_preferences(\n", - " qmod, execution_preferences=ExecutionPreferences(num_shots=10_000)\n", - ")\n", - "qprog = synthesize(qmod)\n", - "\n", - "circuit_metrics = get_transpiled_circuit_metrics(qprog)\n", - "print(\"Circuit depth: %i\\n\" % circuit_metrics.circuit_metrics.depth)\n", - "\n", - "show(qprog)" - ] - }, - { - "cell_type": "markdown", - "id": "7", - "metadata": {}, - "source": [ - "As you can see, because we didn't put constraints on the backend's gate set, the transpiled program only contains one gate.\n", - "\n", - "But now, let's try to target an Alice & Bob backend and see what happens." - ] - }, - { - "cell_type": "code", - "execution_count": 3, - "id": "8", - "metadata": {}, - "outputs": [ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "As explained by Professor John Preskill (https://www.youtube.com/watch?v=uwBv6piN-9s), the quantum computing community increasingly recognizes it needs fault-tolerant quantum computers, implementing quantum error correction. This will give birth to a new type of qubit: logical qubits.\n", + "\n", + "Logical qubits are error-corrected qubits, made out of several physical qubits working together to fix each other's errors. As an algorithm designer, it should matter little to you how these logical qubits are built (although you can learn more about it at https://journals.aps.org/prx/abstract/10.1103/PhysRevX.9.041053 for example). You will however care about how they behave and you will need to adapt your algorithms accordingly. This notebook offers you a glimpse at what this experience will look like.\n", + "\n", + "Two main things in particular will require your attention:\n", + "* Transpilation, because logical qubits use a specific, discrete gate set\n", + "* Error rates, because logical qubits aren't error-free\n", + "\n", + "The first part of this notebook will show you how to study the impact of transpilation to logical qubits in terms of circuit depth and accuracy, and how to find optimal transpilation parameters.\n", + "\n", + "The second part of this notebook will show you how to study the impact of noise on the quality of your algorithm's results, and how it depends on the logical qubit's parameters.\n", + "\n", + "In this notebook, we'll be using Alice & Bob's logical qubit emulator. While some parameters are specific to Alice & Bob's cat qubits, most of the principles we'll use also apply to other architectures." + ], + "id": "1" + }, { - "name": "stdout", - "output_type": "stream", - "text": [ - "Circuit depth: 170\n", - "\n", - "Opening: https://platform.classiq.io/circuit/2v4oqLh7s7fQYOzMCVDjmZxdwmF?login=True&version=0.73.0\n" - ] - } - ], - "source": [ - "backend_preferences = AliceBobBackendPreferences(\n", - " backend_service_provider=ProviderVendor.ALICE_AND_BOB,\n", - " backend_name=AliceBobBackendNames.LOGICAL_TARGET,\n", - ")\n", - "execution_preferences = ExecutionPreferences(\n", - " num_shots=10_000, backend_preferences=backend_preferences\n", - ")\n", - "\n", - "# Prepare for HW aware synthesis\n", - "preferences = Preferences(\n", - " backend_service_provider=ProviderVendor.ALICE_AND_BOB,\n", - " backend_name=AliceBobBackendNames.LOGICAL_TARGET,\n", - ")\n", - "\n", - "# Create Model, set settings and perform HW aware synthesis\n", - "model = create_model(main)\n", - "model = set_execution_preferences(model, execution_preferences)\n", - "model = set_preferences(model, preferences=preferences)\n", - "qprog = synthesize(model)\n", - "\n", - "circuit_metrics = get_transpiled_circuit_metrics(qprog)\n", - "print(\"Circuit depth: %i\\n\" % circuit_metrics.circuit_metrics.depth)\n", - "\n", - "show(qprog)" - ] - }, - { - "cell_type": "markdown", - "id": "9", - "metadata": {}, - "source": [ - "Because the RX gate had to be transpiled, the circuit now has depth 170 instead of 1.\n", - "\n", - "After running the `show()` command, you can check the depth of the circuit and even its detailed gate count in the Classiq GUI:\n", - "\n", - "![image.png](data:image/png;base64,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)\n", - "\n", - "By default, the Classiq platform displays the circuit before transpilation to the logical gate set. But it is easy to display the transpiled circuit.\n", - "\n", - "First, save it as \"Transpiled QASM\":\n", - "\n", - "![image.png](data:image/png;base64,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)\n", - "\n", - "Then, upload it:\n", - "\n", - "![image.png](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAXUAAABvCAYAAAATx1CBAAASxElEQVR4Xu2dXWhdxRbHV/xC1JqUFknh9gNjH67WIxzS0nCxkmJfWtO8aHsx0D70QQQxYlPBQlpsoIK2cFMFRRG0ELmtoNzmpgiVBCtqqSUPaa5VQ0ralFpKSz7Ul4L2zuzPmdmzP7N39sne/4B4ss+embV+a5//rFkzOa1raWm5TfgBARAAARAoBIG6ZcuWQdQLEUo4AQIgAAJEEHU8BSAAAiBQIAJ1dvllYmLCcGvVqlUFcg+ugAAIgEB5CFy8eJEg6uWJNzwFARAoOIHx8XGIesFjDPdAAARKRACiXqJgw1UQAIHiE4CoFz/G8BAEQKBEBCDqJQo2XAUBECg+AYh68WMMD0EABEpEAKJeomDDVRAAgeITgKgXP8bwEARAoEQEIOolCjZcBQEQKD4BiHrxYwwPQQAESkQAol6iYMNVEACB4hOAqBc/xvAQBECgRARSFPVm2rlvO61ZZNO7Ql/v6aX/CjCf6Xybmsb3UK9zkbfZTHTyAH1yTqTOr/+Dbh6Q2xM9Q51vN9G41K94TbXB7fO30WN0gA/SvJPMIT8hZ8hnOuntpnHaYxnWvHMfbW8Ydn53euFttzfQsOKXaDn38am/acY1LnFbnyL3bS8j4rYIHTh2Kw+lOs6Vr12uQe+53QQxrtL0MTUmzHrmW3Xa4qj15zca1bQr0ecJroJA7gRSEnVTTFdeEj7whjiRJOyRRd0SNlGoTFKWKF75WhBcndCzW3XizbuIKOqbVxLNDB9QJiA+aWmE2HfiUrkotnI/q9N0zJ5gPMw0XMmauGZEBvJzJHPmY2pEOojxvirV0yXvxMcmG3GS8Yp87s8zDACB0hNIR9R9BFQV8aiibtw3PUr1DTfpgJvWW6LeRNOj9bSSTpqZtzZ7T0HUG2aI6qddYWMiuG/JNM2saVBWCkGCyucQMetXJyD5dy8fjR/qRKB5hMO5m1l3EGO6wtYTzqrKzOrpksjdnFwahsWVV+k/TwAAArkTSEfUlfKF7RUXtM2O+FpCElZ+cSaI/9FjntKMLYLf0hLnvYwydWb3SWa9aX+jVfYZpyZP+SdI1FXhk22VBd+vFOVtIzLVPUGSqOtKRpEYu75es+Lo8rALV3Y5KXj1kvtTDgNAoEQEak7UxYlAnRSkrNwRKx+hnWv5RRBzvjJouMlLMT4TiFJ+iVxT/23ULb0YZRXd/kKAqAv1d7Us4trgrXNHZWyK+SWaYaWob1mJiBkoTdKu27qyWIk+RXAVBGqIQDqi7rOBGF4GUIVMt9EpZoGamnTTNI3WN3g3VVMRdZaRSquQaKIubwaL0Xbbc8HcvvKSIOq6jciI5RejNPStVY4SVkTX+MbuSrokbV7GYSzHxzvJBpeeaug5hykgUBoC6Yi6bvNOs1FqlBtEIVPv0dSLvZt+8ukX86SHZvnvJ+rWZivbwbU2Qb2bkf7ilZ6o8wNAno1Gg0e9cILEf6NU3ZTWiro5iHczVtyctexwJyJ/H4NF3WdDtjQfJTgKArVBICVR586EH2nkd8nH7cTSgM/GmyT8OsHxOZrnK+pW9rt9DbmnL+WTJPMl6g4z8SRLpCON3mxbPdIorhaMyXTNDJvH+F6EZnMzlLH5sMpc1OOZRN7TSrXxkMMKECgTgRRFvUzY4CsIgAAI1CaBVEXdzAh5/os/QqnNcMMqEACBohNIVdRdWHJ5wO+vIosOF/6BAAiAwHwTyEjU59sNjAcCIAACIMAJQNTxHIAACIBAgQhA1AsUTLgCAiAAAhB1PAMgAAIgUCACEPUCBROugAAIgABEHc8ACIAACBSIAES9QMGEKyAAAiAAUcczAAIgAAIFIgBRL1Aw4QoIgAAIQNTxDIAACIBAgQhoRf2vv/6i27dvG27a/y+Qz3AFBEAABApFoK6uzvCH/59rdl1LS4uh4BMTExDyQoUazoAACJSNgFbUGxsby8YB/oIACIBAIQhcvXrVm6lD1AsRWzgBAiBQQgIQ9RIGHS6DAAgUlwBEvbixhWcgAAIlJABRL2HQ4TIIgEBxCUDUixtbeAYCIFBCAhD1EgYdLoMACBSXAES9uLGFZyAAAiUkkEjUt27dSnv37qV77rmnhMjgMgiAAAjMP4Fbt27RwYMH6cSJE4GDJxL1M2fO0LZt2+jy5cvz7xlGBAEQAIESElixYgUdP36c1q9fn76oDw8PU7VaLSFWuAwCIAAC+RGIor2JMvUoHefnNkYGARAAgWISiKK9EPVixh5egQAIFJAARL2AQYVLIAAC5SUAUS9v7OE5CIBAAQlA1AsYVLgEAiBQXgIQ9fLGHp6DAAgUkABEvYBBhUsgAALlJQBRL2/s4TkIgEABCUDUF3BQ+V+P8a9jePjhh2nRokX0888/0+eff04XL15cwF7BdBAAgbkQgKjPhV5Obfn36ezevZueffZZ418GV39OnjxJ+/fvpz///DMnCzEsCIBAXgQg6nmRn8O4H3zwATU3Nwf2MDQ0RF1dXcT/1fB4P210+NQb1DhQpY5/CS3bDtOpNxppoNpB4mVt36/00fCWa7R/027qjzd46N2v9A3Tlmv7adNuv55N+1uXuF1dOKr4EjrKAriBM97xd8nQm0NBXBaATzAxFQIQ9VQwzk8nd911F3V0dFBnZ6c0IP9mNv6jfiPmm2++SZ999llM4xayqFuCfv0oVe0ZyZiMWokyFzwfbjHpR75dnTjnzc/IFuLGnAhA1HMCH2fY++67j1599VXavHkz3XvvvR5Bf+mll4wyzDvvvCMJ++TkJLW3t8cZit27gEXdyF6JjiqribbDp+iN1uue6zHBhNyes6jzyHE/KyOZrJDSZYXesiQAUc+Sbgp933nnnXTs2DFjM1T9+eOPP+jFF1+k0dFR460nnniC3n33Xbr//vudW7/88kvq7++n77//PqI1UUT9FeobXkvXhh6iVrvOcXPIFRNd+UUpF4glEV5SkSoJF4RMm/hYO0gsNPiVGQxRaxxws3TbYyOLrdDI/k20u5/3t4WuGa/NG8SSjjkBCLUbwS/+3ss0QCOVHU55x7SF9CWfcbVkJbP19neTLSiOEL3slo98S0caxo6o8y5eJhq53kqtDJzNS+Z8QZnkAjhzfkp/RxgJP058nLU/HCXaYceNj/UDrXXiyP10+Ud8MHFbRAIQ9Yig8rrtueeeo9dff90z/O+//04vvPACXbhwQXrv0Ucfpffff58eeOAB6fp3331nlG3CN0+jijr7wDriq5Q9fEoD1+3atlUqcH6XLOV9MQU5wj/0Zr+VEbdWHFRT93/PFCymLGyfIFjUVdCmQJk1eVPweSXHEiRpZaDh5tmH8Iq62J89oThCHrQ3EcTYmExaSeSrrlbk30M4B8bLnRhtTubk4U4a5u+ukPtOvnl9yAo2LkS9xgP68ccfU6VSkazkm59vvfUWjY+PG/9NTU0Z7y9evJiamprokUceoT179nhOxrz33nv04YcfhngcVdTlbJelu+7mqCo4GnEKE2dDIDyZrpxV6wRYv4maXNTNbPqIsTHrFSNxgkgo6uLKQivUPpvTmo1SZzLQbGp7eQu2k3cTXLo/wia5yEkdy8Mtw430Gv84z4t5EPV5wZx8kG+++UYqp6g9vfbaa/TVV18Zl59++mlD7P1+fvrpJ3r++efnXdR1mZl0zcoE3aKHldU1eU/RBE0G/hmgKL5hmbq3DGGLZc2Jut8Jo5AVgvkACJMQhXDWiro/J4h68s97Gi0h6mlQzLCPwcFBamho8B0hjqjzGvyTTz4ZSdTFkofRQMquvMIobdLFytSbhNKILTZW+YWLurLxGXik0Wej1LDd6SdI1M3auFrukcovUs0+50w9sqjrVjiC7WGcfSYJP04Q9QwFIULXEPUIkPK85fDhw2wzkhVyfX7iiPr58+dp586doe54T4uoNVdVGMXyhjoBGDOCLNxijdYosdibmDyBVDc17Vq4/V7Q8USrtk/Cpq3nqJ/ii/S+OsHIdgdn6n7CKdhvlUx8M/+45ZcYoi5PbPb+gH0iyPTzIfvYp8rMI+pKPJX4QtRDP2KZ3gBRzxTv3DvnNfJPP/2U7r77bm1n/CsBxJq67pSM3bC7u5sGBgYiGeU5BRLrRIq7NHdOqiglFvFUhzQWO21ydKRCayc3mX/8JNWO2eYbO1SxZfm/A/74yBRX8TSN5wSJ2Cc/3cJPi/xzkjbxAQPGCxN1yQ+Ll+faD2vplGV/aK05qJYdVJf2aSfHVDn9ojAZYidnKvYfeen6C+AEUY/0EcvsJoh6ZmjT63jjxo1GrfyOO+5I3OkXX3xBPT09idvLDb0ljJQ6Rjc1QiD8L3drxFCY4SEAUV8gD8WSJUto27ZtVK1WI1vMT8n8+OOPxL8L5pdffoncLvzG2hZ1XcYc7hPucAmo5RWwWUgEIOoLKVo1Y2tti7qISS0jFfJ7YFJ4LtSSFb5HJgWoOXUBUc8JPIYFARAAgSwIQNSzoIo+QQAEQCAnAhD1nMBjWBAAARDIggBEPQuq6BMEQAAEciIAUc8JPIYFARAAgSwIQNSzoIo+QQAEQCAnAhD1nMBjWBAAARDIggBEPQuq6BMEQAAEciIAUc8JPIYFARAAgSwIZCbqZ86cMf6s/fLly1nYjT5BAARAAAQUAitWrKDjx4/T+vXrA9lcvXqV6lpaWm7zuyYmJoybGxsbAxtt3bqV9u7d6/kX7hEFEAABEACBbAjcunWLDh48SCdOnEhf1LMxGb2CAAiAAAjMlUCiTH2ug6I9CIAACIBANgQg6tlwRa8gAAIgkAsBiHou2DEoCIAACGRDAKKeDVf0CgIgAAK5EICo54Idg4IACIBANgQSivo62tXTQZUHLaNmR6iv+yM6m42NyXtdt4t6Ntyg7kP/kfpo7+qljcutS5OD1Mneb+/qoaWnu+mjmnMiufu6lmXxM11q6A0EFg6BZKLe3kU9S09Tdw4KGEuUtKLeTl09S+m0MgnF6nfhxNdjaVn8XMAhgukgMCcCyUSdi2UbUb8kjKJY8kx+A93oPkS/7uqhtlVEDz7I0/pZGulj2fAyNik011vXiCYHO8lIptlk0Wun0FYGza91LZ2i+kqFZqYmafliM8WeHeljkwoJKwar77PKKsLux2ilvMcvaTL1dczmDmsZYo5zlplhZ/fWOMQYdCymc52HSF4H8GH4exUyFzKuz45v9spGvM+wg9iE00z1jJVBa3KSaPly87VlhxNtkZXdH59sw7ja9uhWJD52e/tkse5aSlP1FarMWHb3biQzMpM0aDHRrYjm9LSiMQiAQCiBZKJu6KMlXE7pJUDUqd/M6u3MeWw19a4eM8oeTMmtzPk8PW5NBKa+99LqMSb2xIS+ecop70iZprhisF/f2OCuIsIydeF9t1/RD/v1Ddqgye71dN0JzfTDW9axr51/vIc23Og2JzTjh43X20xTfOI7y1+vpjEukD5lJKeVPQabLB1WTptfnQnWzx6zHx+7eZ+eWDEejp08rIIffLLh97MYO6u5EPtDn1LcAAIgEJlAclG3h3CydlH45EzdFS5LJM8tpjanfGPfO0arBeF0hIKJuljqEUVSzKjNJHGQ+qaaXaFMIupGBm5n2UanRubJVxxG9i5l/jrOcnnHsVfq115VcOHmGa7wu8NAN7kI+xZ+WbXDVT8h+ZdffOzmq6qQWEl9Wsz7Q+MQ+RnFjSAAAjEIpCvqYmZplSa4GDqi7pfFGaUcnqkbL4zNSjFT9xN1Xprx1PaV7N3NMoVs2BbO0EzdS3Ldri56/PyhgA1VMePlr02fbmxwM3avsPJyBtEho/xi1/uDRV3sw3ktCbBuBeTa490O0dttlMpsUddO4Gam3mavxnQxtq8pG9YxnlPcCgIgEJFAIlGXM2Q7yzSF2CyJTxIvB48xlXIyXDOVNuutYj1YrPH61NRF4XbGNso+fCJwT+GYdedlVvbLh2N21E8pm6KCWAqibvfL6/unl7o1dVbMpr5+ojY7e59lPvTzOrpaU3dLJ7ysYtbkZ2l2ln1RGp+oeBnD2i+YZRdnznXT2Gr3FM4ks/00s90t84Rk6gIruz9eqnJZue3ZzOLYw+NCY/qST5jdzv4ALw1J5Sh7xSHE2CglWXV25u/szDnPKaSIzyhuAwEQiEEgkajH6F+utzrJcn6nZ+LYnsa9C/W0iT77T0gEmXpCcGgGAvEJQNTjM4vVoryiLmbv7mouFjzcDAIgEJtA5qIe2yI0AAEQAAEQSEwAop4YHRqCAAiAQO0RgKjXXkxgEQiAAAgkJgBRT4wODUEABECg9ghA1GsvJrAIBEAABBITgKgnRoeGIAACIFB7BCDqtRcTWAQCIAACiQlA1BOjQ0MQAAEQqD0CEPXaiwksAgEQAIHEBCDqidGhIQiAAAjUHgGIeu3FBBaBAAiAQGICEPXE6NAQBEAABGqPABf1/wOLN4To1l+jawAAAABJRU5ErkJggg==)\n", - "\n", - "And you should see something like this:\n", - "\n", - "![image.png](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAABcYAAACwCAYAAAAlt73DAAAgAElEQVR4Xu3dD7hUVb3/8S8mHCqVP3YD1EAgSilFyCLyFgUpmmhRKBkaXTQeu49minY1la6opXnRTCseU5TUa5pd+l21RIFEn3vV9KKSf1MQSQ+oxT/NMAJ+810ze86aPXvP7D3775z9nufxkXNm/1n7tdfea83nrFm7x6BBg3YKLwQQQAABBBBAAAEEEEAAAQQQQAABBBBAAAEECiLQY9y4cTtXr15tDnfYsGEFOWwOEwEEEEAAAQQQQAABBBBAAAEEEEAAAQQQQKCoAiYYX7VqlTn+4cOHF9WB40YAAQQQQAABBBBAAAEEEEAAAQQQQAABBBAoiADBeEFONIeJAAIIIIAAAggggAACCCCAAAIIIIAAAgggUBYgGKcmIIAAAggggAACCCCAAAIIIIAAAggggAACCBRKgGC8UKebg0UAAQQQQAABBBBAAAEEEEAAAQQQQAABBBAgGKcOIIAAAggggAACCCCAAAIIIIAAAggggAACCBRKgGC8UKebg0UAAQQQQAABBBBAAAEEEEAAAQQQQAABBBAgGKcOIIAAAggggAACCCCAAAIIIIAAAggggAACCBRKgGC8UKebg0UAAQQQQAABBBBAAAEEEEAAAQQQQAABBBAgGKcOIIAAAggggAACCCCAAAIIIIAAAggggAACCBRKgGC8UKebg0UAAQQQQAABBBBAAAEEEEAAAQQQQAABBBAgGKcOIIAAAggggAACCCCAAAIIIIAAAggggAACCBRKgGC8UKebg0UAAQQQQAABBBBAAAEEEEAAAQQQQAABBNpf4CMf+YhMmzZNevToUT2Y73//+7Jhw4ZAB0cwHoiJhRBAAAEEEEAAAQQQQAABBBBAAAEEEEAAAQTyJHDQQQfJcccdJ7vssospVirB+MEz5si0vivkrCvvtCwOlhlzpknfFWfJletnyJxpQ+SlW+fKwkfj5Josp102XFaddaWU96w/jxdZXtqnXZQIu5x82mUyXpa7ji3CBlkVAQQQQAABBBBAAAEEEEAAAQQQQAABBBBAIFaBAw88UL7yla/I9u3bpVevXukE4+VA2g6oNaM+TS4bvirhQNljv1E4Dy4F+J8T+c3chRJrfh+lTKyLAAIIIIAAAggggAACCCCAAAIIIIAAAggg4Cvw4Q9/WKZPny4333yzbN26Vb7+9a/LpZdems5UKjpq/HPyG5lbGRKuI62Hr3JGbtcG2GaE+Yd3rxzIy6UB3qUR365QumZ7GrKP36d64G88eWtlP+5gXEepm2S7NDK9PHq8ay2Rlysjyc0o8Oobb8iTZiR77fLOPtzHVVP2N56UW50QXct/SF/ZvM8+lX0626XGIoAAAggggAACCCCAAAIIIIAAAggggAACCCQhYIfiTz75pNnFqFGjZO3atbJx48ZAu4w2x3hNsO01xYkzotwOr61yNQrG7eI33E+DbU/rKyuqU650bbAm+PYYMV4X0I/ZVA3DNWAfs6kS0uu61nQxNe8F4mchBBBAAAEEEEAAAQQQQAABBBBAAAEEEEAAgaACXqF40HXt5aIF46UtTT5tjuz5P6XR1wNPkzl7/k919HjdVCvVEeDWqOqGwbhr9Hd1pHajEePOoekyY2STPb+53wj0JsG4e/R4zXQxHuWvn3e9ldPCOggggAACCCCAAAIIIIAAAggggAACCCCAQLEFdtttN+nTp4+88sorBsKZU/w///M/ZeXKlZFwIgfjTlC8XMaUA/LqRN0+c4GbUdaVkdwNgvG6kdnVecCbBePWA0CrD+OsDcrDjBgnGI9Uv1gZAQQQQAABBBBAAAEEEEAAAQQQQAABBBBoSaBfv35yxhlnyDXXXGMCcmdOcWf6lJY2WlkpejCuD+GcM0b6bF4hc6+sJtGlzfs9JNP6vR2SSznQHvJSeZoSe75yM8f3kJcq05k0Dsa9pzOx16ndj9SUoawSaioV68Gdppx9VyT88NEop5t1EUAAAQQQQAABBBBAAAEEEEAAAQQQQACB9hDo37+/nHPOOebhmj179pQ4Roo7Rx5DMF4Okg/5y1ypycVrgnHvh1xqIboeilmaYmX5SzJk+F/KAbsJrD8s+rjON55cLi8NGS5/mVt6YGclQNfneJYflimBHr7Z9QBN136s7ZU2aML30gZrHipa8/DNl5d3Bd9MpdIeVxClRAABBBBAAAEEEEAAAQQQQAABBBBAAIG2E3CCcS34jh075Prrr5dnn302luOIJRiPpSRsBAEEEEAAAQQQQAABBBBAAAEEEEAAAQQQQACBioAdjOuvtm3bJvPnz5e1a9dGNiIYj0zIBhBAAAEEEEAAAQQQQAABBBBAAAEEEEAAAQTiFtDpUwYPHlyz2b/97W/S2dkZeVcE45EJ2QACCCCAAAIIIIAAAggggAACCCCAAAIIIIBAOwkQjLfT2aKsCCCAAAIIIIAAAggggAACCCCAAAIIIIAAApEFCMYjE7IBBBBAAAEEEEAAAQQQQAABBBBAAAEEEEAAgXYSIBhvp7NFWRFAAAEEEEAAAQQQQAABBBBAAAEEEEAAAQQiCxCMRyZkAwgggAACCCCAAAIIIIAAAggggAACCCCAAALtJEAw3k5ni7IigAACCCCAAAIIIIAAAggggAACCCCAAAIIRBYgGI9MyAYQQAABBBBAAAEEEEAAAQQQQAABBBBAAAEE2kmAYLydzhZlRQABBBBAAAEEEEAAAQQQQAABBBBAAAEEEIgsQDAemZANIIAAAggggAACCCCAAAIIIIAAAggggAACCLSTAMF4O50tyooAAggggAACCCCAAAIIIIAAAggggAACCCAQWaDHgAEDdpZeZkM9evQQ59/O/yPvgQ0ggAACCCCAAAIIIIAAAggggAACCCCAAAIIIJADAc3ATRY+cODAmmA8B2WjCAgggAACCCCAAAIIIIAAAggggAACCCCAAAIIJCbQY/To0Ts7OzvNDjo6OhLbERtGAAEEEEAAAQQQQAABBBBAAAEEEEAAAQQQQCAPAgTjeTgLlAEBBBBAAAEEEEAAAQQQQAABBBBAAAEEEEAgNQGC8dSo2RECCCCAAAIIIIAAAggggAACCCCAAAIIIIBAHgQIxvNwFigDAggggAACCCCAAAIIIIAAAggggAACCCCAQGoCBOOpUbMjBBBAAAEEEEAAAQQQQAABBLoEdu7cKT169MiUpJUytLJOpgeZ4s5bsWllnRQPiV0hkHuBVq6hVtaJGyIPZYj7mNptewTj7XbGKC8CCCCAAAIIIIAAAggggEC3FdCgJMlXUkF80uVO0iTKtvGMose6CLQm0K7XXVLlbk2RtVSAYJx6gAACCCCAAAIIIIAAAggggEDCAu6RgU6QnHVQ4lUOu6x5LXfCp6vlzePZMh0rItCyQLted83K3TIIKwYWIBgPTMWCCCCAAAIIIIAAAggggAACCEQT8Aud0x5x7QTyjUJw+0jzUu5o+smtjWdytmwZAT+Bdr3uwpabGpCcAMF4crZsGQEEEEAAAQQQQAABBBBAAIE6ATsE14Ck0c9x8jXbV7PR61mVO06DOLeFZ5yabAuBYALtet1FLXcwHZYKK0AwHlaM5RFAAAEEEEAAAQQQQAABBBAIIOA1DYk9UtC9iaSnV2m0fXe5mv1slz3pcgegzmQRPDNhZ6cFF2jX6y5oue0/UPJwzuQrO8F48sbsAQEEEEAAAQQQQAABBBBAoOACXlOluKcnUSJ3KBIHm9c2vb7Kb++rWYDvF5zrNtKeFiYOozDbwDOMFssiEI9Au153UcrtJdfd76/x1JbyVpp9C8osM3r06J2dnZ1mhY6Ojjj3z7YQQAABBBBAAAEEEEAAAQQQKLSAV/itIEHCjSDLBMENFA6UpnRxXvZX/t1f/w9SpiDLBCl3XpfBM69nhnJ1Z4F2ve5aKbfTRiTxh9LuXEf8jq3ROSAYL2KN4JgRQAABBBBAAAEEEEAAAQRSF3AC4969e5uBabvsskvqZfDa4Y4dO+Ttt9+WrVu3mrfdIUJey50LPI9C4JnXM0O5urNAu153zcrthOSHTx0kM8/cV/r279mdT2Osx7ZpwzZZ8B9r5O7b1/mOHg8VjM9ZcIVsuO50ufp/rHIeO0cWjNsg151+tdi/DnMkx85ZIIfL3TJz7m1hVmNZBBBAAAEEEEAAAQQQQAABBHIn4IwSt//vFFJ/17dv39yE4k65NJzZuHFjXbnsY8hjuXN38isFwjOvZ4ZydWeBdr3utNybNm2qCW/tb+voffiXD3+CULyFyqvh+LEff9Cs6TVyPFQwfsgpV8hUuV1Orybjh8gpV0wVud0VlrdQUFZBAAEEEEAAAQQQQAABBBBAoDsIeAXielzOyOv+/fvn7jC1bBs2bGg4J2sey507yEqB8MzrmaFc3Vmgna87vf/6hbcanC954dPd+dQlemyHjlhu2rbIwbjIsTJnwX7y7My5YsZ2H3KKlHPx0mhx/feJY6SPOZTNsqIysvzYOVfIfqXf7LtvH1lz90x5dr/S6PB9K8e7eYUZaV5K163AXcP2E2VMeUOyecV1lSC+tO8rzJaktCnz0u0xyDzRusPGEUAAAQQQQAABBBBAAAEEIgrYc27rv/MYMGu5dMS431yseS13xFOT2Op4JkbLhhHwFWjn6879h0n3iPF7nx/PmW9RwAnGdXV3GxdqxLhuQKc92e/ZciDdNYJcs21r5Lg1vcrepeXHbbDCbTtYrxyQPRJdt1+7/LjK9C0ayh8uUgnDdZ0T+z/I9CstVgpWQwABBBBAAAEEEEAAAQQQSEeAYDwd5zztpZ0DukGDBsm6devyxElZEAgk0M7XHcF4oFPc0kKxBuNmlPjE1+T0ua+UwvCJ8trpOnq8HFrvaxevMhpcg3EnSNe3TaBthoOXJj+vjDz3DdhrgnjXaPUY5jZvSZOVEEAAAQQQQAABBBBAAAEEEAgo4A7FdbU8jxjX8jkj6txTwuSx3AFPQ+qLOQFdO3oSjKdeXdhhTALtfN01mkpFj4sR461XkniDcanMK/7gKhm+nwbkZuh4aRqV/vKgM8WKVVZ7hHnNIVjBdtdUKq6R5wTjrZ911kQAAQQQQAABBBBAAAEEEMhcwAmXdY5Y55XHgNkOlNxhbp7LnfkJ9ilAO3sSjOe1VlGuZgLtfN05wbge4y677FJ9JoX+zBzjzc584/c/+/77qg+WjjyViu7KjPAevlFW3T5Xys/hLM8L3v/B+jm/fYNxa35ye47xxlOpWPObM2I8Wq1gbQQQQAABBBBAAAEEEEAAgcQE3KOt7Z/zHIzb89ra/1aoPJY7sRMYccP2lA7OtwbaxZNgPOLJZ/XMBNr5unOmUnHaCgdRf9b/ePhm69Uq9mDcPITzivfKUn3oplOumodvln655m4z/3dNMO5axnl4pj3HuBOyOw/f7HrAJlOptF4FWBMBBBBAAAEEEEAAAQQQQCBNAYLxNLXzt692DugIxvNXnyhRMIF2vu4IxoOd41aWSiAYb6UYrIMAAggggAACCCCAAAIIIIBAMQTcwbhz1Pr7MCOvn3jiiUBgP/3pT2X+/PmBlvVayP3QOnvUojPiOUy5Wy5IN1mxnT0JxrtJJSzgYbTzded++KbdZjBiPFplJhiP5sfaCCCAAAIIIIAAAggggAACCIQS8ArGWwmYgwbjWrjLL79cFi5cGKqcdviyceNG86Mz5Yf9EE79fRGCcZ3bt2/fvtKrVy8zfcGrr76aK8+BAwfK5MmT5YgjjjBz5t5zzz1y9913y4svvlhXzne84x0yfvx4Oeqoo2TkyJEyadKkQMdCMB6IiYVyKOB++GYSf+DzuyePGjUqkojfwzeZSiUSq1mZYDy6IVtAAAEEEEAAAQQQQAABBBBAILCAXzCuv99zzz0DbydMMK4bbTUc13I5Ixa9gvGw5W50gBro6sPkevbsKdu2bTOL6u90v9u3bw9sk8SCWqbjjjtODjvsMNFR+I8++qi8/fbboXcVp+cee+xhynPkkUfK6NGjjZP7tXr16mpIrqH+5z//efnc5z4n/fr1qy4aNLgLGow7dTPodv0Q49pO6JPECt1OIM7rrll9db8f9Tr4y1/+Yq5t9/VNMB69mhKMRzdkCwgggAACCCCAAAIIIIAAAggEFsgqGNcCthKOpxEoOXj77LOPaIi09957y9atW01IrsH4li1b5LnnnpNnnnkmsHPcC2oI/W//9m8miP7hD38oN998c0u7iNPzgQceEC2XvjSkX758uSmfvnS0+Cc/+Ul597vf7VlODducP8QEDe4Ixls65azUokCcfxiJ87rzO5ykRowTjLdYgQKsRjAeAIlFEEAAAQQQQAABBBBAAAEEEIhLIMtgXI8hbDieRqDk2A4fPlyuvvpq2X333WXXXXc105a89dZb8uabb5p50u+4445MR46fc845ZsT1JZdcIr/5zW/k73//e+hqEaenE8RpYH/fffeZPybYYaIafvzjH5fPfOYzMnXqVFPW2267zYwg/7//+z957LHHzO8IxkOfRlZIQYBgvIxMMJ5cZSMYT86WLSOAAAIIIIAAAggggAACCCBQJ5B1MK4FChOOxxnkNqsOH/zgB82UIPvuu6+ZSuWvf/2rmSZEp/245ppr5KabbjKjyLN46TQGGkB/8YtflO9973smXP7HP/5hwvGOjo7A06rE6ekVHPqFiWGW9fNlxHjCNe+MW+SJI9fL+RNPl/927+roK2TphRPkPc7vn14oo467vGapo69YKhdOqC4hTy8cJa5FGh/A2JPk4uNHSfk7CFvkiZvOlWsftlb5wlly1Yjn5dTLfp0wRHnzBONlh+SD8c1y7WH3ya1/qj2tg076tPx8dp9UznVWOyEYz0qe/SKAAAIIIIAAAggggAACCBRSIMlgfMmSJXLrrbfK73//e2M7duxY+fKXvywTJkyosw46SjjOIDfICd9tt91MIP7Od75T+vTpY0Zoz5o1y4T5Goxn9dJR7N/85jfNAysffPBBM22JvnSqkjVr1sgLL7wQ6IGccXqGCbvDLOtnHDUY/8Y3vmHmZ/d6eb0XZzCaVb0Jut9qqP3nZfXBeCUUf60adJ8htzwxQ0Za4Xh5/ddk4ajjxMTlGrLPGBkiHB8rJ118vPR75FTR3HvsSRfL8UNflJvOvVZMNm5C837yyE33y7qHHy7/LuFXnOc/zuvO77DbdyqVcjC+5tTPy0VHJXxSA2x+1bx75eTn95N7578vwNLRFiEYj+bH2ggggAACCCCAAAIIIIAAAgiEEkgqGJ83b578/Oc/9yzLySefLBo82q+8BuN2Gd/1rneZch9zzDHy4x//WG688cZQ1nEurNO6nHHGGeYBnH/729/M3OfOHOg6//lZZ50l69evb7rLOAO6MGF3mGX9DiJKMK7nUeuhX73T8ul0OXZwHmcw2vTEZLjAGbc8ITNGPi3Llr1XJhy4si4YN6H3wLtqR4ib4FsqQfjRcsXSC2XgXbUjxM12pX5kufehfkHOuuqjstEZJa6jwz+6sRKM63sTRZaWQ/O0XnGe/zivO+f4nTodxsNdx4Osm9aIcYLx2ocX9yh9fWlnZ2enOUf6tSBeCCCAAAIIIIAAAggggAACCCAQTSCJYHzx4sXy7W9/W3S6j69//etmlLi+brnlFvnZz35m/q2B4yc+8Ylq4dshGHemL5k8ebIJ/a+//nozxUpWLx15P2bMGJORbN++3RSjd+/esmrVKrnzzjtl48aNTYsWZ0AXJuwOs6zfQbQajNsBYqNgXPdrB4dxBqNNT0xWC1jTp5TSbbmwLhgvh94HrjxfJp5uT7BSHjVeSsbluBd0mpUDZeX5E6V2ETs8b3aAfiPG/yAHlEaSD33xJjm3Zl6VZtuL/n6c5z/O684+Mv1j2YwZpfMQ4LVw4ULzzZewr2yD8T/JefuvkIffN0Lm3zNShpcKb0Z0XysybdGhctJ+zs9vVQ5rgJz9zMel9GcU81p68v+TS8pfrjGvsT8ojUof8bR8dcoWmVFdrmvE+r/8UbftbKu0wvgxlZHjlXJUthPXNC+MGA9bG1keAQQQQAABBBBAAAEEEEAAgQgCSQTjxx57rOio5TPPPFNOOOGEmtLp3Nw62nrcuHEmdHReWQXjOtJ67733Fh0NrqGy3/QDWk6dVkVDcQ2errrqKvPAy6xfOnJcg3F9IKieS51iRR96qUF5kPnP4wzowoTdYZb1M24lGI8yqjbOYNR9TI3qXaM6FvS6aaWempHhdcG4FYDXZKrW78UnAK8ZVR6gRDpKfOLgyoLlOcb/cEBpSpV+jyQ6r3ga5yLO684tGSQcbzUU132lFYy75xg3IbaZWqUcXN8/qTTn+JGvlELtV+RTNaH47tUw3J4GpRygd71XdXvWPxjX/dVPpVIOxddW5zzXn5+VfStlCFCzfRchGI+ix7oIIIAAAggggAACCCCAAAIIhBRIIhjXB1ZqKKvzXvft27emRH/+859l4sSJZr7u+++/v/pe0IAviUDpsMMOM1OP6JzhixYtki1btvgq6gM59SGXGj6vW7cuUPgc8pSYaVF69uxpgvrNmzebf+vc4W+99ZZ5uGacrzg9w4TdYZb1O16CcfGdCiaOOpJ5MO4+iJrpVOI4Qu9ttHswrkfVKByPEorrttMKxhtOpVIJswePf1XkyK65yHVE+MIR1kM6rdBb3O85pz9sMF63fHkkes1+W6ye8QXjU6+RR+ftJYuGTJaL3YU59055aZbINV7vtVhwVkMAAQQQQAABBBBAAAEEEECgHQWSCMZ1NLiGuMuWLZM999yzhsUJxjUwdx4YqQtkFYy/4x3vkOnTp8tJJ50kS5culYsvvtgE31m+1OZLX/qSDBs2TN5++21TFA3LddqWRx55RO65557Yile0YFzhmEolWPXJVTBuHrY5VF50Ro2P2qN8EFue6HogZ7DDanmpOL8xEOd153dAXuF41FBc95WLYLxUDjMtyuquKVWckeTukeZipl3ZW353mM8DPcMG43c8JId+uxTIu15dI9pbrmISczA+Sf7pD9fIkMmuaLzgwbj+VX7kyJHygQ98wJwp/Xrb008/3fAv4q2fUtZEAAEEEEAAAQQQQAABBBDIs0ASwbhONfL444/LaaedJjNnzqw5/LxNpaKF0znQTz31VLnrrrvkhz/8oQn1s3zpSOjvfe97csABB5hgXMN7nd9cR5Dfdtttctlll8U2cjzOgC7MKPAwy/qdi1ZGjDvb4uGbzWu4dzDeaI7xI2W9zisuDeYYP3J93cM8m5fEetjmOg3I+8kjp14mv5byPORpzTfebsG4utrheByhuG4zF8G4htNX7SHThj0vt4oz73c5LP+dNYLcrlu+o7rDBuO6/DdFvluZ47x5/Q2+RMzB+BiR1/9JZMVsOXjW7V2lKGgwPmDAALngggvkiCOO8Dwjd9xxh8yZM0c2bNgQ/IyxJAIIIIAAAggggAACCCCAQFsLJBGM60jx008/3YS5OhJbR2TraOebb75ZbrjhBuP1gx/8QCZNmlS1y2rEuBZA50Q/55xzTNn+67/+ywQ/OmWJzjveaFqVJE/8P//zP8vAgQPN3OEajB9yyCFmCprf/va3JrzftGlTLLsvajCueBqO60NgvV5e78UZjMZy8hLeiHcwLuL5+5r5w73D8zNueUJmyEIZdVy4Bz5+4ayr5KMbKw/bdE2nou9NlKWJzjnuMMd5/uO87ppVAw3H9dXKgza9tp19MG7P6V2e71sq84/7ziNeOhD/92q3IZUR4dUR4JUQ3nnYp4h7jvFmZyD4+7EH4ysWry81tANl8eyDpZqNewXj5ncHdJW0MtJ86jWPyrxJ62unXfFY33O54Med+JIjRoyQX/ziF7LHHnuYp4Bfe+21snbtWrPfwYMHy6xZs8xfyF9//XWZNm1a9b3EC8YOEEAAAQQQQAABBBBAAAEEMhVIIhh3Qhgdoej3Gjp0qCxYsED69+9vFskyGNfPwaeccooZna2DxnQ+b53Xe82aNWbke6tzDsdxYrUcOo3KZz/7WTn//PPNqPZLLrnE/KEhjlecAV2YUeBhlvU7zigjxluxizMYbWX/aa/jF4yXknFZeuEEkWXny8TT/7tUrPKDN99b/bkSnptFSiPIzSL6QM73dv0c8GDGnlR62ObQF7umSzFTqjBiPCBfIoulFYzXTYkyvjQy/FtvlB62+bxI9cGXpUN0BdnlANz61o+uN/99xsJMv7K8i8UJv2vW0eX1oZ5/3F9+PruPiBlR/rysM6sNqDzYsxyOP1zd1LtkWq4evmnmGB9TGix+sNxzmCvcdgfb5mc7PD9X7ixNQj5wsY40/6D5dykZl/KMLFPlmkfnyaTSQPQ/VH8ncu6dL8mUTtfI9ESqX/iN7rXXXqZh1792H3/88bJq1SrPjegDRPRBI7rcUUcdxcjx8NSsgQACCCCAAAIIIIAAAgi0nUBSwbhCLFmyxHzOfOyxx8xc4/vvv78ZJT5//nx55ZVXzECt66+/Xt7znvdkFoxr6PzFL35RvvrVr0q/fv1kt912M1OpbN++3QTlGpjrFKRZvjQc19HiGowvXrxY5s6dG1txkgjG9eGrH/nIR0Qfaqqj8fV1++23mznnH374YTOHux0y6xQxn/70p+XSSy81ywb9IwnBeGzVwNpQebT3hPe4t/20LBx1nFTHelfCcWexP1uhuLOmCdarG/pz6FBcakLwrvKYsJw5xpM4+YG2mXwwHqgY3XKh+EeMm5HilTB7fWW+cVcw7hVqmxHgey0y85Pr+7Oksm7loZ4rFg+USZX3S7F4KTyfIp32qHSP06NfI/vWt77V8MTp16GuuOKKWE+uzt+mDejRRx8tTz31VHXb3/3ud82/dXoV5zV27FgzX5l+ve073/lOrOVgYwgggAACCCCAAAIIIIAAAvkTSDIY9zva1157zQTR69atk3322ceE44ceemggnDiDXGeHGtB/9GjAsEoAACAASURBVKMflV133VV0+xqW9+rVS9avXy/PPPOM/OlPfwpUtiQXmjp1qpx99tkmGNdpaDZv3hzL7uL0dMJuDc7cD111CvvXv/5VHnjgATn88MPNr/RBouPHj5eOjg7zsx7Xpz71qUDHRjAeiImFYhKI8xsDcV53zuG1+s2WoH+IcvZDMB5ThfLYTELBeGlPJtAuzV2mo8Bf+lpphLgOAp8sF1sjwOvK4zy40wrSn3MC8xuGVEekz/pgacT5lE6ZffAssWYy91RqFI4nEYprI/HQQw+Jfn1N5w+3X17BuL7/ox/9SI488kjzgE7n6dfJnXK2jAACCCCAAAIIIIAAAgggkKVAFsG4Hq9O5akP5tRpPvWbzp2dnYEYkgiUdMcahu/YsaNaBp3XW0eNu38fqJAJLKRzjp944okmVNbBbHF9Xo/T0w7mNm7caKZ9WbRokXHUIFxHkA8bNqxOR8ug3yrQ5TUoDzqvO8F4AhWNTaYiEOd15xSYYDyVU5foTpILxrXYzpQpZt7x2mB8jPsBnTWHWZ5aRa6ZLZ1Tzha5pGsUuq63aK95oaZR8QrHkwjF9RD0L8rz5s0zf3n/4x//GOjkjRs3zsxHfsIJJ8j9998faB0WQgABBBBAAAEEEEAAAQQQaE8Bv2Bcj8aZ/zvIkbUSyujIQx05/vLLLwfZhVlGy6uhq7704Z5O+Z33wpY78I5zsKAGwTrNyxtvvFET4kcpWpyeOpr96aefNtO5Ll++3ATi7pfOLe+E5PqHCH2Y6J133mlG54d9BQ3Gw26X5RFIWiDO6y7psrq3v2HDhur9135Pj0n/W/LCp9MuUrfZX7LBeInJTIsy8HV5/Z/WyyIzYrzyO2eqFB/K6nqyopSLV0aGa9A+pTTXuAyUThOWBz8PdjieVCiupdGnKOtXrYYPH27m8LJffiPG+/TpIytXrhR933laePAjY0kEEEAAAQQQQAABBBBAAIF2EvAKxrX8+vukg3HdT9hw3AmUNBR3ymn/W38XptztdK6SKGs7exKMJ1Ej2GYaAu183Wkw7txzbSuC8eg1J/FgvOvhmX+oTKVSKrQZSX5AzcM06w6lsszr5oGcTgJeHkl+wOuLA02j4t6mhuP6intOcXs/s2bNknPPPdc84ET/qmy/br31VvOjPn3bfunTt/UvvBdddJH87Gc/i35W2QICCCCAAAIIIIAAAggggEBuBdzBuP1zHgNmO1DSf+vLGTnuIOex3HmtAO3sSTCe11pFuZoJtPN15wTj9rd19HgJxpud9ebvpxCMlwpReYCmM2LcFKsSfNtFrA/Bx8mDlVHmznL6kM6z5RIrLG9+kGkuoXOF/+QnPzFzhj/55JM1u/YLxvXp0b/+9a9FQ3X9GhQvBBBAAAEEEEAAAQQQQACB7itAMN59z22QI2vngI5gPMgZZpk8CrTzdUcwnlyNii8YT66MbbXlfv36yeOPPy433XSTGTluv/yC8csvv1ymTJkiBx54oJm3jBcCCCCAAAIIIIAAAggggED3F3ACcvsBlHkceW3PzatnxT2Niv4uj+XOaw1qZ0+C8bzWKsrVTKCdrztnjnE9Rn04sfPNHf1Z2w/mGG929v3fJxhv3c53zauvvlqOOOIIOeqoo8wUKc7La47xj33sY/LLX/7S/HfmmWcmUBo2iQACCCCAAAIIIIAAAgggkEcBO9xw/p3HgNn90Dq1dI96z2O583jOHTv7Yabt5EkwntdaRbmaCbTzfczv4ZsE483OevP3CcabG4VeQhuKu+66S7Zu3SrHH3+8rF692nMbI0eOlBtvvNEsd/TRR5sHoPBCAAEEEEAAAQQQQAABBBAojoA7HM9jwOx+aJ377IR9aGhxzq73kbazJ8F40Wtv+x5/O1937odv2s94YMR4tDpJMB7Nz3ftESNGyC9+8QvZfffdzbQq+lDNdevWmeWHDRtm5hM/5phj5JVXXjHh+dq1axMqCZtFAAEEEEAAAQQQQAABBBDIqwDBeF7PTHLlaueALjkVtoxAsgLtfN01Csb1uO59fnyyeN1464eOWF6dHsyZJsw53B6lh0Lu7OzsND93dHR0Y4ZkDm3AgAFy4YUXyqRJkzx38Ktf/UouuugisecKSqYkbBUBBBBAAAEEEEAAAQQQQCAPAu4pSJwy5X0qFXcw47bM40j3PJxvrzLoucYzr2eHcnVXgXa+7rymUrGfUcEc463XWoLx1u0Cr9m3b1/50Ic+JB/4wAdk+/bt8txzz8lTTz0lb775ZuBtsCACCCCAAAIIIIAAAggggED7C9jBuP11eD0yfU8/P+rD1fL00q/q65zY7nLZx5LHcufJ0C4Lnnk9M5SrOwu063Wn5d60aVN1VLOeI2079PfO/2///SHSt3/P7nz6Ejm2TRu2yTFj/5cR44noslEEEEAAAQQQQAABBBBAAAEEAgo4I8Z79+5tvrGdl3Bcw5e3337bPBvLCWTsQ8pruQOyp74YnqmTs0METIjcjvexIOXWe/CkLw2Uk749jHA8RF3XUPzaH6yWxb9ab4Jx9zQqpr1jKpUQoiyKAAIIIIAAAggggAACCCCAQAgBZ8S1ruKea7zZZuzlmy3b6H2vMMC9vL2MPcrda8R7s7LEVe5m+8nqfTyzkme/RRZo1+uulXI77YVz/9V7qv6nIbrOUtHd77Fx1HO10z8+O/8RjMehyjYQQAABBBBAAAEEEEAAAQQQaEHAK8jwCs3tECWu8MNrm87v7DLYh2W/7z7ctMrdAnMqq+CZCjM7QaBGoF2vuyjldgA0EHfCcaddiKt96I7VzDF3wnAnJPc61lAjxhcsWNAdvWTmzJnd8rg4KAQQQAABBBBAAAEEEEAAgewE3KGz3+hxp4RO0BFkhGErR9Vo++4gvNnP9v6TLncrx5rGOnimocw+EKgVaNfrLmi53UG687OG47xaE2g0bVmoYLy13bMWAggggAACCCCAAAIIIIAAAgi4A3D92T1VifvnONWa7atZIG+PUGy2rTjLnddtNTPAM69njnK1s0C7XndRy+3VfrTzeUyj7M3uwaYNZo7xNE4F+0AAAQQQQAABBBBAAAEEEECgPM+41zQmaX8t3q8MfkFCXsqd1zqEZ17PDOXqzgLtet2FLXd3PodZHxvBeNZngP0jgAACCCCAAAIIIIAAAgh0ewGvaVX0oIOMaEsSx+vr/X4huJajqNOmBD0HeAaVYjkE4hNo1+uuWbnjE2JLfgIE49QNBBBAAAEEEEAAAQQQQAABBHIikPTI8aSC+KTLnZPTU1cMPPN6ZihXdxZo1+suqXJ353Od9LERjCctzPYRQAABBBBAAAEEEEAAAQQQ8BBwjyLPAqmVMrSyThbHlsU+W7FpZZ0sjo19IpBXgVauoVbWifv481CGuI+p3bZHMN5uZ4zyIoAAAggggAACCCCAAAIIIIAAAggggAACCEQSIBiPxMfKCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAu0mQDDebmeM8iKAAAIIIIAAAggggAACCCCAAAIIIIAAAghEEggVjK9duzbSzlgZAQQQQAABBBBAAAEEEEAAAQQQQAABBBBAAIE0BAYPHuy7m9DBeKONpXEw7AMBBBBAAAEEEEAAAQQQQAABBBBAAAEEEEAAgUYCOsibYJw6ggACCCCAAAIIIIAAAggggAACCCCAAAIIIFAYAYLxwpxqDhQBBBBAAAEEEEAAAQQQQAABBBBAAAEEEEBABQjGqQcIIIAAAggggAACCCCAAAIIIIAAAggggAAChRIgGC/U6eZgEUAAAQQQQAABBBBAAAEEEEAAAQQQQAABBFIJxrdt24Y0AggggAACCCCAAAIIIIAAAggggAACCCCAAAKpC/Ts2bNunwTjqZ8GdogAAggggAACCCCAAAIIIIAAAggggAACCCCQlgDBeFrS7AcBBBBAAAEEEEAAAQQQQAABBBBAAAEEEEAgFwIE47k4DRQCAQQQQAABBBBAAAEEEEAAAQQQQAABBBBAIC0BgvG0pNkPAggggAACCCCAAAIIIIAAAggggAACCCCAQC4ECMZzcRooBAIIIIAAAggggAACCCCAAAIIIIAAAggggEBaAgTjaUmzHwQQQAABBBBAAAEEEEAAAQQQQAABBBBAAIFcCBCM5+I0UAgEEEAAAQQQQAABBBBAAAEEEEAAAQQQQACBtAQIxtOSZj8IIIAAAggggAACCCCAAAIIIIAAAggggAACuRAgGM/FaaAQCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAmkJEIynJc1+EEAAAQQQQAABBBBAAAEEEEAAAQQQQAABBHIhQDCei9NAIRBAAAEEEEAAAQQQQAABBBBAAAEEEEAAAQTSEiAYT0s65H4Gj+gpQ0r/BX3tvls/6blrr6CLF3q5DZteLfTxc/AIIIAAAggggAACCCCAAAIIIIAAAggUXeChe7fVEaxdu1YGDx7sS9Nj0KBBO3fs2GEW6OjoaGjot7Ft2+p3XPSTYR//Jz/3LvmX00bKviP2CMzylU88HXjZIi+4fv36Ih8+x45AqgI7hg6XHUOH1e1zlxdXm9/t8uKqVMvDzrIVoD5k68/eEcizAPeHPJ+d9MtGfUjfnD0igAAC7ShAe9GOZy25MrdSHxgxntz5iLRlDcYvuPrjobbRKBifMWOGnHbaaTJmzJhQ2/Rb2L29FStWyJVXXikLFy6sWWXevHnymc98pm4zs2fPlt/97nfm97qu83Jvw+89Z/+63ubNm2v20eg9XZ5gPJYqwEYQ8BX4x4RDzXv/mHBYICUNx3dddi8heSCt9luI+tB+54wSI5CWAPeHtKTbYz/Uh/Y4T5QSAQQQyFqA9iLrM5Cv/UetDwTj+Tqf1dLEHYwnfZh+wbh7vwsWLDC/mjlzpvn/okWLZPXq1aJBuQbaX/va16ohd6P3dH+33XabXHLJJWYbGzdurG6z0Xu6z0bBuF5QQcO8pE2d7e+67B4TGqb5wqGsPfv9A2T2iAFp0jfd17znX5V5L+RzOqA46k2eQ/I4jq/pCQ65QBb3h6BFjMMrz/WB+0O5JsRxnoPWqaDLZXFdUB+Cnp346k2e7w9cF9QHW4D7Q3zXfbia1Xxp2ouyURafL7hP8nmz+RVav0Qc9Yb+Qzj5LO6TQUsYV31498+vq9tl06lURo8evbOzs9OsyFQqQU9ZuOWiBuP2SGsdJW6P8Hb+/dJLL8mQIUOqo8j91nFGd5999tkyadIkE1zb29OR33369DEHaI8Edx+xe5S5bmfOnDmeI8qbvacj0Z196b+HDRsmU6ZMMdvye88pT6NgfOtFl4U7USkt3fu8s1LaU3k3OJQdOo84MFX3oDvb67crgy6aynLNGiRnuhT9WpO+7OlTnN+5C5rHBpjrIlh1Kkp94P5Ae2FfEdQH7g+2AO0F9YH7Q30d4Lrg8wX3yfrrgv4D7QXXRbA6YC8V9+fN3S/4Tl0hCMbDn5fY14gSjGtQvXjxYjOaWkPifv36yfLly6tTqTgBtTPiWgvfaJ1mwbiuH2TEuD0CXNfRoH3s2LHGTgN6fdn78nvPXV73iHH7WNzv6boE482rKx1XOq7Na4mU5g4fLn8/8eS6RTX4dv4S77xpN1526O0E4/q+OyTP21/zuS4a14qi1Qc+yJTrA9cF7QXtRb0A1wXthS1Ae0F7QX3gPul3V+T+QHthC9B/yKY+EIwH6c1nsIw7GL/6Iu8Roqec1zWiVecY95pLXEdR69NUnTnGnWWcELrZOnEE485IbnuOcw3Gjz322OqUKBri6/u6bKP3nNPhjFTX/2sZ7Vej9wjGm1dobsgEHc1qiddfaTXw1pfX1D9+wbi9Hw1WvQLyvIwe57rwrxVFrA98kCHoIOho1lKU3y/i/YH2gvaC+wNBKEFo4zaC+ySfN5v1Iug/NBNK7/20ZzDwOrIk6wNTqaRXl0LtKc5gXHfsNZVKo2DcXidMMD5+/Hg56KCDzLE+/vjj1Xm/nZHrztzi+r49NYv+bE+DoqPFnWlb3O85Ib89lYoTqLtDfztsd04AwXjzqkhHhY5Ko1ri1yg1mgs/SDDu7NNr5HEewnGuC+9aUdT6QDBerg9cF7QXtBf1AlwXtBe2AO0F7QX1gfukX1vJ/YH2whag/5BNfeDhm80zwkyWaHUqFa/R33oArQTj7vm6/eYY1+03m0pFpzR5+OGHzfQuzstrznFnfnB7hLs7GG8Umjd6T0eR64tgvHmV5oZM0OFXS9whqE530uu6+U0rVZhg3NmYTtNiT6+SdTjOdVF/motcH/ggQ9BB0NH41l/k+wPtBe0F9weCUILQxm0E90k+b/J5k/tk0xChtEAa/UmC8SBnIoNlWg3G3SG1M2L6hhtu8J1KxW+duXPnmjnKr7zySlm4cKFouN23b9+6h28GCcY1OPd6MKc9H/iCBQvMfOj6EE19+b3XaFQ4I8bjqax0VOioeNUk90juoKG4bquVYFzXc4fjGsLbD++Mp8YH2wrXRa1T0esDwTjBOMGX/72z6PcH2gvaC+4PBD4E4wTjQT5h0J+kvbAF6D9kUx9aCsanT5++c8mSJabEHR0dDa93vyd5btu2Lch9orDLRAnGnZHeDp5OM9JoxLgu57WO/l6DcX1PXzo1ytChQz2DcQ3N9QGaTohunziv+cXt9zU0t8sa5D1nDnJnWTt0b/SeLs+I8eaXFTfkshEdldq6YofUYUJx3Uqrwbiu6w7Hs5rjjOuC+mALcH8oa3Bd0F549SpoLy5r3tnKYIms2s+i1wfaC9oL+g/1Nzz6D/Qf6D9wXTTrCqXVfyAYb3YmMno/SjCeUZHbZrcE481PFR0VOiruWuL+ClPYD9dRgnF3+JbVlCpcF121gvrAH86c2sB1QXtBe8EH20Y9S9oL2gvai9orhD+U8IcS/lDi3WrQXjDgxK4ZadYHgvHmGWEmSxCMJ8dOMN7clqCDoMOuJe6vxLcynUnUYDxqw9i81jdfguuibER94P5gXy1cF9QH2guCcb8WlPaC+wPtRf3VQTBOME4wXn9d0F5wXWTZnyQYb56FZLKEBuMP/OatTPZd5J3yAZ8bMh2V+jtAlK8wOVuLGozrduLYRpT7G/eHsh71gaCDoIOgw+9eyv2BfpRdN6gPtBe0F7QXfu0F/WruD7QX9VcH10U2nzcJxqOkJAmuSzCeIG6DTXMj4gMdwXjjBrqV0eJxhdpZjxrn/lB/fyhyfWDEF+0F7QXtBYFP4/663W7SXmTz2abRXvf67cpUC0U/iiCUP5Twh5Ig7WaR2wvuk9l83iQYT7U7EHxnBOPBreJckhsRQQdBR+0VZX+tLewDN+0txTXa2x59lvZc49wfaqdRKXp9IBinvaC9oL0I8gE/zn5q1G2FfT5IlP3Rf+jSo72gvaC9aPyH1Cj3mrjXTfM+qWXn/sDnC/5glH1/kmA87jtpTNsjGI8JMuRmCL7ouNJxrb1o7CC61b/e6xbjCsbj2k7IW4NZnPtD7TQqRa8PfJChvaC9oL0gGPdvTek/EIy7awf9qLII/Qf6D/Qf6D/Qf8hX/4FgvJV0JIV1CMZTQPbYBR02Oip0VGovjDi+Bh1nMO4OqNMc1cH9ofaPA3kIxrOsD3ywpb2gvaC94IOtf3+d/gPBOMG49/VB/4H+A/0H+g/0H/LVf+iWwfjhhx8uCxYsqEpv3rxZ9t9//2yS1hb3SjDeIlzE1aIEXxtnzRDZvt2zBP2uuylSydIM/9xBU9iCdyeHKB3Xf3/sBbl9zavy3YOGyzFDBxpG/d1Pn/mT/PuY98s39ntfWNrq8mnNCRnX16CTDMajhLNhT0DR7w/Uh9oaU/T7g6NR9OvCcSh6feD+4P8hP2xb0x36UdQH2guvek97UVYpentB/4H7gy1Ae0H/IQ/1oVsG4y+//LL06NFD9t57b7nxxhtl4sSJsnTpUjnhhBPC9k0zW55gPBv6KB02p8TbnvqDvHn5pfLOKVOl9+QvxHIg7RSMdyeHondc89pRyWqe8aLfH6gPfJCJO+igvSgL8IfU2poV55RZtBe1tmn1J2kvaC9oL/w/Ahb980UcwTj9B/oPXlcY/YeySjvnUVn1H9o2GHcCb/uC2GuvvcQZLW4H4RqUv/HGG201apxgPJY8OfRGih580VHhg4wtYHcu9EGL+l+rL23k9D99xbmtNB/AWfT7A/WB+wNBB0GHnwD3h1oZ2otDS88WOSz2Nr9d+w8EoeXro+jXhXOXoD5QH+wWo+j1gf4D/Yc85A/vfOC+ui7u2rVrZfDgwb6d/x7Tp0/fuWTJErNAR0dHw5zEb2Pbtm1rNV+pht/PPvusTJgwQZYtWyb77befaDD+r//6r3LeeefJRRddJD/5yU/MPtasWWNGkA8ZMiTwPgcOLE99kNVrxJgt8vyKPbLafWH3u+aU2ZGPPYm/0O179bzI5QqzARzKWitGvzcMW82yOgLwgsfqg+T39u4VeSqVMY+91nK5wqy46WOfkE0fGxdmldSX7fv7B6Xv7/83lf0W/bqgPtRWs6LfHxyNol8XjkPR6wP3h9r7Q9GvC+oD7YVXx6zo1wXtBfdJr+uC/gOfN+16UfT7ZFb9h90v+E7d5Zn7YNwZLT5z5ky5++67CcZTiYSKsZOi34gIOuL9IJPUHOME413niWBcJK0/nGXVUQnT+qRZH6J+kGn3+wPtBe2FLcD9gcCH+uDfWtFelG34nFV2oD5QH+y7RdHrA/0H+g956D+0ZTDujBD3CsaZSiVMhMCybgG+4lcWwaHswFfb+Cq0fY8o+nXBVx1rW4yi3x8cjaJfF45D0esD94fa+0PRrwvqA+2F16fMol8XtBfcJ72uC/oPfN7k82aXQFb9h7acSsWZLsWZSkWnSunVq5eZSkVfPHyTwLtVATpsBON23aGjUttR6XXd/FYvrdJco13bijovuP0wNS1TlLnPwxxQ0e8P7o5K0etD0e8PBOMEX7YA9wcCH+qDf4+C9oLPF3y+qL8+it6v5g8lZQH6D/Qf8tB/aNuHbz7zzDPSp0+fmlrkBOPOqHHnzc2bN7fVgze13Dx8M0xcFd+yNNB0XOm4dgnYT4XW3/Y+76yWLzaC8TJdEs8giHJewpxQ6gNBqFd9od0sqxQ9+OL+wAdbW4D6QHtBe+Hfwyp6e+HI0H+g/6ACtBf0H/LQf2jbYNzGsx++GeZDfp6XJRjP5uzE0UAnUfK0gq84OyrdwSFKxzWJ43e2uddvVya5+Zpt29dElHoYVzAeZ+cpLCL3h9pplopeH7g/lK8grovoH2zD3ovCLE97cXKVK8o9K4w510X9vSGKfXfoP9Be0F7Y9xDqA/WB+uAfBhe9vaBfnc3nTYLxsD3dlJYnGE8J2rUbbkR0VOio1F4UcX0gjWs7djCuU6hEmc4j7F2G+0Pt1x2jTInTHeoDH2xpL2gvaC/82hHaC9oL7g/1VwfXBX9ItWsF9YH64NSHuD4XxLUdPm/W37+j/MEi7GfuuM5jmO0QjIc9SyktTzCeEjTBuCc0HRU6Kl4dlShBdJiGqdHVn9X84lomrov45gHsDvWBYJxgnODLPxinvbgsm45sk71m9cG26PWB9oL2gvaCP5T43Z65P/D5gj8YZd+f7BbBeC57nhELRTAeEbDF1Qm+6LjScW3ccW11lHAcQWiW06gQjHfVC/s+WeT6wAcZ2gvaC9oLv+4m/cn6+wPtRYsfThJcLc2pluhHdZ1I+g/0H+g/0H+g/9C4cUv78ybBeIKdjSibJhiPotf6unyQoaNCR6X++okj1I5jG/Zo8Sijz1q9Q3B/KMvFcS7j2EbW9YEPtrQXtBe0F3ywbdyixnGvj2MbtBfe54lgvOyS5jcpdH/0H+g/0H+g/0D/IV/9B4LxVhOShNcjGE8Y2GfzBF90VOioeF8cUf9qG/WDrXu0uM4truF4mi/uD13a1Ac+2Dq1geuiLEHQwf3Bbo+4LqgP9Cfre2hcF7QX3Cfrrwv6D7QXXBfZ5w8E42mmKiH2RTAeAivGRemwEYzzQcb7grKDbV0i7OiaqMF41CA2jtsE94cuReoDQSjBeO1dhQ+23B/4YEv/wa+vwf2Bzxd8vuAPJdwfmn8a4/MFz7Sya0ma9YFgvPn1mckSBOOZsPNwvQo7AWAZgg8ytdehXS/CTmUSJRjP+ivQBIDe9+Oi1wfuDwQdBB3+fbWi3x/oR9F/4P5AEEoQ2vjzPPdJPm961RD6Dzy822+gQZL5A8F4Nvlr070SjDclSmQBGmiCDj7I+F9a7ulMwjROrQbjdiiuJctiChWCce86UfT6QDBOe0F7QXvhJ0B/slaG9uLARD63RN0oc4yXBcN+CzKqO/0H+g/0H+g/0H8IdidNq/9AMB7sfKS+FMF46uRmh3yQoaNCR6Xxtef+SlPQcLyVYNwdiu+67B7Zddm92dwcuD94uhe5PvDBlvaC9oL2gg+2wZtk2ovgVmktSTBOMG7XNeoD9SHL+mDvu8jtBXlUfQuYRn0gGE+r5xFyPwTjIcFiWpwbEUEHQUfzi8ndOOkazUZyhwnGvbafdSjOH87860VR6wPBOO0F7QXtBcF48zrQKOwoSv+B9oL2gvai/l7B5+6yCfcH73akqJ8vuC6yqQ8E4+H6c6ktTTCeGnXNjrgR0XGl4xrs2vPqrOjocR3Rrf93v4IE47qMvv4x4bCa1fMQihOMN64XRawPfJChvaC9oL0gGA9WB5qF4929/0B7QXtBe0Ew7ne35P7g344U8fMFeVQ29eGdD9xXt+O1a9fK4MGDfQvUY/r06TuXLFliFujo6GjYI/Lb2LZt28L3pAq0BsF4NiebGxEdVzquwa89nfNLOyz6f/vlfMDV3zkheaNg3NmGezu6frOR6MFLG31J7g+NDYtWH/ggQ3tBexH8vlq0+wPtBe0F9weCUILQxvcB7pNlH/qTtBe2ANdFNvVh9wu+U7djgvHg/fzEliQYiaOU4gAAA/VJREFUT4y24Ya5ERF08EEm/LXn9dd8Zyv26HEn+HZ+5xWEO+vlZZQ4HRXqAx9s+WAb5Crgg20QJf1G0KF13wqivQhmF8dSaT9ksFmZi1IfuD/w+YLPF/yhhP5ksxah8ftFaS/Io4LVk7jrA8F4MPfUlyIYT53c7LDRBZZNiaQ0NUX6DxzEoXy2Z79/gMweMSCrU++533nPvyrzXng1V2XSwviNBgxb0Czqe9Aycl0ElSpGfeD+UK4PXBe0F8HvDOUlaS/CisWzfF7b1yLUB9oL2gv7KqY+UB+oD621a0VoL+hXB68bcdYHplIJ7p7qkgTjqXKzMwQQiFEgbCOlH9b1pfOT8+p+AtSH7ndOOSIE4hLg/hCXZPfYDvWhe5xHjgIBBBBIWoD2Imnh9tp+1PrQ0sM3Bw0atHPHjh1GijnGk6kwGoyvfGirbN5QduaFAAIItKOAM13KjqHD6oq/y4urPR/U2Y7HSZmDCVAfgjmxFAJFFOD+UMSz7n/M1AfqAwIIIIBAEAHaiyBKxVmmlfpAMJ7T+jF4RE8ZUvqPFwIIIIAAAggggAACCCCAAAIIIIAAAggggEC8Ag/du61ug00fvjlixIidW7ZsMSsyYjzeE8LWEEAAAQQQQAABBBBAAAEEEEAAAQQQQAABBJIVaGnE+Lhx43auXr2aYDzZc8PWEUAAAQQQQAABBBBAAAEEEEAAAQQQQAABBBIQIBhPAJVNIoAAAggggAACCCCAAAIIIIAAAggggAACCORXgGA8v+eGkiGAAAIIIIAAAggggAACCCCAAAIIIIAAAggkIEAwngAqm0QAAQQQQAABBBBAAAEEEEAAAQQQQAABBBDIrwDBeH7PDSVDAAEEEEAAAQQQQAABBBBAAAEEEEAAAQQQSECAYDwBVDaJAAIIIIAAAggggAACCCCAAAIIIIAAAgggkF8BgvH8nhtKhgACCCCAAAIIIIAAAggggAACCCCAAAIIIJCAAMF4AqhsEgEEEEAAAQQQQAABBBBAAAEEEEAAAQQQQCC/AgTj+T03lAwBBBBAAAEEEEAAAQQQQAABBBBAAAEEEEAgAQGC8QRQ2SQCCCCAAAIIIIAAAggggAACCCCAAAIIIIBAfgUIxvN7bigZAggggAACCCCAAAIIIIAAAggggAACCCCAQAICBOMJoLJJBBBAAAEEEEAAAQQQQAABBBBAAAEEEEAAgfwKEIzn99xQMgQQQAABBBBAAAEEEEAAAQQQQAABBBBAAIEEBAjGE0BlkwgggAACCCCAAAIIIIAAAggggAACCCCAAAL5FSAYz++5oWQIIIAAAggggAACCCCAAAIIIIAAAggggAACCQi0Eoz/f8KNtNBlFx0QAAAAAElFTkSuQmCC)\n", - "\n", - "You may now explore how the circuit was transpiled to a series of X, T and H gates." - ] - }, - { - "cell_type": "markdown", - "id": "10", - "metadata": {}, - "source": [ - "Importantly, the above is only an approximation of the rotation gate we specified (`RX(0.1)`).\n", - "\n", - "What if it does not reproduce the desired gate with enough precision?\n", - "\n", - "In this case, you may increase the `solovay_kitaev_max_iterations` parameter, like so:" - ] - }, - { - "cell_type": "code", - "execution_count": 4, - "id": "11", - "metadata": {}, - "outputs": [ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Helpers" + ], + "id": "2" + }, { - "name": "stdout", - "output_type": "stream", - "text": [ - "Circuit depth: 1006\n", - "\n", - "Opening: https://platform.classiq.io/circuit/2v4oqldPKfks4zAhuYBrUjNG87t?login=True&version=0.73.0\n" - ] - } - ], - "source": [ - "# Prepare for HW aware synthesis\n", - "preferences = Preferences(\n", - " backend_service_provider=ProviderVendor.ALICE_AND_BOB,\n", - " backend_name=AliceBobBackendNames.LOGICAL_TARGET,\n", - " solovay_kitaev_max_iterations=3,\n", - ")\n", - "\n", - "# Create Model, set settings and perform HW aware synthesis\n", - "model = create_model(main)\n", - "model = set_execution_preferences(model, execution_preferences)\n", - "model = set_preferences(model, preferences=preferences)\n", - "qprog = synthesize(model)\n", - "\n", - "circuit_metrics = get_transpiled_circuit_metrics(qprog)\n", - "print(\"Circuit depth: %i\\n\" % circuit_metrics.circuit_metrics.depth)\n", - "\n", - "show(qprog)" - ] - }, - { - "cell_type": "markdown", - "id": "12", - "metadata": {}, - "source": [ - "With 3 iterations, the transpiled circuit now has 1006 gates.\n", - "\n", - "Higher values will yield even deeper, but even more accurate circuits.\n", - "\n", - "Interestingly, the smallest value (1) yields an empty circuit, because the identity gate is the best approximation of our rotation at this level of precision.\n", - "\n", - "The default parameter should be just fine for most of the work you will do, especially if you want to execute the circuit on an emulator. But should you notice errors even when working with very low noise levels, then you might want to tweak the `solovay_kitaev_max_iterations`." - ] - }, - { - "cell_type": "markdown", - "id": "13", - "metadata": {}, - "source": [ - "## Second Part: The Impact of Noise" - ] - }, - { - "cell_type": "markdown", - "id": "14", - "metadata": {}, - "source": [ - "Now that we understand how \"logical\" circuits differ from \"physical\" circuits, let us look at noise. Even if they are error-corrected, logical qubits aren't perfect. How good do they need to be to run your algorithm? This is what we will study in this part.\n", - "\n", - "We will use a simple algorithm (the swap test), define a quality metric for its results, then run it on a noisy backend emulating logical qubits and study the influence of backend parameters over the quality metric." - ] - }, - { - "cell_type": "markdown", - "id": "15", - "metadata": {}, - "source": [ - "### The Swap Test on a noiseless backend" - ] - }, - { - "attachments": { - "image.png": { - "image/png": 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" - } - }, - "cell_type": "markdown", - "id": "16", - "metadata": {}, - "source": [ - "In this first part, we're using the swap test demonstrated in https://github.com/Classiq/classiq-library/tree/main/algorithms/swap_test\n", - "\n", - "Let us just quickly remember that the swap test is a way to compute the overlap between two quantum states $|\\phi\\rangle$ and $|\\psi\\rangle$.\n", - "\n", - "Using the circuit below, it sets the first qubit in state $|q\\rangle_{\\rm test} = \\alpha|0\\rangle + \\sqrt{1-\\alpha^2}|1\\rangle$, with $\\alpha^2 = \\frac{1}{2}\\left(1+|\\langle \\phi |\\psi \\rangle |^2\\right)$.\n", - "\n", - "![image.png](attachment:image.png)\n", - "\n", - "When mesauring the first qubit, we therefore expect to get:\n", - "- 0 with probability 1, if the states are identical (up to a global phase)\n", - "- 0 and 1 with probability 1/2 each, if the states are orthogonal\n", - "\n", - "Let us check this with identical states and a noiseless emulator." - ] - }, - { - "cell_type": "code", - "execution_count": 5, - "id": "17", - "metadata": {}, - "outputs": [], - "source": [ - "# Compute amplitudes for a random 3-qubit state\n", - "\n", - "np.random.seed(12)\n", - "\n", - "NUM_QUBITS = 3\n", - "amps1 = 1 - 2 * np.random.rand(\n", - " 2**NUM_QUBITS\n", - ") # vector of 2^3 random numbers in the range [-1,1]\n", - "amps1 = amps1 / np.linalg.norm(amps1) # normalize the vector\n", - "amps2 = amps1 # we're testing identical states" - ] - }, - { - "cell_type": "code", - "execution_count": 6, - "id": "18", - "metadata": {}, - "outputs": [], - "source": [ - "# Write the main function preparing the states from their amplitudes, then performing the swap test on them\n", - "\n", - "\n", - "@qfunc\n", - "def main(test: Output[QBit]):\n", - "\n", - " state1 = QArray()\n", - " state2 = QArray()\n", - " prepare_amplitudes(amps1.tolist(), 0.0, state1)\n", - " prepare_amplitudes(amps2.tolist(), 0.0, state2)\n", - " swap_test(state1, state2, test)\n", - " drop(state1)\n", - " drop(state2)" - ] - }, - { - "cell_type": "code", - "execution_count": 7, - "id": "19", - "metadata": {}, - "outputs": [ + "cell_type": "code", + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 400 + }, + "outputId": "67b5b3f3-59be-44c7-9860-2d443000365f" + }, + "source": [ + "import time\n", + "\n", + "import matplotlib.pyplot as plt\n", + "import numpy as np\n", + "from matplotlib.colors import LinearSegmentedColormap\n", + "\n", + "from classiq import *\n", + "from classiq.execution import *\n", + "from classiq.interface.backend.quantum_backend_providers import (\n", + " AliceBobBackendNames,\n", + " ProviderVendor,\n", + ")\n", + "from classiq.synthesis import set_preferences" + ], + "execution_count": 1, + "outputs": [], + "id": "3" + }, { - "name": "stdout", - "output_type": "stream", - "text": [ - "Opening: https://platform.classiq.io/circuit/2v4oriRVHjxuxzy19IUGgWXH85b?login=True&version=0.73.0\n" - ] - } - ], - "source": [ - "# Create the model, synthesize and show the circuit\n", - "\n", - "\n", - "qmod = create_model(main)\n", - "qmod = set_execution_preferences(\n", - " qmod, execution_preferences=ExecutionPreferences(num_shots=10_000)\n", - ")\n", - "qprog = synthesize(qmod)\n", - "\n", - "show(qprog)" - ] - }, - { - "cell_type": "code", - "execution_count": 8, - "id": "20", - "metadata": {}, - "outputs": [], - "source": [ - "# Execute quantum program\n", - "res = execute(qprog).result()" - ] - }, - { - "cell_type": "code", - "execution_count": 9, - "id": "21", - "metadata": {}, - "outputs": [ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## First Part: Targeting the Logical Qubits' Gate Set" + ], + "id": "4" + }, { - "name": "stdout", - "output_type": "stream", - "text": [ - "[{'test': 0}: 10000]\n" - ] - } - ], - "source": [ - "# Read results\n", - "print(res[0].value.parsed_counts)" - ] - }, - { - "cell_type": "markdown", - "id": "22", - "metadata": {}, - "source": [ - "We can see that all our shots yield 1: the circuit is working as expected." - ] - }, - { - "cell_type": "markdown", - "id": "23", - "metadata": {}, - "source": [ - "### The quality metric" - ] - }, - { - "cell_type": "markdown", - "id": "24", - "metadata": {}, - "source": [ - "Moving forward, we will use the same model and synthesize it for noisy hardware. This means we'll get imperfect results and will need a quality metric.\n", - "\n", - "We choose to go for the circuit's error rate as the quality metric, i.e. the share of results which are not 0. A 0.0 error rate means a perfect result, while bad results can in theory go all the way up to 1.0.\n", - "\n", - "Note that this choice is a good fit for cat qubits, since a cat qubit decoheres to a statistical mixture of 0 and 1. It would however not be a good metric for transmon-based architectures, which tend to decohere to 0 and will naturally have a low share of 1 in their results. In this case, using orthogonal states rather than identical states is probably a better idea." - ] - }, - { - "cell_type": "code", - "execution_count": 10, - "id": "25", - "metadata": {}, - "outputs": [], - "source": [ - "def results_error_rate(res):\n", - " return 1 - res[0].value.counts[\"0\"] / sum(res[0].value.counts.values())" - ] - }, - { - "cell_type": "markdown", - "id": "26", - "metadata": {}, - "source": [ - "Let us check the quality of the noiseless emulation:" - ] - }, - { - "cell_type": "code", - "execution_count": 11, - "id": "27", - "metadata": {}, - "outputs": [ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The native gates for a logical architecture are discrete, i.e. they do not take parameters like a rotation angle. Most architectures rely on the \"Clifford + T\" gate set, i.e. gates generating the [Clifford group](https://en.wikipedia.org/wiki/Clifford_group) and the [T gate](https://en.wikipedia.org/wiki/Quantum_logic_gate#Phase_shift_gates).\n", + "\n", + "This gate set is said to be \"universal\", meaning that any gate can be approximated with arbitrary precision using a series of these gates, with the number of gates growing as the logarithm of the desired precision.\n", + "\n", + "This means that if the algorithm you want to run contains rotations for example, these rotations will have to be approximated by a series of discrete gates.\n", + "\n", + "Let us see a first example, using a simple 1-qubit rotation:" + ], + "id": "5" + }, { - "data": { - "text/plain": [ - "0.0" - ] - }, - "execution_count": 11, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "results_error_rate(res)" - ] - }, - { - "cell_type": "markdown", - "id": "28", - "metadata": {}, - "source": [ - "As expected, the noiseless emulation has perfect quality." - ] - }, - { - "cell_type": "markdown", - "id": "29", - "metadata": {}, - "source": [ - "### The Swap Test on noisy logical qubits" - ] - }, - { - "cell_type": "markdown", - "id": "30", - "metadata": {}, - "source": [ - "Let us now work with logical qubits.\n", - "\n", - "First, let us remember that a logical qubit, while error-corrected, isn't error-free:\n", - "- Not all errors are caught by error correction\n", - "- The error correction process itself may introduce errors\n", - "\n", - "Several parameters strongly affect the quality of a logical qubit and it is important to study how they affect your algorithm's results. This lets you better understand the specs of the hardware you will need to get reliable results.\n", - "\n", - "Today, we will be looking at three main parameters:\n", - "- The error correction code's distance, `distance`\n", - "- The cat qubit's quality, defined by `kappa_1` and `kappa_2`\n", - "- The number of photons in the cat qubit, `average_nb_photons`\n", - "\n", - "The first parameter, `distance`, roughly translates into how many physical qubits are used to perform error correction. A higher distance is supposed to bring stronger protection against errors, but also requires a bigger chip with more physical qubits. Two important notes:\n", - "- A higher distance only yields fewer errors if your qubits are good \"enough\", i.e. their error rate is below the error correction threshold. Above the threshold, increasing distance actually increases errors!\n", - "- In the specific case of cat qubits, the error correction code is only targeting phase-flip errors. This means that a higher distance actually increases the probability of getting bit-flips. Since the increase is only linear and cat qubits have a strong protection against bit-flips to begin with, the consequences are limited, but they will be visible in our study.\n", - "\n", - "The cat qubit quality parameters `kappa_1` and `kappa_2` can be defined as such:\n", - "- `kappa_1` is the rate at which the cat qubit loses a single photon and produces phase-flip errors\n", - "- `kappa_2` is the rate at which the cat qubit exchanges two photons with the environement and is stabilized\n", - "\n", - "Given this, one wants `kappa_1` to be small and `kappa_2` to be high. We will therefore look at the `kappa_2/kappa_1` ratio as a proxy for our qubits quality. The higher `kappa_2/kappa_1`, the better the cat qubit.\n", - "\n", - "Finally, `average_nb_photons` is the number of photons in the cat qubit. As it increases, bit-flip errors decrease exponentially and phase-flip errors increase linearly." - ] - }, - { - "cell_type": "markdown", - "id": "31", - "metadata": {}, - "source": [ - "Let us now create a custom backend.\n", - "\n", - "You may pick from two preset backends:\n", - "- `AliceBobBackendNames.LOGICAL_EARLY`, which has somewhat high logical error rates (1e-3 to 1e-4)\n", - "- `AliceBobBackendNames.LOGICAL_TARGET`, which has logical error rates low enough to run Shor's algorithm on a 2048-bit number (~1e-15)\n", - "\n", - "These backends can both be customized and this is what we'll do here. We'll start from `LOGICAL_TARGET` and tune it to make it terrible at phase-flips.\n", - "- The `kappa_2/kappa_1` ratio is set to 10, the minimum allowed by the backend. It is below the error correction threshold (which is somewhere around 1e3). This will generate a lot of phase-flips.\n", - "- `distance` is set to 31; it is expected that real logical qubits will not use distances this large. Because we made our qubits under threshold, this will further decrease the performance of our logical qubits.\n", - "- `average_nb_photons` is set to 19, which means excellent bit-flip error rates but also low phase-flip performance." - ] - }, - { - "cell_type": "code", - "execution_count": 12, - "id": "32", - "metadata": {}, - "outputs": [ + "cell_type": "code", + "metadata": {}, + "source": [ + "@qfunc\n", + "def main(q: Output[QBit]):\n", + " allocate(1, q)\n", + " RX(0.1, q)\n", + "\n", + "\n", + "qmod = create_model(main)\n", + "qmod = set_execution_preferences(\n", + " qmod, execution_preferences=ExecutionPreferences(num_shots=10_000)\n", + ")\n", + "qprog = synthesize(qmod)\n", + "\n", + "circuit_metrics = get_transpiled_circuit_metrics(qprog)\n", + "print(\"Circuit depth: %i\\n\" % circuit_metrics.circuit_metrics.depth)\n", + "\n", + "show(qprog)" + ], + "execution_count": 2, + "outputs": [ + { + "output_type": "stream", + "text": [ + "Circuit depth: 1\n", + "\n", + "Opening: https://platform.classiq.io/circuit/2v4opr6xzmMgEnHrNKNAwAoZaJF?login=True&version=0.73.0\n" + ] + } + ], + "id": "6" + }, { - "name": "stdout", - "output_type": "stream", - "text": [ - "[{'test': 0}: 5013, {'test': 1}: 4987]\n", - "Opening: https://platform.classiq.io/circuit/2v4p14CkjQTcfAiQHEXpospBfE6?login=True&version=0.73.0\n" - ] - } - ], - "source": [ - "backend_preferences = AliceBobBackendPreferences(\n", - " backend_service_provider=ProviderVendor.ALICE_AND_BOB,\n", - " backend_name=AliceBobBackendNames.LOGICAL_TARGET,\n", - " kappa_1=100,\n", - " kappa_2=1e4,\n", - " distance=31,\n", - " average_nb_photons=19,\n", - ")\n", - "execution_preferences = ExecutionPreferences(\n", - " num_shots=10_000,\n", - " backend_preferences=backend_preferences,\n", - ")\n", - "\n", - "# Prepare for HW aware synthesis\n", - "preferences = Preferences(\n", - " backend_service_provider=ProviderVendor.ALICE_AND_BOB,\n", - " backend_name=AliceBobBackendNames.LOGICAL_TARGET,\n", - ")\n", - "\n", - "# Create Model, set settings and perform HW aware synthesis\n", - "model = create_model(main)\n", - "model = set_execution_preferences(model, execution_preferences)\n", - "model = set_preferences(model, preferences=preferences)\n", - "qprog = synthesize(model)\n", - "\n", - "# Execute Quantum Program and show results\n", - "res = execute(qprog).result()\n", - "print(res[0].value.parsed_counts)\n", - "\n", - "show(qprog)" - ] - }, - { - "cell_type": "markdown", - "id": "33", - "metadata": {}, - "source": [ - "As you can see, while the expected output was 0 with probability 1, we've managed to make our backend output pure noise. A logical qubit doesn't always mean a good qubit!\n", - "\n", - "But then, how should we tune our logical qubit to get good results? Let us sweep our parameters to find out." - ] - }, - { - "cell_type": "code", - "execution_count": 13, - "id": "34", - "metadata": {}, - "outputs": [], - "source": [ - "distances = [x for x in range(3, 16) if x % 2 != 0]\n", - "ratios = [10**x for x in range(5, 8)]\n", - "nb_photons = [4, 7, 10, 15, 19]" - ] - }, - { - "cell_type": "code", - "execution_count": 14, - "id": "35", - "metadata": {}, - "outputs": [], - "source": [ - "def compute_distance(nb_photons, d, k2, k1=100, sk=2):\n", - " backend_preferences = AliceBobBackendPreferences(\n", - " backend_service_provider=ProviderVendor.ALICE_AND_BOB,\n", - " backend_name=AliceBobBackendNames.LOGICAL_TARGET,\n", - " kappa_1=k1,\n", - " kappa_2=k2,\n", - " distance=d,\n", - " average_nb_photons=nb_photons,\n", - " solovay_kitaev_max_iterations=sk,\n", - " )\n", - " execution_preferences = ExecutionPreferences(\n", - " num_shots=10_000,\n", - " backend_preferences=backend_preferences,\n", - " )\n", - "\n", - " # Prepare for HW aware synthesis\n", - " preferences = Preferences(\n", - " backend_service_provider=ProviderVendor.ALICE_AND_BOB,\n", - " backend_name=AliceBobBackendNames.LOGICAL_TARGET,\n", - " )\n", - "\n", - " start = time.time()\n", - "\n", - " # Create Model, set settings and perform HW aware synthesis\n", - " model = create_model(main)\n", - " model = set_execution_preferences(model, execution_preferences)\n", - " model = set_preferences(model, preferences=preferences)\n", - " qprog = synthesize(model)\n", - "\n", - " # Execute Quantum Program\n", - " res = execute(qprog).result()\n", - "\n", - " end = time.time()\n", - "\n", - " # show(qprog)\n", - "\n", - " error_rate = results_error_rate(res)\n", - "\n", - " print(\"-------------------------------------\")\n", - " print(\n", - " \"Error rate for nb_photons = %i, distance = %i, k1 = %i, k2 = %i: %f. Time elasped: %f seconds.\"\n", - " % (nb_photons, d, k1, k2, error_rate, end - start)\n", - " )\n", - " print(\"-------------------------------------\")\n", - "\n", - " return error_rate" - ] - }, - { - "cell_type": "code", - "execution_count": 15, - "id": "36", - "metadata": {}, - "outputs": [ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "As you can see, because we didn't put constraints on the backend's gate set, the transpiled program only contains one gate.\n", + "\n", + "But now, let's try to target an Alice & Bob backend and see what happens." + ], + "id": "7" + }, { - "name": "stdout", - "output_type": "stream", - "text": [ - "-------------------------------------\n", - "Error rate for nb_photons = 4, distance = 3, k1 = 100, k2 = 100000: 0.497000. Time elasped: 71.169343 seconds.\n", - "-------------------------------------\n", - "-------------------------------------\n", - "Error rate for nb_photons = 4, distance = 3, k1 = 100, k2 = 1000000: 0.499800. Time elasped: 96.857939 seconds.\n", - "-------------------------------------\n", - "-------------------------------------\n", - "Error rate for nb_photons = 4, distance = 3, k1 = 100, k2 = 10000000: 0.502300. Time elasped: 68.482089 seconds.\n", - "-------------------------------------\n", - "-------------------------------------\n", - "Error rate for nb_photons = 4, distance = 5, k1 = 100, k2 = 100000: 0.499200. Time elasped: 75.164038 seconds.\n", - "-------------------------------------\n", - "-------------------------------------\n", - "Error rate for nb_photons = 4, distance = 5, k1 = 100, k2 = 1000000: 0.508200. Time elasped: 70.321209 seconds.\n", - "-------------------------------------\n", - "-------------------------------------\n", - "Error rate for nb_photons = 4, distance = 5, k1 = 100, k2 = 10000000: 0.505100. Time elasped: 73.873376 seconds.\n", - "-------------------------------------\n", - "-------------------------------------\n", - "Error rate for nb_photons = 4, distance = 7, k1 = 100, k2 = 100000: 0.495200. Time elasped: 73.376681 seconds.\n", - "-------------------------------------\n", - "-------------------------------------\n", - "Error rate for nb_photons = 4, distance = 7, k1 = 100, k2 = 1000000: 0.517500. Time elasped: 72.477691 seconds.\n", - "-------------------------------------\n", - "-------------------------------------\n", - "Error rate for nb_photons = 4, distance = 7, k1 = 100, k2 = 10000000: 0.516800. Time elasped: 96.925179 seconds.\n", - "-------------------------------------\n", - "-------------------------------------\n", - "Error rate for nb_photons = 4, distance = 9, k1 = 100, k2 = 100000: 0.509200. Time elasped: 83.217636 seconds.\n", - "-------------------------------------\n", - "-------------------------------------\n", - "Error rate for nb_photons = 4, distance = 9, k1 = 100, k2 = 1000000: 0.509500. Time elasped: 87.689594 seconds.\n", - "-------------------------------------\n", - "-------------------------------------\n", - "Error rate for nb_photons = 4, distance = 9, k1 = 100, k2 = 10000000: 0.500600. Time elasped: 72.159962 seconds.\n", - "-------------------------------------\n", - "-------------------------------------\n", - "Error rate for nb_photons = 4, distance = 11, k1 = 100, k2 = 100000: 0.511800. Time elasped: 70.809266 seconds.\n", - "-------------------------------------\n", - "-------------------------------------\n", - "Error rate for nb_photons = 4, distance = 11, k1 = 100, k2 = 1000000: 0.518800. Time elasped: 71.153163 seconds.\n", - "-------------------------------------\n", - "-------------------------------------\n", - "Error rate for nb_photons = 4, distance = 11, k1 = 100, k2 = 10000000: 0.506800. Time elasped: 70.793602 seconds.\n", - "-------------------------------------\n", - "-------------------------------------\n", - "Error rate for nb_photons = 4, distance = 13, k1 = 100, k2 = 100000: 0.505500. Time elasped: 70.624506 seconds.\n", - "-------------------------------------\n", - "-------------------------------------\n", - "Error rate for nb_photons = 4, distance = 13, k1 = 100, k2 = 1000000: 0.503500. Time elasped: 70.774193 seconds.\n", - "-------------------------------------\n", - "-------------------------------------\n", - "Error rate for nb_photons = 4, distance = 13, k1 = 100, k2 = 10000000: 0.522700. Time elasped: 72.376953 seconds.\n", - "-------------------------------------\n", - "-------------------------------------\n", - "Error rate for nb_photons = 4, distance = 15, k1 = 100, k2 = 100000: 0.511400. Time elasped: 70.389348 seconds.\n", - "-------------------------------------\n", - "-------------------------------------\n", - "Error rate for nb_photons = 4, distance = 15, k1 = 100, k2 = 1000000: 0.510900. Time elasped: 83.862812 seconds.\n", - "-------------------------------------\n", - "-------------------------------------\n", - "Error rate for nb_photons = 4, distance = 15, k1 = 100, k2 = 10000000: 0.503900. Time elasped: 68.846179 seconds.\n", - "-------------------------------------\n", - "-------------------------------------\n", - "Error rate for nb_photons = 7, distance = 3, k1 = 100, k2 = 100000: 0.493300. Time elasped: 71.930928 seconds.\n", - "-------------------------------------\n", - "-------------------------------------\n", - "Error rate for nb_photons = 7, distance = 3, k1 = 100, k2 = 1000000: 0.492900. Time elasped: 68.949645 seconds.\n", - "-------------------------------------\n", - "-------------------------------------\n", - "Error rate for nb_photons = 7, distance = 3, k1 = 100, k2 = 10000000: 0.125900. Time elasped: 68.546538 seconds.\n", - "-------------------------------------\n", - "-------------------------------------\n", - "Error rate for nb_photons = 7, distance = 5, k1 = 100, k2 = 100000: 0.495600. Time elasped: 68.430804 seconds.\n", - "-------------------------------------\n", - "-------------------------------------\n", - "Error rate for nb_photons = 7, distance = 5, k1 = 100, k2 = 1000000: 0.301500. Time elasped: 68.759815 seconds.\n", - "-------------------------------------\n", - "-------------------------------------\n", - "Error rate for nb_photons = 7, distance = 5, k1 = 100, k2 = 10000000: 0.176200. Time elasped: 68.838088 seconds.\n", - "-------------------------------------\n", - "-------------------------------------\n", - "Error rate for nb_photons = 7, distance = 7, k1 = 100, k2 = 100000: 0.508100. Time elasped: 79.019300 seconds.\n", - "-------------------------------------\n", - "-------------------------------------\n", - "Error rate for nb_photons = 7, distance = 7, k1 = 100, k2 = 1000000: 0.268000. Time elasped: 77.329654 seconds.\n", - "-------------------------------------\n", - "-------------------------------------\n", - "Error rate for nb_photons = 7, distance = 7, k1 = 100, k2 = 10000000: 0.273900. Time elasped: 72.517091 seconds.\n", - "-------------------------------------\n", - "-------------------------------------\n", - "Error rate for nb_photons = 7, distance = 9, k1 = 100, k2 = 100000: 0.499500. Time elasped: 69.234349 seconds.\n", - "-------------------------------------\n", - "-------------------------------------\n", - "Error rate for nb_photons = 7, distance = 9, k1 = 100, k2 = 1000000: 0.345300. Time elasped: 68.999759 seconds.\n", - "-------------------------------------\n", - "-------------------------------------\n", - "Error rate for nb_photons = 7, distance = 9, k1 = 100, k2 = 10000000: 0.342400. Time elasped: 68.691098 seconds.\n", - "-------------------------------------\n", - "-------------------------------------\n", - "Error rate for nb_photons = 7, distance = 11, k1 = 100, k2 = 100000: 0.499700. Time elasped: 68.702952 seconds.\n", - "-------------------------------------\n", - "-------------------------------------\n", - "Error rate for nb_photons = 7, distance = 11, k1 = 100, k2 = 1000000: 0.398300. Time elasped: 69.236237 seconds.\n", - "-------------------------------------\n", - "-------------------------------------\n", - "Error rate for nb_photons = 7, distance = 11, k1 = 100, k2 = 10000000: 0.399100. Time elasped: 68.779391 seconds.\n", - "-------------------------------------\n", - "-------------------------------------\n", - "Error rate for nb_photons = 7, distance = 13, k1 = 100, k2 = 100000: 0.498600. Time elasped: 68.886379 seconds.\n", - "-------------------------------------\n", - "-------------------------------------\n", - "Error rate for nb_photons = 7, distance = 13, k1 = 100, k2 = 1000000: 0.435300. Time elasped: 70.253677 seconds.\n", - "-------------------------------------\n", - "-------------------------------------\n", - "Error rate for nb_photons = 7, distance = 13, k1 = 100, k2 = 10000000: 0.427700. Time elasped: 71.385530 seconds.\n", - "-------------------------------------\n", - "-------------------------------------\n", - "Error rate for nb_photons = 7, distance = 15, k1 = 100, k2 = 100000: 0.502800. Time elasped: 78.550687 seconds.\n", - "-------------------------------------\n", - "-------------------------------------\n", - "Error rate for nb_photons = 7, distance = 15, k1 = 100, k2 = 1000000: 0.459000. Time elasped: 71.288507 seconds.\n", - "-------------------------------------\n", - "-------------------------------------\n", - "Error rate for nb_photons = 7, distance = 15, k1 = 100, k2 = 10000000: 0.447000. Time elasped: 73.258285 seconds.\n", - "-------------------------------------\n", - "-------------------------------------\n", - "Error rate for nb_photons = 10, distance = 3, k1 = 100, k2 = 100000: 0.501700. Time elasped: 70.457285 seconds.\n", - "-------------------------------------\n", - "-------------------------------------\n", - "Error rate for nb_photons = 10, distance = 3, k1 = 100, k2 = 1000000: 0.499500. Time elasped: 70.590181 seconds.\n", - "-------------------------------------\n", - "-------------------------------------\n", - "Error rate for nb_photons = 10, distance = 3, k1 = 100, k2 = 10000000: 0.102700. Time elasped: 70.819256 seconds.\n", - "-------------------------------------\n", - "-------------------------------------\n", - "Error rate for nb_photons = 10, distance = 5, k1 = 100, k2 = 100000: 0.499100. Time elasped: 71.996081 seconds.\n", - "-------------------------------------\n", - "-------------------------------------\n", - "Error rate for nb_photons = 10, distance = 5, k1 = 100, k2 = 1000000: 0.358200. Time elasped: 70.039874 seconds.\n", - "-------------------------------------\n", - "-------------------------------------\n", - "Error rate for nb_photons = 10, distance = 5, k1 = 100, k2 = 10000000: 0.054700. Time elasped: 68.721642 seconds.\n", - "-------------------------------------\n", - "-------------------------------------\n", - "Error rate for nb_photons = 10, distance = 7, k1 = 100, k2 = 100000: 0.511800. Time elasped: 74.377347 seconds.\n", - "-------------------------------------\n", - "-------------------------------------\n", - "Error rate for nb_photons = 10, distance = 7, k1 = 100, k2 = 1000000: 0.096800. Time elasped: 70.419338 seconds.\n", - "-------------------------------------\n", - "-------------------------------------\n", - "Error rate for nb_photons = 10, distance = 7, k1 = 100, k2 = 10000000: 0.052700. Time elasped: 70.292175 seconds.\n", - "-------------------------------------\n", - "-------------------------------------\n", - "Error rate for nb_photons = 10, distance = 9, k1 = 100, k2 = 100000: 0.501600. Time elasped: 69.105949 seconds.\n", - "-------------------------------------\n", - "-------------------------------------\n", - "Error rate for nb_photons = 10, distance = 9, k1 = 100, k2 = 1000000: 0.056000. Time elasped: 68.804265 seconds.\n", - "-------------------------------------\n", - "-------------------------------------\n", - "Error rate for nb_photons = 10, distance = 9, k1 = 100, k2 = 10000000: 0.055300. Time elasped: 72.318183 seconds.\n", - "-------------------------------------\n", - "-------------------------------------\n", - "Error rate for nb_photons = 10, distance = 11, k1 = 100, k2 = 100000: 0.504200. Time elasped: 94.127630 seconds.\n", - "-------------------------------------\n", - "-------------------------------------\n", - "Error rate for nb_photons = 10, distance = 11, k1 = 100, k2 = 1000000: 0.054500. Time elasped: 78.572011 seconds.\n", - "-------------------------------------\n", - "-------------------------------------\n", - "Error rate for nb_photons = 10, distance = 11, k1 = 100, k2 = 10000000: 0.059000. Time elasped: 96.247134 seconds.\n", - "-------------------------------------\n", - "-------------------------------------\n", - "Error rate for nb_photons = 10, distance = 13, k1 = 100, k2 = 100000: 0.504400. Time elasped: 70.746398 seconds.\n", - "-------------------------------------\n", - "-------------------------------------\n", - "Error rate for nb_photons = 10, distance = 13, k1 = 100, k2 = 1000000: 0.056400. Time elasped: 70.327472 seconds.\n", - "-------------------------------------\n", - "-------------------------------------\n", - "Error rate for nb_photons = 10, distance = 13, k1 = 100, k2 = 10000000: 0.053400. Time elasped: 72.075044 seconds.\n", - "-------------------------------------\n", - "-------------------------------------\n", - "Error rate for nb_photons = 10, distance = 15, k1 = 100, k2 = 100000: 0.496300. Time elasped: 70.579632 seconds.\n", - "-------------------------------------\n", - "-------------------------------------\n", - "Error rate for nb_photons = 10, distance = 15, k1 = 100, k2 = 1000000: 0.054400. Time elasped: 70.822054 seconds.\n", - "-------------------------------------\n", - "-------------------------------------\n", - "Error rate for nb_photons = 10, distance = 15, k1 = 100, k2 = 10000000: 0.060200. Time elasped: 72.904309 seconds.\n", - "-------------------------------------\n", - "-------------------------------------\n", - "Error rate for nb_photons = 15, distance = 3, k1 = 100, k2 = 100000: 0.496500. Time elasped: 70.265501 seconds.\n", - "-------------------------------------\n", - "-------------------------------------\n", - "Error rate for nb_photons = 15, distance = 3, k1 = 100, k2 = 1000000: 0.499500. Time elasped: 72.351297 seconds.\n", - "-------------------------------------\n", - "-------------------------------------\n", - "Error rate for nb_photons = 15, distance = 3, k1 = 100, k2 = 10000000: 0.157200. Time elasped: 72.740201 seconds.\n", - "-------------------------------------\n", - "-------------------------------------\n", - "Error rate for nb_photons = 15, distance = 5, k1 = 100, k2 = 100000: 0.504500. Time elasped: 74.459069 seconds.\n", - "-------------------------------------\n", - "-------------------------------------\n", - "Error rate for nb_photons = 15, distance = 5, k1 = 100, k2 = 1000000: 0.471200. Time elasped: 70.855352 seconds.\n", - "-------------------------------------\n", - "-------------------------------------\n", - "Error rate for nb_photons = 15, distance = 5, k1 = 100, k2 = 10000000: 0.057400. Time elasped: 70.983077 seconds.\n", - "-------------------------------------\n", - "-------------------------------------\n", - "Error rate for nb_photons = 15, distance = 7, k1 = 100, k2 = 100000: 0.505700. Time elasped: 71.369307 seconds.\n", - "-------------------------------------\n", - "-------------------------------------\n", - "Error rate for nb_photons = 15, distance = 7, k1 = 100, k2 = 1000000: 0.195500. Time elasped: 72.168745 seconds.\n", - "-------------------------------------\n", - "-------------------------------------\n", - "Error rate for nb_photons = 15, distance = 7, k1 = 100, k2 = 10000000: 0.055300. Time elasped: 70.438114 seconds.\n", - "-------------------------------------\n", - "-------------------------------------\n", - "Error rate for nb_photons = 15, distance = 9, k1 = 100, k2 = 100000: 0.493800. Time elasped: 70.558800 seconds.\n", - "-------------------------------------\n", - "-------------------------------------\n", - "Error rate for nb_photons = 15, distance = 9, k1 = 100, k2 = 1000000: 0.074200. Time elasped: 96.405218 seconds.\n", - "-------------------------------------\n", - "-------------------------------------\n", - "Error rate for nb_photons = 15, distance = 9, k1 = 100, k2 = 10000000: 0.053700. Time elasped: 70.337165 seconds.\n", - "-------------------------------------\n", - "-------------------------------------\n", - "Error rate for nb_photons = 15, distance = 11, k1 = 100, k2 = 100000: 0.497500. Time elasped: 72.830533 seconds.\n", - "-------------------------------------\n", - "-------------------------------------\n", - "Error rate for nb_photons = 15, distance = 11, k1 = 100, k2 = 1000000: 0.055600. Time elasped: 95.748791 seconds.\n", - "-------------------------------------\n", - "-------------------------------------\n", - "Error rate for nb_photons = 15, distance = 11, k1 = 100, k2 = 10000000: 0.051100. Time elasped: 70.500518 seconds.\n", - "-------------------------------------\n", - "-------------------------------------\n", - "Error rate for nb_photons = 15, distance = 13, k1 = 100, k2 = 100000: 0.499000. Time elasped: 96.055168 seconds.\n", - "-------------------------------------\n", - "-------------------------------------\n", - "Error rate for nb_photons = 15, distance = 13, k1 = 100, k2 = 1000000: 0.055900. Time elasped: 73.637201 seconds.\n", - "-------------------------------------\n", - "-------------------------------------\n", - "Error rate for nb_photons = 15, distance = 13, k1 = 100, k2 = 10000000: 0.054500. Time elasped: 70.822516 seconds.\n", - "-------------------------------------\n", - "-------------------------------------\n", - "Error rate for nb_photons = 15, distance = 15, k1 = 100, k2 = 100000: 0.494200. Time elasped: 71.481590 seconds.\n", - "-------------------------------------\n", - "-------------------------------------\n", - "Error rate for nb_photons = 15, distance = 15, k1 = 100, k2 = 1000000: 0.054200. Time elasped: 70.463998 seconds.\n", - "-------------------------------------\n", - "-------------------------------------\n", - "Error rate for nb_photons = 15, distance = 15, k1 = 100, k2 = 10000000: 0.052700. Time elasped: 72.105492 seconds.\n", - "-------------------------------------\n", - "-------------------------------------\n", - "Error rate for nb_photons = 19, distance = 3, k1 = 100, k2 = 100000: 0.496900. Time elasped: 70.332159 seconds.\n", - "-------------------------------------\n", - "-------------------------------------\n", - "Error rate for nb_photons = 19, distance = 3, k1 = 100, k2 = 1000000: 0.513500. Time elasped: 78.706125 seconds.\n", - "-------------------------------------\n", - "-------------------------------------\n", - "Error rate for nb_photons = 19, distance = 3, k1 = 100, k2 = 10000000: 0.201900. Time elasped: 77.739521 seconds.\n", - "-------------------------------------\n", - "-------------------------------------\n", - "Error rate for nb_photons = 19, distance = 5, k1 = 100, k2 = 100000: 0.498000. Time elasped: 70.559857 seconds.\n", - "-------------------------------------\n", - "-------------------------------------\n", - "Error rate for nb_photons = 19, distance = 5, k1 = 100, k2 = 1000000: 0.499000. Time elasped: 82.915350 seconds.\n", - "-------------------------------------\n", - "-------------------------------------\n", - "Error rate for nb_photons = 19, distance = 5, k1 = 100, k2 = 10000000: 0.051700. Time elasped: 73.195369 seconds.\n", - "-------------------------------------\n", - "-------------------------------------\n", - "Error rate for nb_photons = 19, distance = 7, k1 = 100, k2 = 100000: 0.499300. Time elasped: 70.454549 seconds.\n", - "-------------------------------------\n", - "-------------------------------------\n", - "Error rate for nb_photons = 19, distance = 7, k1 = 100, k2 = 1000000: 0.304700. Time elasped: 75.665987 seconds.\n", - "-------------------------------------\n", - "-------------------------------------\n", - "Error rate for nb_photons = 19, distance = 7, k1 = 100, k2 = 10000000: 0.053900. Time elasped: 70.624962 seconds.\n", - "-------------------------------------\n", - "-------------------------------------\n", - "Error rate for nb_photons = 19, distance = 9, k1 = 100, k2 = 100000: 0.502200. Time elasped: 73.715155 seconds.\n", - "-------------------------------------\n", - "-------------------------------------\n", - "Error rate for nb_photons = 19, distance = 9, k1 = 100, k2 = 1000000: 0.096400. Time elasped: 70.765682 seconds.\n", - "-------------------------------------\n", - "-------------------------------------\n", - "Error rate for nb_photons = 19, distance = 9, k1 = 100, k2 = 10000000: 0.052100. Time elasped: 100.187774 seconds.\n", - "-------------------------------------\n", - "-------------------------------------\n", - "Error rate for nb_photons = 19, distance = 11, k1 = 100, k2 = 100000: 0.500100. Time elasped: 74.620972 seconds.\n", - "-------------------------------------\n", - "-------------------------------------\n", - "Error rate for nb_photons = 19, distance = 11, k1 = 100, k2 = 1000000: 0.061700. Time elasped: 72.562406 seconds.\n", - "-------------------------------------\n", - "-------------------------------------\n", - "Error rate for nb_photons = 19, distance = 11, k1 = 100, k2 = 10000000: 0.055300. Time elasped: 69.534153 seconds.\n", - "-------------------------------------\n", - "-------------------------------------\n", - "Error rate for nb_photons = 19, distance = 13, k1 = 100, k2 = 100000: 0.494600. Time elasped: 94.375211 seconds.\n", - "-------------------------------------\n", - "-------------------------------------\n", - "Error rate for nb_photons = 19, distance = 13, k1 = 100, k2 = 1000000: 0.054300. Time elasped: 69.341189 seconds.\n", - "-------------------------------------\n", - "-------------------------------------\n", - "Error rate for nb_photons = 19, distance = 13, k1 = 100, k2 = 10000000: 0.052700. Time elasped: 70.512143 seconds.\n", - "-------------------------------------\n", - "-------------------------------------\n", - "Error rate for nb_photons = 19, distance = 15, k1 = 100, k2 = 100000: 0.499500. Time elasped: 68.640973 seconds.\n", - "-------------------------------------\n", - "-------------------------------------\n", - "Error rate for nb_photons = 19, distance = 15, k1 = 100, k2 = 1000000: 0.055900. Time elasped: 75.023128 seconds.\n", - "-------------------------------------\n", - "-------------------------------------\n", - "Error rate for nb_photons = 19, distance = 15, k1 = 100, k2 = 10000000: 0.054500. Time elasped: 68.573808 seconds.\n", - "-------------------------------------\n" - ] - } - ], - "source": [ - "difference = np.zeros((len(nb_photons), len(distances), len(ratios)))\n", - "for n in range(len(nb_photons)):\n", - " for i in range(len(distances)):\n", - " for j in range(len(ratios)):\n", - " difference[n, i, j] = compute_distance(\n", - " nb_photons=nb_photons[n], d=distances[i], k2=ratios[j]\n", - " )\n", - " # The line above is very slow - use the line below instead when debugging\n", - " # difference[n, i, j] = np.random.rand(1)" - ] - }, - { - "cell_type": "code", - "execution_count": 16, - "id": "37", - "metadata": {}, - "outputs": [], - "source": [ - "def plot_results(ratios, distances, difference, n):\n", - " # Create the meshgrid\n", - " ratios_mesh, distances_mesh = np.meshgrid(ratios, distances)\n", - " ratios_mesh_log = np.log10(ratios_mesh)\n", - "\n", - " # Define the colormap\n", - " colors = [(0, 0.5, 0), (0.9, 0.5, 0), (0.9, 0, 0)]\n", - " n_bins = 100 # Discretizes the interpolation into bins\n", - " cmap_name = \"red_darker_green\"\n", - " cmap = LinearSegmentedColormap.from_list(cmap_name, colors, N=n_bins)\n", - "\n", - " # Plotting\n", - " plt.figure(figsize=(10, 8))\n", - " plt.pcolormesh(\n", - " ratios_mesh_log,\n", - " distances_mesh,\n", - " difference[n, :, :],\n", - " shading=\"auto\",\n", - " cmap=cmap,\n", - " vmin=0.0,\n", - " vmax=0.5,\n", - " )\n", - " plt.xticks(\n", - " np.log10(ratios), labels=[f\"$10^{int(np.log10(r/100))}$\" for r in ratios]\n", - " )\n", - " plt.yticks(distances)\n", - "\n", - " # Adding the value on each pixel\n", - " for i in range(len(distances)):\n", - " for j in range(len(ratios)):\n", - " plt.text(\n", - " np.log10(ratios[j]),\n", - " distances[i],\n", - " f\"{difference[n, i, j]:.3f}\",\n", - " ha=\"center\",\n", - " va=\"center\",\n", - " color=\"white\",\n", - " )\n", - "\n", - " plt.colorbar(label=\"Circuit error rate\")\n", - " plt.xlabel(\"$\\kappa_2/\\kappa_1$\")\n", - " plt.ylabel(\"Distances\")\n", - " plt.title(f\"avg number of photons = {nb_photons[n]}\")\n", - "\n", - " plt.show()" - ] - }, - { - "cell_type": "code", - "execution_count": 17, - "id": "38", - "metadata": {}, - "outputs": [ + "cell_type": "code", + "metadata": {}, + "source": [ + "backend_preferences = AliceBobBackendPreferences(\n", + " backend_service_provider=ProviderVendor.ALICE_AND_BOB,\n", + " backend_name=AliceBobBackendNames.LOGICAL_TARGET,\n", + ")\n", + "execution_preferences = ExecutionPreferences(\n", + " num_shots=10_000, backend_preferences=backend_preferences\n", + ")\n", + "\n", + "# Prepare for HW aware synthesis\n", + "preferences = Preferences(\n", + " backend_service_provider=ProviderVendor.ALICE_AND_BOB,\n", + " backend_name=AliceBobBackendNames.LOGICAL_TARGET,\n", + ")\n", + "\n", + "# Create Model, set settings and perform HW aware synthesis\n", + "model = create_model(main)\n", + "model = set_execution_preferences(model, execution_preferences)\n", + "model = set_preferences(model, preferences=preferences)\n", + "qprog = synthesize(model)\n", + "\n", + "circuit_metrics = get_transpiled_circuit_metrics(qprog)\n", + "print(\"Circuit depth: %i\\n\" % circuit_metrics.circuit_metrics.depth)\n", + "\n", + "show(qprog)" + ], + "execution_count": 3, + "outputs": [ + { + "output_type": "stream", + "text": [ + "Circuit depth: 170\n", + "\n", + "Opening: https://platform.classiq.io/circuit/2v4oqLh7s7fQYOzMCVDjmZxdwmF?login=True&version=0.73.0\n" + ] + } + ], + "id": "8" + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Because the RX gate had to be transpiled, the circuit now has depth 170 instead of 1.\n", + "\n", + "After running the `show()` command, you can check the depth of the circuit and even its detailed gate count in the Classiq GUI:\n", + "\n", + "![image.png](data:image/png;base64,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)\n", + "\n", + "By default, the Classiq platform displays the circuit before transpilation to the logical gate set. But it is easy to display the transpiled circuit.\n", + "\n", + "First, save it as \"Transpiled QASM\":\n", + "\n", + "![image.png](data:image/png;base64,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)\n", + "\n", + "Then, upload it:\n", + "\n", + "![image.png](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAXUAAABvCAYAAAATx1CBAAASxElEQVR4Xu2dXWhdxRbHV/xC1JqUFknh9gNjH67WIxzS0nCxkmJfWtO8aHsx0D70QQQxYlPBQlpsoIK2cFMFRRG0ELmtoNzmpgiVBCtqqSUPaa5VQ0ralFpKSz7Ul4L2zuzPmdmzP7N39sne/4B4ss+embV+a5//rFkzOa1raWm5TfgBARAAARAoBIG6ZcuWQdQLEUo4AQIgAAJEEHU8BSAAAiBQIAJ1dvllYmLCcGvVqlUFcg+ugAAIgEB5CFy8eJEg6uWJNzwFARAoOIHx8XGIesFjDPdAAARKRACiXqJgw1UQAIHiE4CoFz/G8BAEQKBEBCDqJQo2XAUBECg+AYh68WMMD0EABEpEAKJeomDDVRAAgeITgKgXP8bwEARAoEQEIOolCjZcBQEQKD4BiHrxYwwPQQAESkQAol6iYMNVEACB4hOAqBc/xvAQBECgRARSFPVm2rlvO61ZZNO7Ql/v6aX/CjCf6Xybmsb3UK9zkbfZTHTyAH1yTqTOr/+Dbh6Q2xM9Q51vN9G41K94TbXB7fO30WN0gA/SvJPMIT8hZ8hnOuntpnHaYxnWvHMfbW8Ydn53euFttzfQsOKXaDn38am/acY1LnFbnyL3bS8j4rYIHTh2Kw+lOs6Vr12uQe+53QQxrtL0MTUmzHrmW3Xa4qj15zca1bQr0ecJroJA7gRSEnVTTFdeEj7whjiRJOyRRd0SNlGoTFKWKF75WhBcndCzW3XizbuIKOqbVxLNDB9QJiA+aWmE2HfiUrkotnI/q9N0zJ5gPMw0XMmauGZEBvJzJHPmY2pEOojxvirV0yXvxMcmG3GS8Yp87s8zDACB0hNIR9R9BFQV8aiibtw3PUr1DTfpgJvWW6LeRNOj9bSSTpqZtzZ7T0HUG2aI6qddYWMiuG/JNM2saVBWCkGCyucQMetXJyD5dy8fjR/qRKB5hMO5m1l3EGO6wtYTzqrKzOrpksjdnFwahsWVV+k/TwAAArkTSEfUlfKF7RUXtM2O+FpCElZ+cSaI/9FjntKMLYLf0hLnvYwydWb3SWa9aX+jVfYZpyZP+SdI1FXhk22VBd+vFOVtIzLVPUGSqOtKRpEYu75es+Lo8rALV3Y5KXj1kvtTDgNAoEQEak7UxYlAnRSkrNwRKx+hnWv5RRBzvjJouMlLMT4TiFJ+iVxT/23ULb0YZRXd/kKAqAv1d7Us4trgrXNHZWyK+SWaYaWob1mJiBkoTdKu27qyWIk+RXAVBGqIQDqi7rOBGF4GUIVMt9EpZoGamnTTNI3WN3g3VVMRdZaRSquQaKIubwaL0Xbbc8HcvvKSIOq6jciI5RejNPStVY4SVkTX+MbuSrokbV7GYSzHxzvJBpeeaug5hykgUBoC6Yi6bvNOs1FqlBtEIVPv0dSLvZt+8ukX86SHZvnvJ+rWZivbwbU2Qb2bkf7ilZ6o8wNAno1Gg0e9cILEf6NU3ZTWiro5iHczVtyctexwJyJ/H4NF3WdDtjQfJTgKArVBICVR586EH2nkd8nH7cTSgM/GmyT8OsHxOZrnK+pW9rt9DbmnL+WTJPMl6g4z8SRLpCON3mxbPdIorhaMyXTNDJvH+F6EZnMzlLH5sMpc1OOZRN7TSrXxkMMKECgTgRRFvUzY4CsIgAAI1CaBVEXdzAh5/os/QqnNcMMqEACBohNIVdRdWHJ5wO+vIosOF/6BAAiAwHwTyEjU59sNjAcCIAACIMAJQNTxHIAACIBAgQhA1AsUTLgCAiAAAhB1PAMgAAIgUCACEPUCBROugAAIgABEHc8ACIAACBSIAES9QMGEKyAAAiAAUcczAAIgAAIFIgBRL1Aw4QoIgAAIQNTxDIAACIBAgQhoRf2vv/6i27dvG27a/y+Qz3AFBEAABApFoK6uzvCH/59rdl1LS4uh4BMTExDyQoUazoAACJSNgFbUGxsby8YB/oIACIBAIQhcvXrVm6lD1AsRWzgBAiBQQgIQ9RIGHS6DAAgUlwBEvbixhWcgAAIlJABRL2HQ4TIIgEBxCUDUixtbeAYCIFBCAhD1EgYdLoMACBSXAES9uLGFZyAAAiUkkEjUt27dSnv37qV77rmnhMjgMgiAAAjMP4Fbt27RwYMH6cSJE4GDJxL1M2fO0LZt2+jy5cvz7xlGBAEQAIESElixYgUdP36c1q9fn76oDw8PU7VaLSFWuAwCIAAC+RGIor2JMvUoHefnNkYGARAAgWISiKK9EPVixh5egQAIFJAARL2AQYVLIAAC5SUAUS9v7OE5CIBAAQlA1AsYVLgEAiBQXgIQ9fLGHp6DAAgUkABEvYBBhUsgAALlJQBRL2/s4TkIgEABCUDUF3BQ+V+P8a9jePjhh2nRokX0888/0+eff04XL15cwF7BdBAAgbkQgKjPhV5Obfn36ezevZueffZZ418GV39OnjxJ+/fvpz///DMnCzEsCIBAXgQg6nmRn8O4H3zwATU3Nwf2MDQ0RF1dXcT/1fB4P210+NQb1DhQpY5/CS3bDtOpNxppoNpB4mVt36/00fCWa7R/027qjzd46N2v9A3Tlmv7adNuv55N+1uXuF1dOKr4EjrKAriBM97xd8nQm0NBXBaATzAxFQIQ9VQwzk8nd911F3V0dFBnZ6c0IP9mNv6jfiPmm2++SZ999llM4xayqFuCfv0oVe0ZyZiMWokyFzwfbjHpR75dnTjnzc/IFuLGnAhA1HMCH2fY++67j1599VXavHkz3XvvvR5Bf+mll4wyzDvvvCMJ++TkJLW3t8cZit27gEXdyF6JjiqribbDp+iN1uue6zHBhNyes6jzyHE/KyOZrJDSZYXesiQAUc+Sbgp933nnnXTs2DFjM1T9+eOPP+jFF1+k0dFR460nnniC3n33Xbr//vudW7/88kvq7++n77//PqI1UUT9FeobXkvXhh6iVrvOcXPIFRNd+UUpF4glEV5SkSoJF4RMm/hYO0gsNPiVGQxRaxxws3TbYyOLrdDI/k20u5/3t4WuGa/NG8SSjjkBCLUbwS/+3ss0QCOVHU55x7SF9CWfcbVkJbP19neTLSiOEL3slo98S0caxo6o8y5eJhq53kqtDJzNS+Z8QZnkAjhzfkp/RxgJP058nLU/HCXaYceNj/UDrXXiyP10+Ud8MHFbRAIQ9Yig8rrtueeeo9dff90z/O+//04vvPACXbhwQXrv0Ucfpffff58eeOAB6fp3331nlG3CN0+jijr7wDriq5Q9fEoD1+3atlUqcH6XLOV9MQU5wj/0Zr+VEbdWHFRT93/PFCymLGyfIFjUVdCmQJk1eVPweSXHEiRpZaDh5tmH8Iq62J89oThCHrQ3EcTYmExaSeSrrlbk30M4B8bLnRhtTubk4U4a5u+ukPtOvnl9yAo2LkS9xgP68ccfU6VSkazkm59vvfUWjY+PG/9NTU0Z7y9evJiamprokUceoT179nhOxrz33nv04YcfhngcVdTlbJelu+7mqCo4GnEKE2dDIDyZrpxV6wRYv4maXNTNbPqIsTHrFSNxgkgo6uLKQivUPpvTmo1SZzLQbGp7eQu2k3cTXLo/wia5yEkdy8Mtw430Gv84z4t5EPV5wZx8kG+++UYqp6g9vfbaa/TVV18Zl59++mlD7P1+fvrpJ3r++efnXdR1mZl0zcoE3aKHldU1eU/RBE0G/hmgKL5hmbq3DGGLZc2Jut8Jo5AVgvkACJMQhXDWiro/J4h68s97Gi0h6mlQzLCPwcFBamho8B0hjqjzGvyTTz4ZSdTFkofRQMquvMIobdLFytSbhNKILTZW+YWLurLxGXik0Wej1LDd6SdI1M3auFrukcovUs0+50w9sqjrVjiC7WGcfSYJP04Q9QwFIULXEPUIkPK85fDhw2wzkhVyfX7iiPr58+dp586doe54T4uoNVdVGMXyhjoBGDOCLNxijdYosdibmDyBVDc17Vq4/V7Q8USrtk/Cpq3nqJ/ii/S+OsHIdgdn6n7CKdhvlUx8M/+45ZcYoi5PbPb+gH0iyPTzIfvYp8rMI+pKPJX4QtRDP2KZ3gBRzxTv3DvnNfJPP/2U7r77bm1n/CsBxJq67pSM3bC7u5sGBgYiGeU5BRLrRIq7NHdOqiglFvFUhzQWO21ydKRCayc3mX/8JNWO2eYbO1SxZfm/A/74yBRX8TSN5wSJ2Cc/3cJPi/xzkjbxAQPGCxN1yQ+Ll+faD2vplGV/aK05qJYdVJf2aSfHVDn9ojAZYidnKvYfeen6C+AEUY/0EcvsJoh6ZmjT63jjxo1GrfyOO+5I3OkXX3xBPT09idvLDb0ljJQ6Rjc1QiD8L3drxFCY4SEAUV8gD8WSJUto27ZtVK1WI1vMT8n8+OOPxL8L5pdffoncLvzG2hZ1XcYc7hPucAmo5RWwWUgEIOoLKVo1Y2tti7qISS0jFfJ7YFJ4LtSSFb5HJgWoOXUBUc8JPIYFARAAgSwIQNSzoIo+QQAEQCAnAhD1nMBjWBAAARDIggBEPQuq6BMEQAAEciIAUc8JPIYFARAAgSwIQNSzoIo+QQAEQCAnAhD1nMBjWBAAARDIggBEPQuq6BMEQAAEciIAUc8JPIYFARAAgSwIZCbqZ86cMf6s/fLly1nYjT5BAARAAAQUAitWrKDjx4/T+vXrA9lcvXqV6lpaWm7zuyYmJoybGxsbAxtt3bqV9u7d6/kX7hEFEAABEACBbAjcunWLDh48SCdOnEhf1LMxGb2CAAiAAAjMlUCiTH2ug6I9CIAACIBANgQg6tlwRa8gAAIgkAsBiHou2DEoCIAACGRDAKKeDVf0CgIgAAK5EICo54Idg4IACIBANgQSivo62tXTQZUHLaNmR6iv+yM6m42NyXtdt4t6Ntyg7kP/kfpo7+qljcutS5OD1Mneb+/qoaWnu+mjmnMiufu6lmXxM11q6A0EFg6BZKLe3kU9S09Tdw4KGEuUtKLeTl09S+m0MgnF6nfhxNdjaVn8XMAhgukgMCcCyUSdi2UbUb8kjKJY8kx+A93oPkS/7uqhtlVEDz7I0/pZGulj2fAyNik011vXiCYHO8lIptlk0Wun0FYGza91LZ2i+kqFZqYmafliM8WeHeljkwoJKwar77PKKsLux2ilvMcvaTL1dczmDmsZYo5zlplhZ/fWOMQYdCymc52HSF4H8GH4exUyFzKuz45v9spGvM+wg9iE00z1jJVBa3KSaPly87VlhxNtkZXdH59sw7ja9uhWJD52e/tkse5aSlP1FarMWHb3biQzMpM0aDHRrYjm9LSiMQiAQCiBZKJu6KMlXE7pJUDUqd/M6u3MeWw19a4eM8oeTMmtzPk8PW5NBKa+99LqMSb2xIS+ecop70iZprhisF/f2OCuIsIydeF9t1/RD/v1Ddqgye71dN0JzfTDW9axr51/vIc23Og2JzTjh43X20xTfOI7y1+vpjEukD5lJKeVPQabLB1WTptfnQnWzx6zHx+7eZ+eWDEejp08rIIffLLh97MYO6u5EPtDn1LcAAIgEJlAclG3h3CydlH45EzdFS5LJM8tpjanfGPfO0arBeF0hIKJuljqEUVSzKjNJHGQ+qaaXaFMIupGBm5n2UanRubJVxxG9i5l/jrOcnnHsVfq115VcOHmGa7wu8NAN7kI+xZ+WbXDVT8h+ZdffOzmq6qQWEl9Wsz7Q+MQ+RnFjSAAAjEIpCvqYmZplSa4GDqi7pfFGaUcnqkbL4zNSjFT9xN1Xprx1PaV7N3NMoVs2BbO0EzdS3Ldri56/PyhgA1VMePlr02fbmxwM3avsPJyBtEho/xi1/uDRV3sw3ktCbBuBeTa490O0dttlMpsUddO4Gam3mavxnQxtq8pG9YxnlPcCgIgEJFAIlGXM2Q7yzSF2CyJTxIvB48xlXIyXDOVNuutYj1YrPH61NRF4XbGNso+fCJwT+GYdedlVvbLh2N21E8pm6KCWAqibvfL6/unl7o1dVbMpr5+ojY7e59lPvTzOrpaU3dLJ7ysYtbkZ2l2ln1RGp+oeBnD2i+YZRdnznXT2Gr3FM4ks/00s90t84Rk6gIruz9eqnJZue3ZzOLYw+NCY/qST5jdzv4ALw1J5Sh7xSHE2CglWXV25u/szDnPKaSIzyhuAwEQiEEgkajH6F+utzrJcn6nZ+LYnsa9C/W0iT77T0gEmXpCcGgGAvEJQNTjM4vVoryiLmbv7mouFjzcDAIgEJtA5qIe2yI0AAEQAAEQSEwAop4YHRqCAAiAQO0RgKjXXkxgEQiAAAgkJgBRT4wODUEABECg9ghA1GsvJrAIBEAABBITgKgnRoeGIAACIFB7BCDqtRcTWAQCIAACiQlA1BOjQ0MQAAEQqD0CEPXaiwksAgEQAIHEBCDqidGhIQiAAAjUHgGIeu3FBBaBAAiAQGICEPXE6NAQBEAABGqPABf1/wOLN4To1l+jawAAAABJRU5ErkJggg==)\n", + "\n", + "And you should see something like this:\n", + "\n", + "![image.png](data:image/png;base64,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)\n", + "\n", + "You may now explore how the circuit was transpiled to a series of X, T and H gates." + ], + "id": "9" + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Importantly, the above is only an approximation of the rotation gate we specified (`RX(0.1)`).\n", + "\n", + "What if it does not reproduce the desired gate with enough precision?\n", + "\n", + "In this case, you may increase the `solovay_kitaev_max_iterations` parameter, like so:" + ], + "id": "10" + }, { - "data": { - "image/png": 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", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" + "cell_type": "code", + "metadata": {}, + "source": [ + "# Prepare for HW aware synthesis\n", + "preferences = Preferences(\n", + " backend_service_provider=ProviderVendor.ALICE_AND_BOB,\n", + " backend_name=AliceBobBackendNames.LOGICAL_TARGET,\n", + " solovay_kitaev_max_iterations=3,\n", + ")\n", + "\n", + "# Create Model, set settings and perform HW aware synthesis\n", + "model = create_model(main)\n", + "model = set_execution_preferences(model, execution_preferences)\n", + "model = set_preferences(model, preferences=preferences)\n", + "qprog = synthesize(model)\n", + "\n", + "circuit_metrics = get_transpiled_circuit_metrics(qprog)\n", + "print(\"Circuit depth: %i\\n\" % circuit_metrics.circuit_metrics.depth)\n", + "\n", + "show(qprog)" + ], + "execution_count": 4, + "outputs": [ + { + "output_type": "stream", + "text": [ + "Circuit depth: 1006\n", + "\n", + "Opening: https://platform.classiq.io/circuit/2v4oqldPKfks4zAhuYBrUjNG87t?login=True&version=0.73.0\n" + ] + } + ], + "id": "11" }, { - "data": { - "image/png": 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MXhuqz8ZV6jus6XplluJM+ZYuXWonBS5iPsszzzzTTiJcnqysLLVs2dJ+Zz7uuOPseFEz6XGoHPLBiQlMmjdvHupiAAAA4AA2btyoww8/XE4LTFrWq6fyO0ZVr7i4OBtAFGe6bd17770ltqWlpcnn8+3T8mHWV61aVea527dvb1tVjj32WKWnp+uRRx7RCSecYOcoC9XP4ZAPTkyLibHU/HBDXRigtmkQ6gIAtVBEqAsA1D5Zfqnb9r3f25zEtEiYwGSJ+V5Zw9fOlNQ9K8sGbWZsSJHSrSaVZTJrmqWICUyOOuooPfvss7rvvvsUCod8cFLUDGYCE+f9ugMO57yWdcD5qDdApTm5C379EH6XjI+PLxGclKVhw4YKCwvTtm3bSmw362YsSUVERESoa9euWrNmjUKF/4UCAAAAtVxkZKS6deumefPmBbeZcSRmvXjryP6YbmE//PCDmjZtqlA55FtOAAAAgLpgxIgRGjx4sLp3727nNpk0aZKys7ODc5kMGjRIhx12mCZMmGDXx40bp+OPP17t2rXT7t277fwoJpXwtddeG7J7IDgBAAAADgEDBw5UamqqxowZYydh7NKli2bNmhUcJL9hw4YS2dB27dplUw+bY5OSkmzLy4IFC2wa4lA55GeIz8jIUEJCglYz5gQ4eI1CXQCgFmJAPHDQMv1S+62yGaMONLYiZN8l3VL9Gh4SkxmQ2vud+blUF8acAAAAAHAEghMAAAAAjkBwAgAAAMARCE4AAAAAOALBCQAAAABHIJUwAAAAUJFH+jU9gX3AzKSoOoWWEwAAAACOQHACAAAAwBEITgAAAAA4AsEJAAAAAEcgOAEAAADgCGTrAgAAAA4kLETZuryqU2g5AQAAAOAIBCcAAAAAHIHgBAAAAIAjEJwAAAAAcASCEwAAAACOQLYuAAAAoCKP9EORrauOoeUEAAAAgCMQnAAAAABwBIITAAAAAI5AcAIAAADAEQhOAAAAADgCwQkAAAAARyCVMAAAAHAgYaQSrgm0nAAAAABwBIITAAAAAI5AcAIAAADAEQhOAAAAADgCwQkAAAAARyBbFwAAAFCRR/pk66p2tJzgT4kZNkyN1q5VSm6uGixapIgePco9tt7gwWoaCJRYzPtKixs7Vo03b1ZKTo6S58xRWLt2JfYnvf++Gq9fb99rjkt4+WW5mzatlvsDqkPMkGFqtGStUjbkqsHHixTRtfx6U1x0/4Fquj2gpGn/LbE94YmX7PbiS9KbH5c4JrxTVyW//Yma/LpLTValKeGRZ+WKja3S+wKqW8zgYWq0aK1SfstVgw8WKaJLBevOhQPVdFNASS+UrDvFxT/wtD0m5tpbg9sie59qt5W1RHTuXiX3BKAkghNUWvSAAYqfOFFZY8cq7bjj5F2+XMmzZ8vdqFG57/Gnp2tbSkpw2d6yZYn9sXfdpdhbblH69dcrrVcvBbKz7TkVFRU8puCzz7RrwACltm+vXX/5i8LbtlXSO+9U670CVSX6ogGKHztRWY+MVdqZx8n703IlT58td8Py640R1ryl4u99RPkLvyxzf968j7XtmJTgsvu6K4L73E2aqsE7c+Vdu0Zp/Xpp5+X9FN7haCU8MbXK7w+oLtEXDlD8PROVNXGs0vodJ+/Py5X82my5Gxyg7hzeUvFjHlH+orLrjhHVr78ijztevi2bSmwvWLJA27qklFhyXpsi7/rf5Vm+pMruDYBDgpMvv/xSF1xwgZo1ayaXy6UZM2aU2H/VVVfZ7cWXfv36hay8KCl2xAjlTJmi3KlT5V250gYUgZwc1RsypPw3BQLyb9u2d9m+veQ5hw9X1v33K3/mTHl/+EG7Bw1SWLNmiu7fP3hM9qRJ8nzzjXwbNsizcKGyHnhAEccfL4XTSxHOF3v9COW8OkW5b06V95eVSr/zegVyc1Tviv3UG7dbiU+/psyH7pFv/e9lH1OQL//2bcElkL47uCvq7PMV8HqU8c8b5fvtF3mWLbHXrXfBpQpr3bYa7hKoerFDRyjn9SnKfWuqvL+uVPrIwrpz+QHqzlOvKfORe+TbUHbdcac0U8L9T2r3TVfaelKCxyN/6ra9y64diup7kXLfeqmK7w6AI4KT7Oxsde7cWZMnTy73GBOMbNmyJbi88cYbNVpGlCMiQhHduil/7ty92wIBux7Zu3e5b3PFxanRunVqvGGDkmbMUHjHjsF9Ya1bK6xp0xLnDGRkqOCbb8o9pyspSfWuvFKeBQskr7eq7g6ovnrTuZvyvyxVb76cq8ju5debuDvGyJ+2Xbmvv1juMZEn9FHjn7ap0YJVin/o/+RKSg7uc0VGSQUF9lrBy+bt6VIZ2fOkP39fQE3UnWO7Kf+rUnVn/lxFdttP3bmtsO68WU7dcbmU+MQrynr6YXl/+fmAxYg++0K5kxooZzrBCVBdQvqo+ZxzzrHL/kRFRSklJaXGyoSKcTdsKFd4uG39KM6sh3foUOZ7vKtXK33IEHlWrJA7IUGxd9yhBgsWKPXoo+XftEnuwp9zWecs2lek/gMPKOamm+SOjVXBwoXaef75VX6PQFVzJxfWm9RSv+Op2xTerux6E9HrRMX89Rqlnt6l3PPmfzpLef97T74NaxXWqq3qj/6Pkt/4WDvO7S35/SqY/6nc4yYq9sY7lP3c43LFxKr+vx/YU6YmjNdCLao7aWXUnbbl1J0eJyrmimuUelb5dSf2xn/aB1s5LzxRoXLUu/wa5X8+W/5S3b8A1KExJ59//rkaN26s9u3b64YbbtCOHTv2e3x+fr4yMjJKLHAGz6JFyn3lFTs2peDLL7XrkkvkT01VzHXXHfS5sh5+WGldu2rHWWdJPp8SX365WsoMhJIrNk6JT72i9BFDFdhZ/v/78mZMV/7sD+Rd+aPyP35fu/52viKP66nIE/vY/d7VP2v3zYMVe8PtSlmfoyY/brWBjG/7Vingr8E7Amqw7jzxitLvHKrArrLrTnin4xR7za3afdtVFTqnu+lhiurTV7lvvlDFpUWtERaipY5xdCd906XrkksuUevWrfXbb79p9OjRtqVl4cKFCgsr+6c1YcIEjR07tsbLWtf409IU8HrlbtKkxHaz7t+6tWIn8Xrl+f57hRdm4yp6X+lzmHXvsmUl3hrYsUM+s/z6q3atXKkmf/xhx52YAAhwKv/OwnrTqFS9adREfhMolGLGg4S3bK2kVz8odvCeZ0opmz1KPaG9fOv27UfvW79WvrRUhbdup4KvPrXb8t57wy7uRo0VyMm2XWLM+Jey3g84tu40LKPupJZRd1q1VXiL1kqaWkbdWe9R6intFdnrZLkbNlbjxRuCh5jWmfgxjyr22uFKPb51iXPGDLzajjnJ+2Rm1d8ggNrRcnL55ZfrwgsvVKdOndS/f399+OGH+vbbb21rSnlGjRql9PT04LJx48YaLXOd4fHIs3Spos44Y+82l8uum25WFeJ2K6JTJ/m2bLGrvrVr7evi53TVr6/IXr32f87CPziuYhm9AMfWm+VLFXVyqXpz8hkqWLLv77j311VKPeUYpZ3eJbjkz56pgvmf2de+TRvLfcLrTm4g37Y9das4f+p2mwUv+qKBCuTlKf+LOVV7j0B11Z0VSxV1Uqm6c9IZKlhaRt1Zs0qppx+jtLO7BJf8T2aqYMFn9rVv80blvvuK0s48tsQxJltX9tMPa+eVffc5Z70BVyv3nZcZ3wjU5ZaT0tq0aaOGDRtqzZo1OqP4l+JSY1TMguqXPXGiEqdNk2fJEnkWL1bM8OF23oTcl/YMFEyYNs2OJckcPdqux919twoWLZJvzRq5EhMVd+edCmvZUrnPP7/3nJMmKe7f/5b3119tsFL/vvvk27xZeYWZ3CJ69rRzqRTMn6/Arl0Ka9vWHuNds6biQREQQtnPTFTik9NsGlLPd4sVc91wOwYk983CevPUNNufPXP8aNNPVd5VP5V4vz99t32qVLTd1Lm4O+5R3ofv2tYX88Q4fsxD8q1do/zPZgffFzPkRhV8u0CB7CxF9TlL8WMeVsb9IxXISK/hTwConOwpE5X42DR5ViyR5/vFihk6XK56scotHJye8Hhh3XmgsO6sLlV3MgrrTuH2wK6d8u7aWeIYk63Ll7rVZrUrLvKk0xXeso1yXt/79wpA9ahVwckff/xhx5w0ZcI9R8h76y1lNGqkuHHjFJaSIs+yZdrZr18wPXBYixZ2MG7xzFoJU6bYY/27dtmWl7QTTrBpiItkP/SQ/bKV8Nxzcicm2iDEnNP8oTFMquLoSy5R/bFj7XGmpSV/1iybfthmIwIcLu/9t5TRoJHi7hqnsMYp8vy4zM47Ylo0jLDDStabAwn4fIroeKzqDRgsd0KifFs3q+DzT5T54N0l6kTEcT1V/y5Tb+LsU+X0O69T7tuvVss9AtUhb+ZbykhupLg7ximsUYo8Py3Tzr/1s9m4jLBmB1d3DkbM5deo4Nuv5fttdbWcH8BerkCgWG7JGpaVlWVbQYyuXbtq4sSJOu2005ScnGwXM3bkL3/5i83WZcac3HXXXcrMzNQPP/xQ4dYRMyA+ISFB5n8n9av5foBDzv7nNgNQlohQFwCofTL9Uvutsl3y4+Pj5STB75JJUn1XzV47MyC13+XMz+WQbDlZsmSJDUaKjBgxwv47ePBgPf3001qxYoWmTZum3bt324kazz77bN1333102wIAAEDNcodgtLZfdU5Ig5M+ffpofw03s2fv7S8NAAAA4NDm6GxdAAAAAOoOghMAAAAAjkBwAgAAAMARCE4AAAAAOEKtmucEAAAAqDPZuuogPmIAAAAAjkBwAgAAAMARCE4AAAAAOALBCQAAAABHIDgBAAAA4Ahk6wIAAAAOJCwEj/VdqnNoOQEAAADgCAQnAAAAAByB4AQAAACAIxCcAAAAAHAEghMAAAAAjkC2LgAAAKAij/R5rF/t+IgBAAAAOALBCQAAAABHIDgBAAAA4AgEJwAAAAAcgeAEAAAAgCMQnAAAAABwBFIJAwAAAAcSFoLH+i7VObScAAAAAHAEghMAAAAAjkBwAgAAAMARCE4AAAAAOALBCQAAAABHIFsXAAAAUJFH+jzWr3Z8xAAAAAAcgeAEAAAAgCMQnAAAAABwBIITAAAAAI5AcAIAAADAEcjWBQAAABxIWAge67tU59ByAgAAAMARaDkBUL6YUBcAqIUiQl0AoBbyh7oAcApaTgAAAAA4AsEJAAAAAEcgOAEAAADgCIw5AQAAACrySN9k7EK1ouUEAAAAgCMQnAAAAABwBIITAAAAAI5AcAIAAADAEQhOAAAAADgC2boAAACAijzSr+nH+gHVObScAAAAAHAEghMAAAAAjkBwAgAAAMARCE4AAAAAOALBCQAAAABHIFsXAAAAcCBhhQuqFS0nAAAAAByB4AQAAACAIxCcAAAAAHAEghMAAAAAjkBwAgAAAMARCE4AAAAAOAKphAEAAICKPNKv6cf6AdU5tJwAAAAAcASCEwAAAACOQHACAAAAwBEITgAAAAA4AsEJAAAAAEcgWxcAAABwIGGFC6oVLScAAAAAHIHgBAAAADhETJ48Wa1atVJ0dLR69eqlxYsXV+h9b775plwul/r3769QIjgBAAAADgHTp0/XiBEjdM899+i7775T586d1bdvX23fvn2/71u3bp3uuOMOnXzyyQo1ghMAAADgEDBx4kQNHTpUV199tTp27KhnnnlGMTExevHFF8t9j8/n05VXXqmxY8eqTZs2CjWCEwAAAMDBMjIySiz5+fn7HFNQUKClS5fqzDPPDG5zu912feHCheWee9y4cWrcuLGuueYaOQHBCQAAAFDRbF01vUhq3ry5EhISgsuECRP2KV5aWpptBWnSpEmJ7WZ969atZd7S/Pnz9cILL2jKlClyClIJAwAAAA62ceNGxcfHB9ejoqL+9DkzMzP197//3QYmDRs2lFMQnAAAAAAOFh8fXyI4KYsJMMLCwrRt27YS2816SkrKPsf/9ttvdiD8BRdcENzm9/vtv+Hh4Vq9erXatm2rmka3LlRazLBharR2rVJyc9Vg0SJF9OhRofdFDxyopoGAkv773xLb3Y0bK+Gll9R40yalZGcr6eOPFdauXYljwtq0UdJ776nx9u1qkp6uxOnT7fuA2iTm78PUaP5apazOVYMZixTRuYJ154KBarouoKTnStaduOH3qNG8lWryc5aaLN+p5FfnKKJLzxLHmOuZ9xZfYm/4Z5XeF1DdYq4cpkafrVXKj7lq8M4iRRxbwbpz3kA1/TWgpP8rVnfCw1X/zgfU8MMVarI8S43nb1LCQ9Pkbty0xHvDWh2hpKdnqMk3qWryfboavPGVInv1qepbA/60yMhIdevWTfPmzSsRbJj13r1773N8hw4d9MMPP2jZsmXB5cILL9Rpp51mX5uuZKFAcIJKiR4wQPETJypr7FilHXecvMuXK3n2bLkbNdrv+8JatlT8I48o/8sv99mXNGOGDT52XXSRUrt2lW/9eiXPnStXTIzdb/5N/uQTKRDQztNP144TT5QrMlJJH3wguVzVdq9AVYo+f4Di/z1RWY+PVdp5x8n783Ilvzxb7gYHqDuHt1T86EeU/82+dcf7+y9KH3OT0vp20o5LT5Lvj3VKfvkTuZNLNtNnPnq3tvVICS45U5+s8vsDqkv0uQMUP3qisp4aq7T+x8m7crmSX5wtd/IB6s5hLRU/8hHlf1uy7riiYxRx9HHKmnyfPd+umy5ReJv2SnpmZonjkp/70AYyOwadrrT+3eRZtVxJz30od8OS/foBJxgxYoTtpjVt2jStXLlSN9xwg7Kzs232LmPQoEEaNWqUfW3mQTnmmGNKLImJiapfv759bYKdOhecfPnll7YpqVmzZnbSlxkzZpTYf++999qoLjY2VklJSTbbwDfffBOy8mKv2BEjlDNlinKnTpV35UqlX3+9Ajk5qjdkSPlvcruV+NpryrznHvl+/73ErrAjjlBk797KuOEGeZYske+XX+xrV716ir7iCntMxIknKqxVK+2+6ip5f/zRLrsHD1ZE9+6KPP306r5loErEXjtCOW9OUe7bU+Vds1Lp/7pegdwc1RtwgLoz6TVlPnaPfBtL1h0jb+YbKvh6nnwb18r768/KuH+E3PEJCu9wbInj/NmZ8qduCy7mukBtETtkhHKmT1Huu4V1Z0xh3bn0AHXn0deU+fi+dSeQlaGdV52tvI/flm/tL/Is+0YZY29SZKfucjfd88TYldRA4a2PVNazD8i7+gf51q9R5iMj5Y6JVfiRx1T3LQMHbeDAgXrkkUc0ZswYdenSxbaAzJo1KzhIfsOGDdqyZYucLKTBiYnkzOQwZibLshx55JF66qmnbJOTySZgZrs8++yzlZqaWuNlRTEREYro1k35c+fu3RYI2HUTYJQnbswY+bdvV24ZubZdhQO7Anl5Jc6p/HxFnnTS3mMCAQWKpc+zx/v9wWMAx9edY7op/+tSdefruYo8bj9159Yx8u/Yrty3XqzQNWKu+If8GbvlWbm85HluGKkm36ep4f++U+w/7pDCCtPAALWh7hzdTfkLStWdBXMV2XU/deemwrrzTgXqjvk7Uz9BAb9fgczdey6xa4e8v61STP9BctWLsXUm5vLr5EvbJs+PS//8faF2cYdoOUg33XST1q9fb9MNm4f6Zpb4Ip9//rmmTp1a7nvNvtKNBXVqQPw555xjl/L89a9/3WdiGZPubMWKFTrjjDNqoIQoi7thQ7nCw+UvNeDKrId36FDme0yrR8w11yi1S5cy93tXrZJ3/XrVnzBB6dddp0B2tmJvu01hzZsrrOme/r+eRYvs9vgHH1TG6NG2ta3+Aw/YsrgLjwGczJ1UWHfSStWd1G0Kb1tO3el+omIGXKPUc8uuO0WiTj9PiU++ab9A+bdv0c6/nWW/WBXJeekJeX76Tv7dOxXZ7QTVv2uC7Vufef/tVXR3QAjqzo791J1uJyrmsmuUeuH+605QZJTi73xQeR++oUBWZnDzjqvOVNL/zVCTZZn2YZgJdnZe00+BjD0BDIA6OubETCzz3HPP2dzOprWlPCZKLD1RDULLFRenxFdeUfrQoQrs2PtlqQSvV7suuUThRx6plF27lJKTo8jTTlPeRx/Zp1iGPy1Nuy67TFEXXKCUrCw7IN6VmCjP0qX2DwZwqHHFxinxsVeUPmpoiUCjLAULP1PauV204y8nKP+LWUqc/FaJcSzZLzymgkVfyLvqB+W89qwy7r9dsYNvNiMoa+BOgBDUnYdfUfq/Dlx3rPBwJT3xlh2/mH7PDSV2Jdwz2QYkO644WWl/6am8uTOU/OwHcjfaN/sRgDqQSvjDDz/U5ZdfrpycHDVt2lRz5szZby5mMynN2LFja7SMdY0JEgJer9ylJvkx6/4yJvkJa9tW4a1b7xm4Hjx4T1yc4vEotX17OwbF+913SuvaVa74eDvQ3VzHZAEzY1CKFMyZo9R27eRq0MAGNIH0dDXesmWfMSyAE/l3FdadUgNp3Y2ayJ9aRt1p2VbhzVsr6fky6s4aj1JPby/fhj2/+6bvvW/9b3ZJ//4bNfrsF9UbeI2y/++BMsti+te7IiIUdngr+X7/pWpvFKiputOgnLrTorDuPFtG3VnpUWrfvXXHBiaPv6WwZi3toPfirSaRvU9X1Gnna1v3pOD2jHtvVNSJZ6nexYOV/dyD1XTHQN3l+JaTonRmCxYsUL9+/TRgwABt37693ONNBoL09PTgYiatQRXzeGxrRVTxrnUul10vWLiwzC5bqccco7QuXYJL/syZKvjsM/vaV+pnFMjIsIGJSSNsBrvnvf/+Puc0LTAmMDGtKyaVcN7MktlVAMfWnR+XKuqEUnXnhDNU8F0Zdee3VUo9+xjbIlK05M+dGWwl8W3Zz//f3G65IsufpCu8YxcFfD7508r//yngqLrz01JF9S6j7nxfTt059xilXdgluOTPm6mCRZ/Z18G6UxSYtDpCO686U4HdO0ucx44zMUq3zpv1wmAHQB1rOTGZutq1a2eX448/XkcccYQdd1KUBq00M2NmVcyaif3LnjhRidOm2VYNz+LFihk+XK7YWOW+9JLdnzBtmvybNilz9Gg7qN37008l3u/fvdtGxsW3R196qfypqfJt2KDwTp0U//jjypsxw7aWFKlnMnWtXGmPM4PvzTHZjz1ms3sBtUH28xOV+Og0eX5YIs+yxYq5ZrhcMbHKfbuw7jw6Tf5tm5T5UGHd+aVU3ckorDuF282Xp7ib/qW8uTPtWBNXUkPFDrpRYSmHKe9/b9tjIo47XhFdetmgxjz9jTiut+Lvfky5M16l3zxqjewXJyrxoWny/LhEnhWLFXPVcLnqxSr33cK681Bh3Xl0tFSQL++vpepOZmHdKdpuApMn37HphHf+43zJHRZsmfGn77QBkQl8Aum77LmznhqnQF6uYgYOVdjhrZX/+f9q/kMA6gDHByelmclkzLgShFbeW28po1EjxY0bp7CUFHmWLdPOfv1sNi4jrEWLgx4HYga1m7lTTPcw35Ytyn35ZWXdd1+JY8Lbt7eD5t3JyfKtW6es8eNtcALUFnkfvqWM5EaKu22cwhqlyLNymXYO7hdswQg7rIUUqHjdCfh9dkBw0l8G20HD/t075FnxrXZcdrJNK2yPyc9XvQsuV/3h99rWFO/Gtcp+8TEbKAG1Rd5HhXXn1mJ155p+djyIEdbs4OpOWJPDFH3mRfZ1ow9KZrbbcWUfFSz+wo5XMdeoP2K8Grz8qc0aZoKbXTdcJO+qFVV8h3A8E93WdJLDgOocVyBg8rWGRlZWltasWWNfd+3a1WbjMt24kpOT1aBBA40fP97OVGnGmqSlpdmUw6+//rqWLl2qo48+ukLXMAPizSD61ZLqV/P9AIeclqEuAFALRYS6AEDtk+mX2v8u2yU/Pj5eThL8LtlDql/Dj/UzvVL7b535uRySLSdLliyxwUjxWS2NwYMH65lnntGqVavsDJcmMDHBSo8ePfTVV19VODABAAAAUHuENDjp06eP9tdw895779VoeQAAAACEDqkmAAAAADgCwQkAAAAAR6h12boAAACAkDzSr+nH+m7VOXXwlgEAAAA4EcEJAAAAAEcgOAEAAADgCAQnAAAAAByB4AQAAACAIxCcAAAAAHAEUgkDAAAABxJWuNSkgOocWk4AAAAAOALBCQAAAABHIDgBAAAA4AgEJwAAAAAcgeAEAAAAgCOQrQsAAACoyCP9mn6s71adUwdvGQAAAIATEZwAAAAAcASCEwAAAACOQHACAAAAwBEITgAAAAA4Atm6AAAAgAMJK1xqUkB1Di0nAAAAAByB4AQAAACAIxCcAAAAAHAEghMAAAAAjkBwAgAAAMARyNYFAAAAHAjZumoELScAAAAAHIHgBAAAAIAjEJwAAAAAcASCEwAAAACOQHACAAAAwBHI1gUAAABU5JF+TT/Wd6vOqYO3DAAAAMCJCE4AAAAAOALBCQAAAABHYMwJgPI1CnUBAAB1gi/UBYBT0HICAAAAwBFoOQEAAAAq8kg/rIav6VedQ8sJAAAAAEcgOAEAAADgCAQnAAAAAByB4AQAAACAIxCcAAAAAHAEghMAAAAAjkAqYQAAAKAij/Rr+rG+W3VOHbxlAAAAAE5EcAIAAADAEQhOAAAAADgCwQkAAAAARyA4AQAAAOAIZOsCAAAADiSscKlJftU5tJwAAAAAcASCEwAAAACOQHACAAAAwBEITgAAAAA4AsEJAAAAAEcgWxcAAABQkUf6Nf1Y3606pw7eMgAAAAAnIjgBAAAA4AgEJwAAAAAcgeAEAAAAgCMQnAAAAABwBLJ1AQAAAAcSVrjUJL/qHFpOAAAAADgCwQkAAAAARyA4AQAAAOAIBCcAAAAAHIHgBAAAAIAjkK0LAAAAOBCyddUIWk4AAAAAOALBCQAAAABHIDgBAAAA4AgEJwAAAAAcgeAEf0rMsGFqtHatUnJz1WDRIkX06FHusfUGD1bTQKDEYt5XWtzYsWq8ebNScnKUPGeOwtq1K7HflZSkxFdfVZP0dDXZtUsJzz8vV2xstdwfUB1iLhumRu+vVcr8XDV4aZEiOpZfb6JPu1gNpn2rJp/uUpMvs9Twte9V75y/lTjGndxYCfe8pMYfbVLKV9lKeuJjhTUvWW/cDZooYezLajxry57zvLJU0addUm33CBwqdSfssDZKeug9Nf5ku5p8lq7E/0y37wNQPQhOUGnRAwYofuJEZY0dq7TjjpN3+XIlz54td6NG5b7Hn56ubSkpwWV7y5Yl9sfedZdib7lF6ddfr7RevRTIzrbnVFRU8JjE115T+NFHa+dZZ2nn+ecr8pRTlPDcc9V6r0BViT5rgOKHT1TW82OV9vfj5P11uZKfnC13Utn1xp++U1kvjdeOIb2VdsWxyvngJSWMeUmRx58dPCbp4RkKa9ZGu+64SKl/6yrflvVKnjxXruiY4DGJ976s8JbttWvEhUq7opPyPntPiRPeUviRXWrkvoHaWHfMv8lPfSIpoJ03nK4d154oV0SkkiZ+ILlcNXbvcNC35lAsdUxIb/nLL7/UBRdcoGbNmsnlcmnGjBkl9r/33ns6++yz1aBBA7t/2bJlISsr9hU7YoRypkxR7tSp8q5caQOKQE6O6g0ZUv6bAgH5t23bu2zfXvKcw4cr6/77lT9zprw//KDdgwYprFkzRffvb/eHd+ig6HPOUfq118qzeLE8X3+tjJtvVvTll8vdtGl13zLwp8X+dYRyZkxR7gdT5V27UukTrlcgL0f1Liy73hR894XyP58h77pV8m36XTlvPiHvmhWK7HKS3R/W4ghFHttbGQ/eIM/PS+Rb/4syHrhBrqh6iu57RfA8EceeoJzpT8rz87fybVqrrBfHK5C5WxFHdauxewdqW92J6Hyiwpq20u6xV8n724922X3vYEUc1V2RPU6v0fsH6oqQBifZ2dnq3LmzJk+eXO7+k046SQ8++GCNlw0HEBGhiG7dlD937t5tgYBdj+zdu9y3ueLi1GjdOjXesEFJM2YovGPH4L6w1q0V1rRpiXMGMjJU8M03wXNG9O4t/65d8ixdGjzGHu/3K6JXr6q/T6AqhUcookM35S8uVW8Wz1Vkp/LrTXHmC1FYy/Yq+O5Lu+6K2NOqGMjPK3FOefKDX8IMz4oFij5roFzxSfaJr3mtqGgVLP28ym4PONTqjisyym4LFOTvPaQgz/7Niey8t34BOEQmYTznnHPsUp6///3v9t9169bVYKlQEe6GDeUKD7etH8WZddO6URbv6tVKHzJEnhUr5E5IUOwdd6jBggVKPfpo+TdtkjslJXiO0ucs2mf+Ld3aIp9P/p07FVZ4DOBU7sTCerOz1O/4zm0Kb1V2vTFcsfG2T7z9ouTzKf3BYSoo/JJmngp7t6xX/RsnKH3CdQrkZiv2r7cprElzhTXY25q4a9QAJf1nulLm7VTA67FPnHfdebF8f/xWjXcM1O664/lhkQJ52Yq/+UFlTB5te3HUv+kBWxZ3Q1rrgepwyM0Qn5+fb5ciGRkZIS0P9vIsWmSXIgULFqjRypWKue46ZY0ZE9KyAU4WyMlU2pVd5IqJU1SPMxR/20TbTcV0W5HPq113XaLEu19Qyqe7FPB6lf/tXOV9/VGJPvH1r79PrvqJ2jHsDPl3pyn61P5KmvCWdgw92XZVAQ5Ff7bumLqya+RlShj5tFIG3mJbTHI/eUOelUvtawBV75ALTiZMmKCxY8eGuhiHPH9amv0fubtJkxLbzbp/69aKncTrlef77xVemI2r6H2lz2HWvYXjjcx2d+NSWVLCwuROTpavotcFQsR80bH1JrlUvUluIv+O/fz+BgLBFg7vL8sV3uooxV01SjvNFyyzbdV3Sruyq31KbAbrmuuYTEaelUuC2YZiB96s1IFHy/v7z3Zb1q8rFNn1ZMVcdqPtZw84WajqjlHwzRylXtxOroQGNqAJZKXbrHe+T36vrtsF6rRDLgfAqFGjlJ6eHlw2btwY6iIdmjweO+4j6owz9m5zuex6wcKFFTuH262ITp3k27LFrvrWrrWvi5/TVb++Inv1Cp7Ts3Ch3ElJCj/uuOAxkaefbs/l+eabKrs9oFp4PfKsWmqf4JaoNz3OUMEPFaw3htstmW4qpQSyM+yXK5MK1QzYzfvi/T2XKMraVfpJr88nlzkX4HQhqjsljknfYQOTyO6nyZ3UWHlfzaz07aCWMv+7DKvhxa0655BrOYmKirILql/2xIlKnDZNniVLbOasmOHD7XwjuS+9ZPcnTJtmx5Jkjh5t1+PuvlsFixbJt2aNXImJirvzToW1bKnc55/fe85JkxT373/L++uvNlipf9998m3erLzCTG7eVauU9/HHSpwyxWYHMwPzE556Snlvvil/YZADOFn26xOVeM80+2TW89NixVwxXK56scr9oLDe3DtN/tRNypy8p97EXjVyTyahTb/ZAbxRJ56reuf+XenFWjuiz7hU/l2p8m3boPC2nRR/++PK+2KGfeIb7Fu/4VfFj3pWmY/fIX/6DkX36a/IXmdp123nh+iTAJxfd4x6F1xls4OZ40x2r/gRjyv7jcdsdi8AVe+QC05Qc/LeeksZjRopbtw4Oxjds2yZdvbrFxywHtaiRYkntWbyxIQpU+yxRRm30k44waYhLpL90EM2wDHzlrgTE1Uwf749p4qNI9p95ZU2IEmeN8+eP+/dd5Vxyy01fPdA5eTNeUsZiY0Ud904hTVIkeeXZdp5Sz/5dxbWm5QWUqBYvYmOVcI//09hjQ9XID9X3vWrtHvM3+x5ipiBuaYvveni4kvbotyPXlbW8/ftvajPq53Dz7UDec38DKb/vW/jGqXfO1j5Cz6u2Q8AqE11x3xRatneDpp3xyfLt3mdnTsl+/XHavDOgbrFFQiYvHmhkZWVpTVr1tjXXbt21cSJE3XaaacpOTlZLVq00M6dO7VhwwZt3rxZ5513nt588021b99eKSkpdqkIMyA+ISFBq82A0Gq+H+CQ0z3UBQAA1AWZPqn997Jd8uPj4+Ukwe+SA6X6kTV77cwCqf10Z34u1SWkPdmWLFligxKzGCNGjLCvxxRmbpo5c6ZdN4GJcfnll9v1Z555JpTFBgAAAHCodevq06eP9tdwc9VVV9kFAAAAwKGvDuYAAAAAAOBEDIgHAAAAKvJIv6Yf67tV59TBWwYAAADgRAQnAAAAAByB4AQAAACAIxCcAAAAAHAEghMAAAAAjkC2LgAAAOBAwgqXmr5mHUPLCQAAAABHIDgBAAAA4AgEJwAAAAAcgeAEAAAAgCMQnAAAAABwBLJ1AQAAABV5pF/Tj/XdqnPq4C0DAAAAcCKCEwAAAOAQMXnyZLVq1UrR0dHq1auXFi9eXO6x7733nrp3767ExETFxsaqS5cueuWVVxRKBCcAAADAIWD69OkaMWKE7rnnHn333Xfq3Lmz+vbtq+3bt5d5fHJysv71r39p4cKFWrFiha6++mq7zJ49W6FCcAIAAAAcAiZOnKihQ4faAKNjx4565plnFBMToxdffLHM4/v06aOLL75YRx11lNq2batbb71Vxx57rObPn69QITgBAAAAHCwjI6PEkp+fv88xBQUFWrp0qc4888zgNrfbbddNy8iBBAIBzZs3T6tXr9Ypp5yiUCE4AQAAAA4kLESLpObNmyshISG4TJgwYZ/ipaWlyefzqUmTJiW2m/WtW7eWe1vp6emKi4tTZGSkzjvvPD355JM666yzFCqkEgYAAAAcbOPGjYqPjw+uR0VFVdm569evr2XLlikrK8u2nJgxK23atLFdvkKB4AQAAABwsPj4+BLBSVkaNmyosLAwbdu2rcR2s56SklLu+0zXr3bt2tnXJlvXypUrbctMqIITunUBAAAAtVxkZKS6detmWz+K+P1+u967d+8Kn8e8p6wxLTWFlhMAAADgEDBixAgNHjzYzl3Ss2dPTZo0SdnZ2TZ7lzFo0CAddthhwTEr5l9zrMnUZQKSjz76yM5z8vTTT4fsHghOAAAAgEPAwIEDlZqaqjFjxthB8Kab1qxZs4KD5Dds2GC7cRUxgcuwYcP0xx9/qF69eurQoYNeffVVe56DlZeXZyd+/LNcAZM37BBm0q2ZrAarzYCfUBcGqG26h7oAAIC6INMntf9+T+aoA42tCNl3yWul+pE1e+3MAqn98878XIq6gI0fP97Op2LGtvzyyy92MP3dd99tZ6m/5pprDvqcjDkBAAAAcNDuv/9+TZ06VQ899JAd81LkmGOO0fPPP3/wJyQ4AQAAAFAZL7/8sp577jldeeWVNlNYkc6dO2vVqlWVOifBCQAAAICDtmnTpmAa4tLdvTwez8GfkOAEAAAAQGV07NhRX3311T7b33nnHXXt2rVS5yRbFwAAAICDZrKCmdTFpgXFtJa89957Wr16te3u9eGHHx78CWk5AQAAACr4rTkUi4NddNFF+uCDDzR37lzFxsbaYMXMMG+2nXXWWZU6Jy0nAAAAACrl5JNP1pw5c1RVHB6PAQAAAHAiM6fJjh079tm+e/duu68yCE4AAAAAHLR169bJ5/Ptsz0/P9+OQ6kMunUBAAAAqLCZM2cGX8+ePVsJCQnBdROszJs3z84QXxkEJwAAAAAqrH///vZfl8tls3UVFxERYQOTRx99VJVBcAKgfE1DXQCgFto7STKAijLz9X0f6kKgokzaYKN169b69ttv1bBhQ1UVghMAAACgIiO1a/rhg1uOtnbt2io/J8EJAAAAgErJzs7WF198oQ0bNqigoKDEvltuueWgz0dwAgAAAOCgff/99zr33HOVk5Njg5Tk5GSlpaUpJiZGjRs3rlRw4vDGIgAAAABOdNttt+mCCy7Qrl27VK9ePS1atEjr169Xt27d9Mgjj1TqnAQnAAAAAA7asmXLdPvtt8vtdissLMzOb9K8eXM99NBDGj169MGfkOAEAAAAQGWYtMEmMDFMNy4z7sQw855s3LixUudkzAkAAABwIO4QPNZ3y9G6du1qUwkfccQROvXUUzVmzBg75uSVV17RMccccyjeMgAAAAAn+s9//qOmTfdMijZ+/HglJSXphhtuUGpqqp577rlKnZOWEwAAAAAHJRAI2K5cRS0k5vWsWbP0Z9FyAgAAAOCgg5N27dpVemxJeQhOAAAAABwUMxDejDXZsWNH1Z63Ss8GAAAAoE544IEHdOedd+rHH3+ssnNWyZgTn8+nH374QS1btrQDYQAAAIBDSljhUtPXdLBBgwbZ2eE7d+6syMhIOxFjcTt37qyZ4GT48OHq1KmTrrnmGhuYmNRhCxYssFPVf/jhh+rTp09lTgsAAACglpg0aVKVn7NSwck777yjv/3tb/b1Bx98oLVr12rVqlU2p/G//vUvff3111VdTgAAAAAOMnjw4Co/Z6XGnJjJVVJSUuzrjz76SJdddpmOPPJIDRkyxHbvAgAAAIAaCU6aNGmin3/+2XbpMvmMzzrrLLvd9DkLC3N45zgAAAAAjlSpbl1XX321BgwYYGeEdLlcOvPMM+32b775Rh06dKjqMgIAAACoAyoVnNx77712Nkgz6Yrp0hUVFWW3m1aTkSNHVnUZAQAAgND3N6rpSTjcqnMqnUr40ksvtf/m5eVV66AYAAAAAM7i8Xhs6uBly5bZRouQxmNmrMl9992nww47THFxcfr999/t9rvvvlsvvPBClRUOAAAAgPNERESoRYsWNi6oSpUKTsaPH6+pU6fqoYceshOuFDFR0/PPP1+V5QMAAADgQGYKkdGjR1dqssUq7db18ssv67nnntMZZ5yh66+/PrjdzA5p5jsBAAAAcGh76qmntGbNGjVr1kwtW7ZUbGxsif3fffddzQQnmzZtUrt27fbZ7vf7bf8zAAAAAIe2/v37V/k5KxWcdOzYUV999ZWNkErPHN+1a9eqKhsAAADgDGYqv5qezi9MjnbPPfc4IzgZM2aMzcxlWlBMa8l7772n1atX2+5eH374YZUXEgAAAIAzLV26VCtXrrSvjz766D/VWFGp4OSiiy7SBx98oHHjxtm+ZSZYOe644+y2otniAQAAABy6tm/frssvv1yff/65EhMT7bbdu3frtNNO05tvvqlGjRrV3NQuJ598subMmWMLlZOTo/nz5+vss8+u7OkAAAAA1CI333yzMjMz9dNPP9mMXWb58ccflZGRoVtuuaXmWk6+/fZb252rV69eJbZ/8803dpb47t27V6owAAAAAGqHWbNmae7cuTrqqKNKjE2fPHlypRstKtVycuONN2rjxo37bDdjUMw+AAAAAIc2v99vJ2MszWwz+2osOPn555/tGJPSzOAXsw8AAAA4JLN11fTiYKeffrpuvfVWbd68uURjxW233WbnQ6yx4CQqKkrbtm3bZ/uWLVsUHl6pnmIAAAAAatkkjGZ8SatWrdS2bVu7tG7d2m578sknK3XOSkUSpg/ZqFGj9P777yshISE4Mt9MX0+2LgAAAODQ17x5czsLvBl3smrVKrvNjD8588wzK33OSgUnjzzyiE455RQ7CWNRHuNly5apSZMmeuWVVypdGAAAAADO5/F4VK9ePRsDmMaJqmqgqFRwcthhh2nFihV67bXXtHz5cluwq6++WldccUWZg2IAAAAAHDoiIiLUokUL+Xy+Kj1vpQeImMkX//GPf1RpYQAAAADUDv/617/ssA7Tcyo5OTm0wcmvv/6qzz77zE7CWDpVmJkxHgAAAMChPSB+zZo1atasmR3uYRovijPjUWokOJkyZYpuuOEGNWzYUCkpKXK5XMF95jXBSd0RM2yYYu+8U2EpKfIsX66Mm2+W59tvyzy23uDBSpw6tcS2QF6ettarV2Jb3Nixihk6VO7ERBV8/bXSb7hBvjVrgvtdSUlKePJJRV1wgUmwrbx331XGrbcqkJ1dTXcJVK2Yc4cp9uI7FZaUIs/a5cp47mZ5fi273kT3vlixl45WeNN2UniEfJt/VfaMR5X7+atlHh9/w9OKPed6pT8/XDkzHw9ubzRlrcKbtCpxbMa0kcp+98Eqvjug+sScM0yx/e9UWGKKPOuWK+P5/dSd4y9W7F8K605YhHxbflX2+48q94ty6s71Tyu27/VKf2G4cj7cU3fCGrVU3IC7FdnpdHtN367N9v1Z74yXvJ5qvVc4kLuyeW7/5DUdrH///lV+zkoFJ/fff7/Gjx+vf/7zn1VeINQe0QMGKH7iRKVff70833yj2OHDlTx7tlLbt5c/NbXM9/jT0+3+oECgxP7Yu+5S7C23aPfgwfKtXav6992355wdO0r5+faYxNdeU1jTptppBl5FRCjxpZeU8Nxz2n3lldV7w0AViD5pgOKvmaj0/7tenl++UeyFw5U8drZSb2gvf/q+9cafuVNZb4+X749VCngLFNXjfCXc+pJ86dtV8P0nJY6NOr6/ItsfL9+OTWVeO/O1u5Uze0pwPZCbWQ13CFSP6BMHKP7qiUp/prDuXDBcyWNmK/Wm/dSdd8bLt6mw7nQ/Xwk3F9adZaXqTq/+ijxy37oTfngHyeVW+tPXybd1jcJbHKOEYVPkiopV5rQ7q/2eASfzer22UWLIkCE6/PDDQxuP7dq1S5dddplqQmZmpoYPH26biszA+xNOOEHflvNkHjUrdsQI5UyZotypU+VdudIGKYGcHNUbMqT8NwUC8m/btnfZvr3kOYcPV9b99yt/5kx5f/hBuwcNUlizZooujMzDO3RQ9DnnKP3aa+VZvFier7+2rTXRl18ud9Om1X3LwJ8We9EI5XwyRbnzpsq7caUNUgL5Oap3Ztn1puDHL5S/aIa8f6ySb+vvyvngCXnXrVBkx5NKHOdObqaEfzyp3Y9eqUA5T3T9uZny794WXMx1gdoi9sIRypkzRbmfTpX3j5U2SLF154xy6s5PXyj/m2J158PCunNUGXXn2ie1+7ErFfCVrDv5389W+lNDVLB8jnzb1ir/2w+U/f4jij7+kmq9V6A2MHMbPvzwwzZIqUqVCk5MYPLJJyWfOlSXa6+9VnPmzLEDbX744Qc7x4rJnWxmn0QIRUQools35c+du3dbIGDXI3v3Lvdtrrg4NVq3To03bFDSjBkKNy0ihcJat7YtIsXPGcjIUME33wTPGdG7t/y7dsmzdGnwGHu836+IXr2q/j6BqhQeoYh23ZS/rFS9WT5XkR3KrzfFRR57usIOa6+Cn77cu9HlUuKIV5T134fl3fhzue+N+8tINXk1TQ0nfafYi++Q3A6fehgoXnfadrN1pUTdWTFXke0rWHc6Fdadn0vVneGvKOv9/ded4lwxCfJn7TzoWwAORaeffrq++OKL0Hfrateune6++24tWrRInTp12id98C233FIlhcvNzdW7775rJ3s086oY9957rz744AM9/fTTtnsZQsPdsKFc4eG29aM4s25aN8riXb1a6UOGyLNihdwJCYq94w41WLBAqUcfLf+mTXKnpATPUfqcRfvMv6VbW+Tzyb9zpx33AjiZO76hXGHhttWiOLMefljZ9cZwxcSr8Uub5IqIkvw+pT8zTAXFApzYv/xT8nltq0p5zFNjz2/f2S9VkR1OUP1BE+ROaqrMF2+vorsDqo+7fmHdSa9E3Xm+WN15bpgKigU4sRcX1p0Py687xYWltFXsuTcrY9odf+JugEPHOeeco5EjR9oGhG7duu0zIP7CCy+smeDkueeeU1xcnI2USkdLpu9ZVQUnppnI5E6Ojo4usd1075o/f36Z78nPz7dLkYyMjCopC/48z6JFdilSsGCBGq1cqZjrrlMWSRSAcpmxIWnDu8gVHaeozmcofshE203FdPkKb3ucYi+4VWm3Hbffc2S//1jwtXfdD7YPfsKwZ5X58ijJW1ADdwGEqO6MKKw7x55hx6zYuvPTFwpvc5xiz79Vabfvv+4U7/6VPGaW8ha8rdw5z1d72YHaYNiwYfbfiRMn7rPPxASVmQOlUsHJ2rVrVRPq16+v3r1767777tNRRx1lZ6B/4403tHDhQtt6U5YJEyZo7NixNVK+usyflqaA1yt3kyYltpt1/9atFTuJ1yvP998rvPBnWfS+0ucw695ly4LHuBs3LnmesDC5k5Plq+h1gRDxZ6Qp4PPKnViq3iQ2kX/3fn5/AwH5tvxmX3rXLlf44Ucp7tJR2vnjF4o8+mS5Exqr8QsbgoebJ8zxVz9qBwynDm1d5ik9q7+RKzxCYU1aybfpl6q6RaBa+DML605CJerO1sK6s66w7vxllHb+9IUiOxbWnSml6s5VhXXnur11x7QyNrjvMxWsWqD0p5njra7yuSSfu+av6WSlpxOpAwnKZMeaBAIBOyt9VFSUnnjiCTsTvdtddtFHjRql9PT04LJx48YaL3Od4PHYcR9RZ5yxd5vLZdcLFi6s2DncbkV06iTfli121WTnMq+Ln9NVv74ie/UKntOzcKHcSUkKP27vk67I00+35zIZwwBH83rkWbPUtn6UqDfHnqGCVRWsN4b5/5/ppmK6v372itJuOVZpt3YJLibjUPZ/H9bOe/uWe4rwNl0UMF0id5fqJgk4te78ttTWlRJ1p9MZKlhdybrzxStKu+1Y27JStNi68/7D2jm2b4kWkwb3f26vn/7U1ftkmQSwR15enkI6CeMff/yhmTNnasOGDSooKNkloKymncpq27at7TqWnZ1tu2g1bdpUAwcOVJs2bco83gQwZkH1y544UYnTpsmzZInNnBUzfLhcsbHKfekluz9h2jQ7liRz9Gi7Hnf33SpYtMjOWeJKTFScmR+lZUvlPr+3eTx70iTF/fvf8v76azCVsG/zZuXNmGH3e1etUt7HHytxyhSbHcwMzE946inlvfmm/IVBDuBk2e9PVOLwafKsWSLPL4sVc+FwuaJjlTuvsN4Mnyb/zk3KfHlPvYm9dKQ91rScmH7zUd3PVb0+f1f60zfY/YHMnfJmlhyca7J1+XZvDbaIRLQ/XhHte6lgxWe2m0tEh96Kv+YxO19DIHt3jX8GQGVkz5yoxFumyfPbEnl+XayY80vVnVsK686rhXXnkpH2WNNyYuvOceeq3ql/V/qz+6k7Po98u7bKt/mXvYHJfZ/Ll7peGVPvkDu+UfDY0mPHgLrI5/PpP//5j5555hlt27ZNv/zyi/2Obsamt2rVStdcc03NBCfz5s2zA1zMxVetWqVjjjlG69atsy0cxxV7ol2VzAAbs5g0xrNnz9ZDDz1ULddBxeW99ZYyGjVS3LhxeyZhXLZMO/v1Cw5YD2vRwmbRKjF54pQp9tiijFtpJ5xg0xAXyX7oIRvgmHlL7CSM8+fbcxbNcWKY+UxMQJI8b97eSRiraJwTUN3y5r+ljIRGivvruD2TMP6+TDvv7RdswQhr1EIKFKs3UbFKuP7/FNbgcAUKcm1a1N0T/2bPU1EBT77qnXy56l9+r/2S5t22VtkzH1P2jKp7kARUt7yv31JGfCPFXV5Yd9Yu085x/eRPL6fuRMcq4R/F6s6mVdo96W/2PBUV1fkshTc7wi5NXiiZJXTLxQ7vbwPUADPv4bRp0+z38qFDhwa3m9hg0qRJlQpOXAETURyknj172tH5ZmyHGReyfPlyNW7cWFdeeaX69etnZ4+vKiYQMUVs37691qxZozvvvNMOkP/qq6/2yRJWFtPakpCQoNVmDEuVlQqoIy4IdQGAWogMzcBBy/RI7f8n2yU/Pj5eTlL0XfLnkVL9kjmaql1mntTxAWd+LoYZA/7ss8/qjDPOCMYERY0XZty4aVSokTEnK1eu1KBBg4ITsJiUvyZ717hx4/Tggw+qKpkfxo033qgOHTrYa5500kk2YKlIYAIAAACgeph5B8tKUmUGyns8ZU8IXC3dukz3qqJxJmYMyG+//aajjz7arqelpakqDRgwwC4AAABAqJh50L0huKaTdezY0fZmatmyZYnt77zzjrp27Vpzwcnxxx9v5xkx6X3PPfdc3X777Xbylffee8/uAwAAAHBoGzNmjAYPHmxbUExriYkFVq9erZdfflkffvhhzQUnJhtXVlaWfW3GnZjX06dP1xFHHFGlmboAAAAAONNFF12kDz74wA7tMD2rTLBikmOZbWeddVbNBSfF0/iagpj0YQAAAADqlpNPPllz5sypsvO5Kxuc7NixY5/tu3fvLnf+EQAAAACo8uDEzGliJl0pLT8/3/Y5AwAAAIBq7dZlZoQvYtL5mpzPRUywYiZnNLNBAgAAAIcSkznLE4Jr1jUHFZz079/f/utyuezI/OLMvCMmMHn00UertoQAAAAA6oSD6tZlUoSZpUWLFtq+fXtw3SymS5dJHXb++edXX2kBAAAAOILJ0pWTk7PPdjNBu9lXY2NO1q5dq4YNG+4zGB4AAABA3TC2cEqR0kzAYvbVWHDy4IMP2nlNilx22WVKTk7WYYcdpuXLl1eqIAAAAABqj0AgYId7lGbiARMb1FhwYuY1ad68uX1t8hrPnTtXs2bN0jnnnKM777yzUgUBAAAA4HxJSUk2+DCByZFHHmlfFy0mYZaZgHHAgAE1Nwnj1q1bg8GJmZreXPzss8+2A+J79epVqYIAAAAATuUJQbYuj5xp0qRJttVkyJAhtvtW8Qy+kZGRNibo3bt3zQUnJlrauHGjDVBMi8n9999vt5tCljX/CQAAAIBDw+DCrL2tW7fWCSecYLP2VpVKBSeXXHKJ/vrXv+qII46wM8Wb7lzG999/r3bt2lVZ4QAAAAA4R0ZGhuLj4+3rrl272sxcZilL0XHVHpw89thjtrnGtJ489NBDiouLs9u3bNmiYcOGVeaUAAAAABzO9KAy3/kbN26sxMTEMgfEFw2Ur0yPqkoFJ6bp5o477thn+2233VaZ0wEAAACoBT799NNgJq7PPvusys9f4eBk5syZtvuWCUzM6/258MILq6JsAAAAABzk1FNPLfN1jQcn/fv3t1m6TBOOeV2eyjbhAAAAAE7lLVxq+ppO9uWXX+53/ymnnFJ9wYnf7y/zNQAAAIC6p0+fPvtsKz4GpTINFgc9CaMJTF588UWdf/75OuaYY9SpUydddNFFevnll+3gFwAAAACHvl27dpVYtm/fbqcZ6dGjhz755JNKnfOgBsSb4MOMJ/noo4/UuXNnG5iYbStXrtRVV12l9957TzNmzKhUQQAAAADUHsUnXyxiZoc3EzGOGDFCS5curd7gZOrUqbZv2bx583TaaaftM3LfjEUxLSiDBg066IIAAAAAqP2aNGmi1atXV+q9BxWcvPHGGxo9evQ+gYlx+umna+TIkXrttdcITgAAAIBD3IoVK0qsmx5VZg6UBx54QF26dKn+4MQUwEy6WB6TaviJJ56oVEEAAAAA1B4mADED4EuPOz/++OPtGPVqD0527txpm2nKY/aZwTAAAADAocRTuNT0NZ1s7dq1JdbdbrcaNWqk6OjoSp/zoIITkw4sPLz8t4SFhcnrdXpGZgAAAAB/VsuWLVXVDjpbl8nKFRUVVeb+/Pz8qioXAAAAAAe75ZZb1K5dO/tvcU899ZTWrFmjSZMmVe88J4MHD7YzxJu0YWUtZh+D4QEAAIBD37vvvqsTTzxxn+0nnHCC3nnnnepvOXnppZcqdREAAAAAh5YdO3aUOddJfHy80tLSKnXOg54hHgAAAADatWtnZ4Qv7eOPP1abNm2qv+UEAAAAqIu8Icie5ZWzmVngb7rpJqWmpto5Dw0zWfujjz5aqfEmBsEJAAAAgIM2ZMgQmxBr/Pjxuu++++y2Vq1a6emnn670OHSCEwAAAAAHxUwf8vrrr+uSSy7RDTfcYFtP6tWrp7i4OP0ZjDkBAAAAcFDM3IfXX3+98vLy7LqZfPHPBiYGwQkAAACAg9azZ099//33qkp06wIAAABw0IYNG6bbb79df/zxh7p166bY2NgS+4899tiDPifBCQAAAFCBzFk1nT3LK2e7/PLL7b/FZ4h3uVwKBAL2X5/Pd9DnJDgBUL6jQl0AoBbyh7oAQC2UH+oCoDLWrl2rqkZwAgAAAOCgtWzZUlWN4AQAAABAhcycOVPnnHOOIiIi7Ov9ufDCC3WwCE4AAAAAVEj//v21detWNW7c2L4uD2NOAAAAAFQrv99f5uuqQnACAAAAHICncKnpa9Y1TMIIAAAAoMI+/fRTdezYURkZGfvsS09P19FHH60vv/xSlUFwAgAAAKDCJk2apKFDhyo+Pn6ffQkJCbruuuv02GOPqTIITgAAAABU2PLly9WvX79y95999tlaunSpKoPgBAAAAECFbdu2zaYSLk94eLhSU1NVGQQnAAAAACrssMMO048//lju/hUrVqhp06aqDIITAAAAoILZump6caJzzz1Xd999t/Ly8vbZl5ubq3vuuUfnn39+pc5NKmEAAAAAFfbvf/9b7733no488kjddNNNat++vd2+atUqTZ482U6++K9//UuVQcsJAAAAcIiYPHmyWrVqpejoaPXq1UuLFy8u99gpU6bo5JNPVlJSkl3OPPPM/R5fpEmTJlqwYIGOOeYYjRo1ShdffLFdRo8ebbfNnz/fHlMZBCcAAADAIWD69OkaMWKE7Vb13XffqXPnzurbt6+2b99e5vGff/65rrjiCn322WdauHChmjdvbjNtbdq06YDXatmypT766COlpaXpm2++0aJFi+xrs61169aVvgdXIBAI6BBmJocx+ZZXS6of6sIAtc1doS4AUAv5Q10AoPbJzJfaP7lnAr+y5s5wwnfJ90ZKsdE1e+3sPOmSByr+uZiWkh49euipp56y636/3wYcN998s0aOHHnA95vuWKYFxbx/0KBBCgVaTgAAAAAHy8jIKLHk5+fvc0xBQYGdW8R0zSridrvtumkVqYicnBx5PB4lJycrVAhOAAAAgAPwSfLW8OIrvLZp/TCtN0XLhAkT9imf6VJlWj5Kj/Uw61u3bq3QPf7zn/9Us2bNSgQ4NY1sXQAAAICDbdy4sUS3rqioqCq/xgMPPKA333zTjkMxg+lDheAEAAAAcLD4+PgDjjlp2LChwsLC7OztxZn1lJSU/b73kUcescHJ3LlzdeyxxyqU6NYFAAAA1HKRkZHq1q2b5s2bF9xmBsSb9d69e5f7voceekj33XefZs2ape7duyvUaDkBAAAADgEjRozQ4MGDbZDRs2dPTZo0SdnZ2br66qvtfpOB67DDDguOWXnwwQc1ZswYvf7663ZulKKxKXFxcXYJBYITAAAA4BAwcOBApaam2oDDBBpdunSxLSJFg+Q3bNhgM3gVefrpp22Wr0svvbTEecw8Kffee69CgeAEAAAAOABP4VLT1zxYN910k13KYga7F7du3To5DWNOAAAAADgCwQkAAAAARyA4AQAAAOAIBCcAAAAAHIHgBAAAAIAjEJwAAAAAcARSCQMAAAAH4C1cavqadQ0tJwAAAAAcgeAEAAAAgCMQnAAAAABwBIITAAAAAI5AcAIAAADAEcjWBQAAAByAp3Cp6WvWNbScAAAAAHAEghNUWsywYWq0dq1ScnPVYNEiRfToUe6x9QYPVtNAoMRi3lda3Nixarx5s1JycpQ8Z47C2rUrsT/siCOUNGOGmqSmqkl6uhp89ZUi+/SplvsDqktM72Fq9M+1Srk/Vw1uXKSIw/dTd3peqwbXf6km9+y0S/K1c8o8PrxxByUNfl9Nxu5Wk/uy1OCmxXInNg/ud8c1UcLAl9X431vs/oa3LFX0MZdU2z0C1SHmhGFqNGqtUv6TqwY3L1JE8wPUnRu+VJOxO+2S/I85+xzf9OFAmUvsqXfse8KwSDW87Xu7P7xZ5+q4PQAEJ6is6AEDFD9xorLGjlXaccfJu3y5kmfPlrtRo3Lf409P17aUlOCyvWXLEvtj77pLsbfcovTrr1dar14KZGfbcyoqKnhM8ocfSuHh2nH66Urr1k2e5cuV9OGHcjdpUq33C1SV6GMHKP78icqaN1ZpTxwn75blSr5mttyxZdedqDZ9lLvsDe147jSl/V9v+dI3KvnaT+SObxY8Jiy5jRpcP1/e7au049k+SnvsWGXNu0/y5AWPSRz4ssIbtdeuqRcq7bFOyvvxPSVe+ZbCm3WpkfsG/qzozgMUf8FEZc0Zq7RJx8m7ebmSr91P3WlbWHeePU1pT/WWb/dGJQ8tWXe2jUspseyefrUCfr/yfnh3n/PFn/eQfOmbq/UeAdSC4KRVq1ZyuVz7LDfeeGOoi1anxY4YoZwpU5Q7daq8K1fagCKQk6N6Q4aU/6ZAQP5t2/Yu27eXPOfw4cq6/37lz5wp7w8/aPegQQpr1kzR/fvb/a4GDRR+5JHKeuABu9+3Zo0yR46UOzZW4cccU923DFSJ2JNHKGfxFOUumSrv9pVK/+/1CnhyVK9H2XVn95t/U86ip20Q40tdrfR3rpVcbkW1OyN4TP1+45W3+iNlfvxPeTcvk2/n78pf+YH82anBYyJanqCcr5+U549v5du5Vlmfjlcgd7ciDutWI/cN/Fmxp4xQzjfF6s57hXWnZzl1542/KWfh0zaIsXXn7cK6c8TeuuPP3FZiiT76IhX89pmtI8VFte+nqCPPVuaHZbSoAKhbwcm3336rLVu2BJc5c+bY7Zdddlmoi1Z3RUQools35c+du3dbIGDXI3v3Lvdtrrg4NVq3To03bLBds8I7dgzuC2vdWmFNm5Y4ZyAjQwXffBM8Z2DHDnlXrVLMoEFyxcRIYWGKue46+bZtk2fp0uq6W6DqhEXYYCD/11J1Z81cRbYov+4U54qIkSssQv6cnYUbXIrqcJ58ab8o+ZpZanz3NttVLKrjRSXe51m/QNGdB8pVL8m+x7xWRLQKfv+8Sm8RqNG68+tcRbasYN2JLFV3SnHHNVbUUecpZ/EL+2xPuHSKdr/5dxsMAajjwUmjRo2UkpISXD788EO1bdtWp556aqiLVme5GzaUKzzctn4UZ9bdKSllvse7erXShwzRrosu0u6//U1yu9VgwQK5DztszzkL33egc+4480yFd+2qJpmZSsnLsy04O/v1U2D37mq4U6BquWMayhUWLn9Wqd/zzG1y1y+77pRW/9wH5cvYbAMae87YxnJH1Vdsn5HKXz1LO58/W3k//VdJf39Pka1PCb5v12sD7BezlHt3KmV8vhIueVa7Xr5Yvh2/VfFdAlXPHVtO3cmqRN0pHuAUU6/7YAXyM22Xx+ISBk5VzqJn5PmDh2B1nbdYxq6aWryqe2pVKuGCggK9+uqrGjFihO3aVZb8/Hy7FMnIyKjBEqI8nkWL7FKkYMECNVq50rZ8ZI0ZU+HzJEyebLuD7Tj5ZAVycxVz7bVK/uADpfXoIf/WrdVUesAZYvv8U/U6X27Hlchb+P85155nTPk/va/s+ZPsa9MFLLLlCYo5/noVrP3Sbqt/9n1yRSdqx3NnyJ+Tpuij+yvpyre045mT5d36Y+huCqgBsaf9U/W6XK4dzxSrO6XE9Bii3O9eK7E/5sSbbfCf9emEGiwtULc5vuWkuBkzZmj37t266qqryj1mwoQJSkhICC7Nm+/NVoOq4U9LU8Dr3WcQulmvcIDg9crz/fcKL8zGVfS+/Z0z8vTTFXX++dp9+eXyLFgg7/ffK+PGG22QYrKBAU5ngoKAz2szZxXnrt9E/sz9153YU25XXJ+RtmXEu/WHUuf0yLv95xLHmz75YYktggPmY0+8WenvDFHBb5/Ku2WFsuaOk+ePJYrpzfg9OJ8/u5y6E1eBunPq7Yo7baR2Tjlb3i17605xEa1PshnvchY/X2J7VLvTFdGyt1Im5CvlAY8a/XON3d7wliW2RQVAHQ9OXnjhBZ1zzjlq1mxvpo3SRo0apfT09OCycePGGi1jneDx2DEeUWfsHVRo+72fcYYKFi6s2DncbkV06iTfli121bd2rX1d/Jyu+vUV2atX8Jx2nInh95c8l1l316pfZdRVPo88m5aWGMxu6067M1Swofy6E3vqnYo7427tfLGfff8+5/zjW4U1al9ic3jDI+XbtX7PJSIL606gVN0J+OQqbHkBam3dWb+futOnsO4832+/3bJiel6jgo1LbOBeXPr7tyhtYmelPdbFLjtfPNdu3/3aQGXO+ldV3BmA2tqta/369Zo7d67ee69kX9DSoqKi7ILqlT1xohKnTZNnyRJ5Fi9WzPDhcsXGKvell+z+hGnT5N+0SZmjR9v1uLvvVsGiRTbDlisxUXF33qmwli2V+/zep1TZkyYp7t//lvfXX22wUv++++TbvFl5M2bY/SZICezaZc+dNW7cnm5dQ4fawfT5//tfiD4J4OBkfzVRiQOm2VYLzx+LFXPScLkiYpW7pLDuDJgmf8YmZc7aU3diT71L9c8ep91v/FW+neuCT44DBVkKFGTb11lfPKykv063XbhMpqGoI/sp6qgLtOO5PXMAmRTD3rRfFX/xs8r83x3y5+yw3boi252lXVPPD9lnARyM7C8nKnFgYd3ZuFgxJw+XKzJWud8W1p3Lp8mfvkmZHxfWnT53qX7fcdr9+l/l27XOtlAagfy9dcdwRdVX9LGXKfOD2/e5pn/3RhUP6cMKsuy/3h2/2WsBqMPByUsvvaTGjRvrvPPOC3VRICnvrbeU0aiR4saNU1hKijzLltmB6UXpgcNatCjRwuFKSlLClCn2WP+uXbblJe2EE2wa4iLZDz1kA5yE556TOzFRBfPn23OqcAyRydZl1uuPH68Gn35qs4Z5f/rJDrL3rij5tAtwqrwVbykjtpHizh6nsPop8mxeZltE/FmFdcd0xSrWwhFz/A1yhUcp6e8l513InHOvsuaOta/zf5phUxLHnTZKYRc+IW/qau169S/yrPt6z8F+r33iW/+cB5R01QdyRcXJl7ZG6W8NVv7qj2vy9oFKy1teWHf6Fqs7z++n7vQurDuDStWdT+61c6UUie5yuVxy2TlRAISeKxAIBORwfr9frVu31hVXXKEHHnjgoN5rBsSbsSerzYDQaishcIi6K9QFAGqhUr3nABxYZr7U/knZLvnx8fFykqLvkpNHSvWia/bauXnSjQ8483OpLrWis7HpzrVhwwYN2d8EfwAAAABqtVrRrevss89WLWjgAQAAAHCot5wAAAAAOPQRnAAAAABwBIITAAAAAI5QK8acAAAAAKHkCcEXZ4/qHlpOAAAAADgCwQkAAAAARyA4AQAAAOAIBCcAAAAAHIHgBAAAAIAjkK0LAAAAOACyddUMWk4AAAAAOALBCQAAAABHIDgBAAAA4AgEJwAAAAAcgeAEAAAAgCMQnAAAAABwBFIJAwAAAAfgk+QNwTXrGlpOAAAAADgCwQkAAAAARyA4AQAAAOAIBCcAAAAAHIHgBAAAAIAjkK0LAAAAOACPpLAQXLOuoeUEAAAAgCMQnAAAAABwBIITAAAAAI5AcAIAAADAEQhOAAAAADgC2boAAACAAyBbV82g5QQAAACAIxCcAAAAAHAEghMAAAAAjkBwAgAAAMARCE4AAAAAOALZugAAAIAD8BYuNX3NuoaWEwAAAACOQHACAAAAwBHo1gWgfDtDXQCg9pl7eKhLANQ+uXwjRSFaTgAAAAA4AsEJAAAAAEegEQ0AAACoQOYsTwiuWdfQcgIAAADAEQhOAAAAADgCwQkAAAAARyA4AQAAAOAIBCcAAAAAHIFsXQAAAEAFMmeFheCadQ0tJwAAAAAcgeAEAAAAgCMQnAAAAABwBIITAAAAAI5AcAIAAADAEQhOAAAAADgCqYQBAACAA/CE4Km+R3UPLScAAAAAHIHgBAAAAIAjEJwAAAAAcASCEwAAAACOQHACAAAAwBHI1gUAAAAcANm6agYtJwAAAAAcgeAEAAAAgCMQnAAAAABwBIITAAAAAI5AcAIAAADAEcjWBQAAAByAT5I3BNesa2g5AQAAAOAIBCcAAAAAHIHgBAAAAIAjEJwAAAAAcASCEwAAAACOQLYuAAAA4AA8klwhuGZdQ8sJAAAAAEcgOAEAAADgCAQnAAAAAByBMSeotJhhwxR7550KS0mRZ/lyZdx8szzffnvA90UPHKikN99U3owZ2nXxxcHt7saNVf/BBxV19tlyJyYq/8sv7Tl9a9aUeH/E8cer/vjxiujVS/L55Fm2TDv79pXy8qrlPoGqFtNnmGL73qmwhBR5Ni5Xxhs3y7Ou7LoT3fVixZ47WuGN20lhEfJt/1XZnzyq3EWvljgu7sKxijl5qNwxiSpY87XSX7tBvu17607cuaMV1ek8RTTvooCvQNtuTar2+wSq2pE9hunoE+5UvbgU7dq6XIs/vlk7NpdddxIadVTnPuPUoFk3xSW20rezhmvVN4+XOObiW9fafaWt/nayFn90U3C94eHHq+vp49XwsF7yB3zatXWZ5r3aVz4vf3eAqkbLCSolesAAxU+cqKyxY5V23HHyLl+u5Nmz5W7UaL/vC2vZUvGPPGIDj9KSZsxQWJs22nXRRUrt2lW+9euVPHeuXDExJQKT5FmzlP/JJ9rRs6fSevRQzlNPSX5/tdwnUNWiuw9Q/ICJyvpgrNLuO07eP5YrefhsueuXXXf82TuV9dF47ZjQW2ljj1XO1y8p4aqXFHn02cFjYvvdpdgzblH6q9cr7T+9FCjItudUeNTeE4VHKm/p28r+4umauE2gyrU8eoC6nz1RK74Yq/89e5x2bVuuM/42W9ExZded8IgYZe3+Xd/PHamczC1lHvPRlB56+5GU4DLn5TPt9vU/vV0iMDnjylna/Nsn+uj5nvp4Sg+tXvyUAgH+7gB1Mji599575XK5SiwdOnQIdbHqvNgRI5QzZYpyp06Vd+VKpV9/vQI5Oao3ZEj5b3K7lfjaa8q85x75fv+9xK6wI45QZO/eyrjhBnmWLJHvl1/sa1e9eoq+4orgcfGPPabsJ55Q9oMPyvvzz/a4vLfflgoKqvN2gSoTe9YI5Xw1RbkLpsq7ZaUNKAIFOap3Ytl1p+CXL5T//Qx5t66SL/V35cx7Qt4/Viiy3Ul7z3nGcGX9737lL58p76YftPvFQQpLbKborv2Dx2TNvFfZcyfZ/UBt1PH4Efr1uyn6bdlUpaet1KIPr5fPk6O2XcuuOzs2L9F3c+7Sup+my+/LL/OY/Jw05WVvCy6HH3m+Mnau0bb1XwSP6d73Ma1a/IR++vpBpaf+rIwdv2j9z2/L7+PvTl3jCdFS1zg+ODGOPvpobdmyJbjMnz8/1EWq2yIiFNGtm/Lnzt27LRCw6ybAKE/cmDHyb9+u3Bdf3GefK2rPE95A8a5ZgYCUn6/Ik/Z8CTOtMpHHH2/P0eDrr9V461Ylf/65Ik48sUpvD6g2YRGKaNlN+StL1Z2VcxXZtvy6U1xkh9MVltJeBb/saX0Ma9haYYlNS5wzkJuhgt+/UWSbip0TcDq3O0LJzbpp6+/F6o4C2vL7XDU6vHeVXaP1sX/Tb9/v/RtlWmUaHX688rK3q++Qr3Xp7Vt19uDP1ag5f3eAOh2chIeHKyUlJbg0bNgw1EWq09wNG8oVHi7/tm0ltpt1d0pKme8xAUTMNddo99ChZe73rlol7/r1qj9hglyJiTYAir3rLoU1b66wpk3tMabLl1H/3nttq83Ofv3k+e47NZg3T2Ht2lX5fQJVzR3XUK6wcPkzStWdjG1yx5dddwxXvXg1eTJTKU8XKPmW/9kxKgWFwYg7Yc/79jln5rbgPqC2i4ppKLc7XLnZJX/PTWuHGX9SFZp36K/I6ETbMlMkLmnP353Op96rNd9N0bzX+mnn1u901qB5qp/M3x2gzgYnv/76q5o1a6Y2bdroyiuv1IYNG8o9Nj8/XxkZGSUWhJYrLk6Jr7yi9KFDFdixo+yDvF7tuuQShR95pFJ27VJKTo4iTztNeR99pEDReBL3nl/XnGef3dOdbNkyZY4YIe/q1YrZX3cyoJYL5GUqbVwXpf2nhzL/+y87ZiXyyFNDXSzgkNKu6zXa/OvHys3aOz7F5drzd+eXpc/aoMUMhF8ye4QydqxWu3K6kwE4xLN19erVS1OnTlX79u1tl66xY8fq5JNP1o8//qj69evvc/yECRPsMag+/rQ0BbxeuZs0KbHdrPu3bt3n+LC2bRXeurWSPvig2MF7/oef4vEotX17OwbF+913SuvaVa74eLkiI+11GixaZMeg2Otu2fMHw4w1Kc6MeQlr0aI6bhWoUv6sNAV8XrnjS9Wd+CbyZ+xbd4ICAflSf7MvvRuXK7zpUYo7d5R2/vKF/Olb956j8LVdr99E3o3LqutWgBplxob4/V7Viy1Zd6Jjmyg3az91p4JiE1oopc2Z+uKtS0psLwpUzFiT4tJTVyo2nr87QJ1sOTnnnHN02WWX6dhjj1Xfvn310Ucfaffu3XrrrbfKPH7UqFFKT08PLhs3bqzxMh/yPB55li5V1Bln7N3mctn1goULy+yylXrMMUrr0iW45M+cqYLPPrOvfaV+RoGMDBuYmK5aEd27K+/99+1237p18m3apLD27Uscb1pbTGYvwPF8HnnWL1XUUaXqzlFnqOC3fetOuczT3MJMXL60tfLt3qKoDnvP6Yqur8g2vVTw+0GcE3Awv9+jnZuXKqVNsbojl11P/ePP/5637XK1HVey6Zf/ldietXudcjI2Kb5hyb878Q2OVFY6f3eAOtlyUlpiYqKOPPJIrSk190WRqKgou6B6ZU+cqMRp02yrhmfxYsUMHy5XbKxyX3rJ7k+YNk3+TZuUOXq0HdTu/emnEu/3795tI+Pi26MvvVT+1FT5NmxQeKdOin/8cTsXSsGcOcFjsh5+WPXHjrWpi838JvUGD1Z4hw7ademlNXj3QOVlz5moxCHT5Fm3RJ61ixVz5nC5ImOV+3Vh3RkyTf5dm5T539F2PfackfZY03LiCo9SVKdzVe/4v9t5TILnnDdJcef9W97tv9pgpf5F98m3e7Pyvp8RPMad3Fzu2GSFJbeQ3GEKb97ZbjdzoQTys2v8cwAO1s+LJurE/tNsFq60TYt11PHDFR4Rq9+W7ak7J/SfptzMTfp+3ujgAHcz14l9HRapmPjDlNSks7wFWcrctaclcg+XDU5+Xz5NgYBvn+v+tOBhde4z1s6rYrp1tekyWPENO+iLt/m7U9d4Q/BU36u6p9YFJ1lZWfrtt9/097//PdRFqdPy3npLGY0aKW7cuD2TMJqJEPv1s5m0DNvN6iDnHnE3bWrnTjHdw3xbtij35ZeVdd99JY7JefxxuaKjbUphV3KyDVJ2nHXWPqmJAafKW/KWMuo3UtxF4xQWbyZhXKadj/eTP7Ow7pjgodj8Ca6oWCVc+X8KSzpcAU+uvFtWafcLf7PnKZI96yEb4CT8/bk9kzD+Ot+eU9696VPrXzROMSdcFVxvNGZPl68dD/ex6YoBp1v/01s2e5aZWHHPJIzL9Olr/WyLR1HXrOJ1p179Zjr/+r1dG83kjWbZuu5zzZl2WnB70zZnKi6xpdYUy9JVnJm4MSw82qYUjqqXrJ3blmvuK2cpaxd/d4Dq4AoETL5W57rjjjt0wQUXqGXLltq8ebPuueceLVu2TD///LMaHWDCP8MMiE9ISNBq88e5RkoMHEKuDXUBgNpn7uGhLgFQ++TmSdc9INslPz4+Xk5S9F1y4EgpMrpmr12QJ0136OdSZ8ec/PHHH7riiivsgPgBAwaoQYMGWrRoUYUCEwAAAKAumTx5slq1aqXo6GibWGrx4sXlHvvTTz/pL3/5iz3eTHQ+adIkhZrju3W9+eaboS4CAAAA4HjTp0/XiBEj9Mwzz9jAxAQbJqHU6tWr1bhx432Oz8nJsVN1mORTt912m5zA8S0nAAAAAA5s4sSJGjp0qK6++mp17NjRBikxMTF68cWyx1T16NFDDz/8sC6//HLHJJQiOAEAAAAcLKPUBONm0vHSCgoKtHTpUp155pnBbW63264vLGOqB6ciOAEAAAAqkNbXU8OLt/DazZs3t4PyixYz6XhpaWlp8vl8alJqkmyzvrWMSbKdyvFjTgAAAIC6bOPGjSWydTmlC1Z1IDgBAAAAHCw+Pv6AqYQbNmyosLAwbdu2rcR2s56SkqLagm5dAAAAQC0XGRmpbt26ad68ecFtfr/frvfu3Vu1BS0nAAAAwCFgxIgRGjx4sLp3766ePXvaVMLZ2dk2e5cxaNAgHXbYYcExK2YQvZnYvOj1pk2b7GTncXFxateuXUjugeAEAAAAOAQMHDhQqampGjNmjB0E36VLF82aNSs4SH7Dhg02g1eRzZs3q2vXrsH1Rx55xC6nnnqqPv/885DcA8EJAAAAcACeWnLNm266yS5lKR1wmJnhA4GAnIQxJwAAAAAcgeAEAAAAgCMQnAAAAABwBIITAAAAAI5AcAIAAADAEcjWBQAAAByAV5IrBNesa2g5AQAAAOAIBCcAAAAAHIHgBAAAAIAjEJwAAAAAcASCEwAAAACOQLYuAAAA4AA8deSaoUbLCQAAAABHIDgBAAAA4AgEJwAAAAAcgeAEAAAAgCMQnAAAAABwBLJ1AQAAAAfgk+QKwTXrGlpOAAAAADgCwQkAAAAARyA4AQAAAOAIBCcAAAAAHIHgBAAAAIAjkK0LAAAAOACPpEANX9OruoeWEwAAAACOQHACAAAAwBEITgAAAAA4AsEJAAAAAEcIr1NhmCvUhQBqmZdCXQCg9llxd6hLANQ++aEuAByj7gQnAAAAQCWRratm0K0LAAAAgCMQnAAAAABwBIITAAAAAI5AcAIAAADAEQhOAAAAADgCwQkAAAAARyCVMAAAAODAtL5e1T20nAAAAABwBIITAAAAAI5AcAIAAADAEQhOAAAAADgCwQkAAAAARyBbFwAAAFCBzFmBGr6mT3UPLScAAAAAHIHgBAAAAIAjEJwAAAAAcASCEwAAAACOQHACAAAAwBHI1gUAAAAcgEeSv4av6VPdQ8sJAAAAAEcgOAEAAADgCAQnAAAAAByB4AQAAACAIxCcAAAAAHAEsnUBAAAAB+CVFKjha/pU99ByAgAAAMARCE4AAAAAOALBCQAAAABHIDgBAAAA4AgEJwAAAAAcgWxdAAAAwAF4JPlr+Jo+1T20nAAAAABwBIITAAAAAI5AcAIAAADAEQhOAAAAADgCwQkAAAAARyA4QaXF3DBMjdasVUpWrhosWKSIHj0q9L7oAQPV1BtQ0rv/LbHd3bixEl54SY03bFJKRraS/vexwtq1K3FM/P89o0ar1yglM0eNt2xX0nszFNa+fZXeF1DdqDtA5ZzQY5hG3bpW//lXrm6+ZpGaNyu/7jRp1FGDLnvHHv/wPQGd1OvWfY457aSRuuXaxbpvZIbuuWObBg/8rxo1OHKf41oefryuGzRP40dl6b6R6brhqi8UHh5d5fcHZ/MWZuyqycWruofgBJUSfdkAxT8yUVn3jVVaj+PkXb5cyR/NlrtRo/2+L6xlS8U/9Ijyv/pyn332y1KbNtp1yUVK7d5VvvXrlTx7rlwxMcFjPN8tVfq1Vyv1mKO089y+ksulBh9/Irn5VUbtQN0BKqfz0QN0wdkTNeeLsZr07HHavG25rv3bbMXGlF13IiJitGP37/po7khlZG4p85i2LU/Vgm8n66kXjtdzr5ylMHeEhv7tE/ve4oHJNVfO0i+/faInnu+pJ6b00NeLn1IgUNNJZYG6wfF/lZ5++mkde+yxio+Pt0vv3r318ccfh7pYdV7sbSOU8/wU5U6bKu/KlUofdr0COTmqd/WQ8t/kdivxldeUOfYe+X7/vcSusCOOUOTxvZVx4w3yLFki3y+/2NeuevUUffkVweNyn5+igq++sl++vN9/r8wx/1ZYixYKa9WqOm8XqDLUHaByTjl+hL75boqWLJuq7Wkr9d6H18vjyVHPrmXXnT82L9H/5tyl5T9Nl9eXX+Yxz792jpYsn6ZtqT9ry7YVmv7+VUpKbKnDm3YLHnNB38f09eIn9NnXD9rjUnf8ohU/vy2fr6Da7hWoyxwfnBx++OF64IEHtHTpUi1ZskSnn366LrroIv3000+hLlrdFRGhiOO6KX/e3L3bAgG7br4klSfu7jHyb9+u3Jde3GefKypqz2ny8kqcU/n5ijzxpDLPZ54K17vqanl//12+jRv/1C0BNYK6A1SKadE4rFk3/fr73roTUMCutzy8/LpzsKKjEuy/Obk77b+mVca0nGRlb9eNQ77WmNu36vrBn6tV8xOr7JoAallwcsEFF+jcc8/VEUccoSOPPFLjx49XXFycFi1aFOqi1Vnuhg3lCg+Xf/u2EtvNujslpcz3RJx4omKuvka7rxta5n7vqlXyrl+v+uMnyJWYaL/Exd55l8KaN1dY06Yljo25/gY12Z1p+9ZH9z1HO/udJXlMz0zA2ag7QOXExjRUmDtcWdkl645Zrx9Xdt05WC65dGG/SVq7Yb62pe55ANogqY3996xT77WtNs+/1k+btn5nx580TC45rgtAHQlOivP5fHrzzTeVnZ1tu3eVJT8/XxkZGSUWhJYrLk6JU19R+vVDFdixo+yDvF7tuuwShR9xpFLSdtlBu5F9TlPexx8p4C/Zrzf39deU1r2rdpx2iry//qKkN96SCp8eA4cS6g5Qcy4+b7JSGh+j1965PLjN5drzNWnR0mdtd7LNW5fpg9kjlLpjtXqU050MwJ8Trlrghx9+sMFIXl6ebTX573//q44dO5Z57IQJEzR27NgaL2Nd4k9LU8DrlbtxkxLbzbp/69Z9jg9r21bhrVsracYHxQ7e8z/8lDyPUju2t/3ovd99Z784ueLj5YqMtNcxmYxMP/riAhkZ8pllzRoVLFqkJmm7FN3/YuVNf7O6bhmoEtQdoHKyc9Lk83sVF1uy7pj1zKx9687B6n/OkzrqiPP1f1NPUXrmpuD2jKw9A+m3p/5c4vhtqSuVGN/iT18XQC1tOWnfvr2WLVumb775RjfccIMGDx6sn38u+T+KIqNGjVJ6enpw2Uh/6qrn8djMP1Gnn7F3m8tl1wsWLSyz20lq52OU1q1LcMn/YKYKPv/Mvi7d5918gTJfrkwq1Ihu3ZX3wfvll8XlksssPP1FbUDdASrF5/do0+alatfmjBLdsMz6+j/2rTsHG5gc0+FiPfvy6dq1e12JfWY9PWOTGjUsmXbbpBvelb7+T10XtY83REtdUytaTiIjI9WuMGd/t27d9O233+rxxx/Xs88+u8+xUVFRdkH1yn5sohJfmibP0iXyfLtYMbcMlys2VrlTX7L7E16aJv/mTcr812g7MNdbKoGBf/duGxkX3x79l0vlT0uVb8MGhR/TSfGPPa6892eoYM4cuz+sdWs7z0P+nE/kT01V2OGHK+6ukQrk5ir/449q+BMAKoe6A1TOl4smamD/aTYL18ZNi3Xy8cMVGRGrb5ftqTuX959mWz0+njc6OIjezHViX4dFKiH+MDVr0ln5BVnases3u/3icyera6e/auqbFyk/P1P1C1tmcvPT5fXuSTLx+YKHdXafsdq8dbnt1tW9y2A1bthBr7x9aYg+CeDQViuCk9L8fr8dW4LQyXv7LWU0aqS4e8cpLCVFnuXLtPO8fjajkGFSlKpUf/cDcTdtaud/cDdpIt+WLcp99WVl3X9fcL/JRhR50smKvWW43ElJ8m/bpoKvvlTaySfYL1xAbUDdASpn+U9v2exZffuMs4PgTaBgBqibTFpGYkKLEnOPxNdvptuuXxZc73PCnXb5bd3nembaacFJHQ0zqWJx02dcZVMMG/O/eVwR4dG6sO9jiqmXbOdXMXOi7NhVMq03gKrhCgRMzknnMt20zjnnHLVo0UKZmZl6/fXX9eCDD2r27Nk666yzDvh+MyA+ISFBq91SfVeNFBkAUIdNvDvUJQBqn/w86ckHZLvkm3ntnKTou2SzkZI7umav7c+TNjv0c6mzLSfbt2/XoEGDtGXLFvuLYSZkrGhgAgAAAKD2cHxw8sILL4S6CAAAAABqgOODEwAAACDUPCFIc+tX3VMrUgkDAAAAOPQRnAAAAABwBIITAAAAAI5AcAIAAADAEQhOAAAAADgC2boAAACAA/CSratG0HICAAAAwBEITgAAAAA4AsEJAAAAAEcgOAEAAADgCAQnAAAAAByBbF0AAABABbJ1uWr4mgHVPbScAAAAAHAEghMAAAAAjkBwAgAAAMARCE4AAAAAOALBCQAAAABHIFsXAAAAcAAesnXVCFpOAAAAADgCwQkAAAAARyA4AQAAAOAIBCcAAAAAHIHgBAAAAIAjkK0LAAAAOAAv2bpqBC0nAAAAAByB4AQAAACAIxCcAAAAAHAEghMAAAAAjkBwAgAAAMARCE4AAAAAOAKphAEAAIAKpBJG9aPlBAAAAIAjEJwAAAAAh4jJkyerVatWio6OVq9evbR48eL9Hv/222+rQ4cO9vhOnTrpo48+UigRnAAAAACHgOnTp2vEiBG655579N1336lz587q27evtm/fXubxCxYs0BVXXKFrrrlG33//vfr372+XH3/8UaFCcAIAAAAcAiZOnKihQ4fq6quvVseOHfXMM88oJiZGL774YpnHP/744+rXr5/uvPNOHXXUUbrvvvt03HHH6amnnlKoHPID4gOBgP03a88/AABUq/y8UJcAqH0K8kt+b3Ok/NBdMyMjo8TmqKgouxRXUFCgpUuXatSoUcFtbrdbZ555phYuXFjm6c1209JSnGlpmTFjhkLlkA9OMjMz7b/dzO+6g3/fAQCHiAdCXQCgdn9vS0hIkJNERkYqJSVFWx/bGpLrx8XFqXnz5iW2mW5b9957b4ltaWlp8vl8atKkSYntZn3VqlVlnnvr1q1lHm+2h8ohH5w0a9ZMGzduVP369eVyuUJdHBRjngKYymZ+PvHx8aEuDlBrUHeAyqHuOJdpMTGBifne5jRmoPjatWtty0SoPhtXqe+wpVtNDiWHfHBimrMOP/zwUBcD+2H+QPBHAjh41B2gcqg7zuS0FpPSAYpZnKxhw4YKCwvTtm3bSmw366blpyxm+8EcXxMYEA8AAADUcpGRkerWrZvmzZsX3Ob3++167969y3yP2V78eGPOnDnlHl8TDvmWEwAAAKAuGDFihAYPHqzu3burZ8+emjRpkrKzs232LmPQoEE67LDDNGHCBLt+66236tRTT9Wjjz6q8847T2+++aaWLFmi5557LmT3QHCCkDH9Jc2ArkO53yRQHag7QOVQd3CoGzhwoFJTUzVmzBg7qL1Lly6aNWtWcND7hg0b7JCHIieccIJef/11/fvf/9bo0aN1xBFH2ExdxxxzTMjuwRVwdM42AAAAAHUFY04AAAAAOALBCQAAAABHIDgBAAAA4AgEJwAAAAAcgeAEAAAAgCMQnMCRdu/ebXN0mxR4Jp3dlClTQl0koNbIyclRy5Ytdccdd4S6KECt0apVKx177LH2785pp50W6uIAdRbznMCR6tevry+//FIxMTF28iAToFxyySVq0KBBqIsGON748eN1/PHHh7oYQK2zYMECxcXFhboYQJ1GywkcKSwszAYmRn5+vsx0PEzJAxzYr7/+qlWrVumcc84JdVEAADhoBCeoFqbV44ILLlCzZs3kcrnsbKOlTZ482TajR0dHq1evXlq8ePE+Xbs6d+6sww8/XHfeeacaNmxYg3cA1M56Y7pyTZgwoQZLDRwadce879RTT1WPHj302muv1WDpARRHcIJqYbpimcDC/DEoy/Tp0zVixAjdc889+u677+yxffv21fbt24PHJCYmavny5Vq7dq1ef/11bdu2rQbvAKh99eb999/XkUceaRegLqmKvznz58/X0qVLNXPmTP3nP//RihUravAOABRxBegrg2pmnkb997//Vf/+/YPbzFMr83Tqqaeesut+v1/NmzfXzTffrJEjR+5zjmHDhun000/XpZdeWqNlB2pTvRk1apReffVV2y0yKytLHo9Ht99+u8aMGRPCOwFq398c01p/9NFH66qrrqrRsgOg5QQhUFBQYJ9OnXnmmcFtbrfbri9cuNCum1aSzMxM+zo9Pd022bdv3z5kZQZqQ70x3bk2btyodevW6ZFHHtHQoUMJTFDnVaTumJaXor85JrD/9NNPbXACoOaRrQs1Li0tTT6fT02aNCmx3aybgbzG+vXr9Y9//CM4EN483erUqVOISgzUjnoDoHJ1xzwQu/jii+1rc6wJ7E1LC4CaR3ACR+rZs6eWLVsW6mIAtRbdUYCKa9OmjR3jCCD06NaFGmeybpk+8aUHuJv1lJSUkJULcDLqDVA51B2gdiE4QY2LjIxUt27dNG/evOA2MzjRrPfu3TukZQOcinoDVA51B6hd6NaFamEGFK5Zsya4btIBm25aycnJatGihU3pOHjwYHXv3t124Zo0aZIdkHj11VeHtNxAKFFvgMqh7gCHEJNKGKhqn332mUlRvc8yePDg4DFPPvlkoEWLFoHIyMhAz549A4sWLQppmYFQo94AlUPdAQ4dzHMCAAAAwBEYcwIAAADAEQhOAAAAADgCwQkAAAAARyA4AQAAAOAIBCcAAAAAHIHgBAAAAIAjEJwAAAAAcASCEwAAAACOQHACAAAAwBEITgAAAAA4AsEJANRSV199tf7973+HuhgAAFSZ8Ko7FQCgpvh8Pn344Yf63//+F+qiAABQZWg5AYAQ2b17t1wul77++mu7vmbNGnXo0MG2hgQCgf2+d8GCBYqIiFCPHj3+9LkAAHAKWk4AIERWrFhhA4rOnTtr/vz5GjhwoCZMmKBBgwYd8L0zZ87UBRdcYN//Z88FAIBT0HICACGyfPlytW3bVu+//74NJt54441gMLFx40b16dNHHTt21LHHHqu33367xHvNey688MIKncu4+OKLlZSUpEsvvbQG7xAAgIPjCtDeDwAhce2112r69OnKy8uzAcjSpUuD+7Zs2aJt27apS5cu2rp1q7p166ZffvlFsbGxWrlype3OlZaWpujo6AOey/j888+VmZmpadOm6Z133qnxewUAoCJoOQGAEDGtHd27d7eBw/fff68ZM2YE9zVt2tQGJkZKSooaNmyonTt3Brt0nXXWWcHA5EDnMkwrTP369Wvs3gAAqAyCEwAIUbatH3/8UbfddptOPPFE293q3nvvLXPwumkFMcc3b97crpuuWxdddFGlzgUAgJMRnABACJguWqYLVlHryN13320Htb/77rsljjOtJWbsyHPPPWfXt2/friVLluj8888/6HMBAOB0BCcAEAKmG1ZiYqJatGhh1zt16qRLLrnEtnj4/X67LT8/X/3799fIkSN1wgkn2G0ffPCBevbsabt5Hcy5AACoDRgQDwAOZP7X/Ne//lXt27e3QUYRk6HrpJNO0l133XXQ5zTjUZ566ikGxAMAHIvgBAAcyMxVcsopp9jMW0VeeeUVffzxx7riiiuC408q6swzz7QtLNnZ2UpOTrapiXv37l0NJQcAoPIITgAAAAA4AmNOAAAAADgCwQkAAAAARyA4AQAAAOAIBCcAAAAAHIHgBAAAAIAjEJwAAAAAcASCEwAAAACOQHACAAAAwBEITgAAAAA4AsEJAAAAAEcgOAEAAAAgJ/h/Gg5m4jZQnzMAAAAASUVORK5CYII=", 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" - ] - }, - "metadata": {}, - "output_type": "display_data" + "cell_type": "markdown", + "metadata": {}, + "source": [ + "With 3 iterations, the transpiled circuit now has 1006 gates.\n", + "\n", + "Higher values will yield even deeper, but even more accurate circuits.\n", + "\n", + "Interestingly, the smallest value (1) yields an empty circuit, because the identity gate is the best approximation of our rotation at this level of precision.\n", + "\n", + "The default parameter should be just fine for most of the work you will do, especially if you want to execute the circuit on an emulator. But should you notice errors even when working with very low noise levels, then you might want to tweak the `solovay_kitaev_max_iterations`." + ], + "id": "12" }, { - "data": { - "image/png": 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", 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" - ] - }, - "metadata": {}, - "output_type": "display_data" + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now that we understand how \"logical\" circuits differ from \"physical\" circuits, let us look at noise. Even if they are error-corrected, logical qubits aren't perfect. How good do they need to be to run your algorithm? This is what we will study in this part.\n", + "\n", + "We will use a simple algorithm (the swap test), define a quality metric for its results, then run it on a noisy backend emulating logical qubits and study the influence of backend parameters over the quality metric." + ], + "id": "14" }, { - "data": { - "image/png": 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", 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" - ] - }, - "metadata": {}, - "output_type": "display_data" + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### The Swap Test on a noiseless backend" + ], + "id": "15" + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In this first part, we're using the swap test demonstrated in https://github.com/Classiq/classiq-library/tree/main/algorithms/swap_test\n", + "\n", + "Let us just quickly remember that the swap test is a way to compute the overlap between two quantum states $|\\phi\\rangle$ and $|\\psi\\rangle$.\n", + "\n", + "Using the circuit below, it sets the first qubit in state $|q\\rangle_{\\rm test} = \\alpha|0\\rangle + \\sqrt{1-\\alpha^2}|1\\rangle$, with $\\alpha^2 = \\frac{1}{2}\\left(1+|\\langle \\phi |\\psi \\rangle |^2\\right)$.\n", + "\n", + "![image.png](attachment:image.png)\n", + "\n", + "When mesauring the first qubit, we therefore expect to get:\n", + "- 0 with probability 1, if the states are identical (up to a global phase)\n", + "- 0 and 1 with probability 1/2 each, if the states are orthogonal\n", + "\n", + "Let us check this with identical states and a noiseless emulator." + ], + "id": "16" + }, + { + "cell_type": "code", + "metadata": {}, + "source": [ + "# Compute amplitudes for a random 3-qubit state\n", + "\n", + "np.random.seed(12)\n", + "\n", + "NUM_QUBITS = 3\n", + "amps1 = 1 - 2 * np.random.rand(\n", + " 2**NUM_QUBITS\n", + ") # vector of 2^3 random numbers in the range [-1,1]\n", + "amps1 = amps1 / np.linalg.norm(amps1) # normalize the vector\n", + "amps2 = amps1 # we're testing identical states" + ], + "execution_count": 5, + "outputs": [], + "id": "17" + }, + { + "cell_type": "code", + "metadata": {}, + "source": [ + "# Write the main function preparing the states from their amplitudes, then performing the swap test on them\n", + "\n", + "\n", + "@qfunc\n", + "def main(test: Output[QBit]):\n", + "\n", + " state1 = QArray()\n", + " state2 = QArray()\n", + " prepare_amplitudes(amps1.tolist(), 0.0, state1)\n", + " prepare_amplitudes(amps2.tolist(), 0.0, state2)\n", + " swap_test(state1, state2, test)\n", + " drop(state1)\n", + " drop(state2)" + ], + "execution_count": 6, + "outputs": [], + "id": "18" + }, + { + "cell_type": "code", + "metadata": {}, + "source": [ + "# Create the model, synthesize and show the circuit\n", + "\n", + "\n", + "qmod = create_model(main)\n", + "qmod = set_execution_preferences(\n", + " qmod, execution_preferences=ExecutionPreferences(num_shots=10_000)\n", + ")\n", + "qprog = synthesize(qmod)\n", + "\n", + "show(qprog)" + ], + "execution_count": 7, + "outputs": [ + { + "output_type": "stream", + "text": [ + "Opening: https://platform.classiq.io/circuit/2v4oriRVHjxuxzy19IUGgWXH85b?login=True&version=0.73.0\n" + ] + } + ], + "id": "19" + }, + { + "cell_type": "code", + "metadata": {}, + "source": [ + "# Execute quantum program\n", + "res = execute(qprog).result()" + ], + "execution_count": 8, + "outputs": [], + "id": "20" + }, + { + "cell_type": "code", + "metadata": {}, + "source": [ + "# Read results\n", + "print(res[0].value.parsed_counts)" + ], + "execution_count": 9, + "outputs": [ + { + "output_type": "stream", + "text": [ + "[{'test': 0}: 10000]\n" + ] + } + ], + "id": "21" + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can see that all our shots yield 1: the circuit is working as expected." + ], + "id": "22" + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### The quality metric" + ], + "id": "23" + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Moving forward, we will use the same model and synthesize it for noisy hardware. This means we'll get imperfect results and will need a quality metric.\n", + "\n", + "We choose to go for the circuit's error rate as the quality metric, i.e. the share of results which are not 0. A 0.0 error rate means a perfect result, while bad results can in theory go all the way up to 1.0.\n", + "\n", + "Note that this choice is a good fit for cat qubits, since a cat qubit decoheres to a statistical mixture of 0 and 1. It would however not be a good metric for transmon-based architectures, which tend to decohere to 0 and will naturally have a low share of 1 in their results. In this case, using orthogonal states rather than identical states is probably a better idea." + ], + "id": "24" + }, + { + "cell_type": "code", + "metadata": {}, + "source": [ + "def results_error_rate(res):\n", + " return 1 - res[0].value.counts[\"0\"] / sum(res[0].value.counts.values())" + ], + "execution_count": 10, + "outputs": [], + "id": "25" + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let us check the quality of the noiseless emulation:" + ], + "id": "26" + }, + { + "cell_type": "code", + "metadata": {}, + "source": [ + "results_error_rate(res)" + ], + "execution_count": 11, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "0.0" + ] + } + } + ], + "id": "27" + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "As expected, the noiseless emulation has perfect quality." + ], + "id": "28" + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### The Swap Test on noisy logical qubits" + ], + "id": "29" + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let us now work with logical qubits.\n", + "\n", + "First, let us remember that a logical qubit, while error-corrected, isn't error-free:\n", + "- Not all errors are caught by error correction\n", + "- The error correction process itself may introduce errors\n", + "\n", + "Several parameters strongly affect the quality of a logical qubit and it is important to study how they affect your algorithm's results. This lets you better understand the specs of the hardware you will need to get reliable results.\n", + "\n", + "Today, we will be looking at three main parameters:\n", + "- The error correction code's distance, `distance`\n", + "- The cat qubit's quality, defined by `kappa_1` and `kappa_2`\n", + "- The number of photons in the cat qubit, `average_nb_photons`\n", + "\n", + "The first parameter, `distance`, roughly translates into how many physical qubits are used to perform error correction. A higher distance is supposed to bring stronger protection against errors, but also requires a bigger chip with more physical qubits. Two important notes:\n", + "- A higher distance only yields fewer errors if your qubits are good \"enough\", i.e. their error rate is below the error correction threshold. Above the threshold, increasing distance actually increases errors!\n", + "- In the specific case of cat qubits, the error correction code is only targeting phase-flip errors. This means that a higher distance actually increases the probability of getting bit-flips. Since the increase is only linear and cat qubits have a strong protection against bit-flips to begin with, the consequences are limited, but they will be visible in our study.\n", + "\n", + "The cat qubit quality parameters `kappa_1` and `kappa_2` can be defined as such:\n", + "- `kappa_1` is the rate at which the cat qubit loses a single photon and produces phase-flip errors\n", + "- `kappa_2` is the rate at which the cat qubit exchanges two photons with the environement and is stabilized\n", + "\n", + "Given this, one wants `kappa_1` to be small and `kappa_2` to be high. We will therefore look at the `kappa_2/kappa_1` ratio as a proxy for our qubits quality. The higher `kappa_2/kappa_1`, the better the cat qubit.\n", + "\n", + "Finally, `average_nb_photons` is the number of photons in the cat qubit. As it increases, bit-flip errors decrease exponentially and phase-flip errors increase linearly." + ], + "id": "30" + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let us now create a custom backend.\n", + "\n", + "You may pick from two preset backends:\n", + "- `AliceBobBackendNames.LOGICAL_EARLY`, which has somewhat high logical error rates (1e-3 to 1e-4)\n", + "- `AliceBobBackendNames.LOGICAL_TARGET`, which has logical error rates low enough to run Shor's algorithm on a 2048-bit number (~1e-15)\n", + "\n", + "These backends can both be customized and this is what we'll do here. We'll start from `LOGICAL_TARGET` and tune it to make it terrible at phase-flips.\n", + "- The `kappa_2/kappa_1` ratio is set to 10, the minimum allowed by the backend. It is below the error correction threshold (which is somewhere around 1e3). This will generate a lot of phase-flips.\n", + "- `distance` is set to 31; it is expected that real logical qubits will not use distances this large. Because we made our qubits under threshold, this will further decrease the performance of our logical qubits.\n", + "- `average_nb_photons` is set to 19, which means excellent bit-flip error rates but also low phase-flip performance." + ], + "id": "31" + }, + { + "cell_type": "code", + "metadata": {}, + "source": [ + "backend_preferences = AliceBobBackendPreferences(\n", + " backend_service_provider=ProviderVendor.ALICE_AND_BOB,\n", + " backend_name=AliceBobBackendNames.LOGICAL_TARGET,\n", + " kappa_1=100,\n", + " kappa_2=1e4,\n", + " distance=31,\n", + " average_nb_photons=19,\n", + ")\n", + "execution_preferences = ExecutionPreferences(\n", + " num_shots=10_000,\n", + " backend_preferences=backend_preferences,\n", + ")\n", + "\n", + "# Prepare for HW aware synthesis\n", + "preferences = Preferences(\n", + " backend_service_provider=ProviderVendor.ALICE_AND_BOB,\n", + " backend_name=AliceBobBackendNames.LOGICAL_TARGET,\n", + ")\n", + "\n", + "# Create Model, set settings and perform HW aware synthesis\n", + "model = create_model(main)\n", + "model = set_execution_preferences(model, execution_preferences)\n", + "model = set_preferences(model, preferences=preferences)\n", + "qprog = synthesize(model)\n", + "\n", + "# Execute Quantum Program and show results\n", + "res = execute(qprog).result()\n", + "print(res[0].value.parsed_counts)\n", + "\n", + "show(qprog)" + ], + "execution_count": 12, + "outputs": [ + { + "output_type": "stream", + "text": [ + "[{'test': 0}: 5013, {'test': 1}: 4987]\n", + "Opening: https://platform.classiq.io/circuit/2v4p14CkjQTcfAiQHEXpospBfE6?login=True&version=0.73.0\n" + ] + } + ], + "id": "32" + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "As you can see, while the expected output was 0 with probability 1, we've managed to make our backend output pure noise. A logical qubit doesn't always mean a good qubit!\n", + "\n", + "But then, how should we tune our logical qubit to get good results? Let us sweep our parameters to find out." + ], + "id": "33" + }, + { + "cell_type": "code", + "metadata": {}, + "source": [ + "distances = [x for x in range(3, 16) if x % 2 != 0]\n", + "ratios = [10**x for x in range(5, 8)]\n", + "nb_photons = [4, 7, 10, 15, 19]" + ], + "execution_count": 13, + "outputs": [], + "id": "34" + }, + { + "cell_type": "code", + "metadata": {}, + "source": [ + "def compute_distance(nb_photons, d, k2, k1=100, sk=2):\n", + " backend_preferences = AliceBobBackendPreferences(\n", + " backend_service_provider=ProviderVendor.ALICE_AND_BOB,\n", + " backend_name=AliceBobBackendNames.LOGICAL_TARGET,\n", + " kappa_1=k1,\n", + " kappa_2=k2,\n", + " distance=d,\n", + " average_nb_photons=nb_photons,\n", + " solovay_kitaev_max_iterations=sk,\n", + " )\n", + " execution_preferences = ExecutionPreferences(\n", + " num_shots=10_000,\n", + " backend_preferences=backend_preferences,\n", + " )\n", + "\n", + " # Prepare for HW aware synthesis\n", + " preferences = Preferences(\n", + " backend_service_provider=ProviderVendor.ALICE_AND_BOB,\n", + " backend_name=AliceBobBackendNames.LOGICAL_TARGET,\n", + " )\n", + "\n", + " start = time.time()\n", + "\n", + " # Create Model, set settings and perform HW aware synthesis\n", + " model = create_model(main)\n", + " model = set_execution_preferences(model, execution_preferences)\n", + " model = set_preferences(model, preferences=preferences)\n", + " qprog = synthesize(model)\n", + "\n", + " # Execute Quantum Program\n", + " res = execute(qprog).result()\n", + "\n", + " end = time.time()\n", + "\n", + " # show(qprog)\n", + "\n", + " error_rate = results_error_rate(res)\n", + "\n", + " print(\"-------------------------------------\")\n", + " print(\n", + " \"Error rate for nb_photons = %i, distance = %i, k1 = %i, k2 = %i: %f. Time elasped: %f seconds.\"\n", + " % (nb_photons, d, k1, k2, error_rate, end - start)\n", + " )\n", + " print(\"-------------------------------------\")\n", + "\n", + " return error_rate" + ], + "execution_count": 14, + "outputs": [], + "id": "35" + }, + { + "cell_type": "code", + "metadata": {}, + "source": [ + "difference = np.zeros((len(nb_photons), len(distances), len(ratios)))\n", + "for n in range(len(nb_photons)):\n", + " for i in range(len(distances)):\n", + " for j in range(len(ratios)):\n", + " difference[n, i, j] = compute_distance(\n", + " nb_photons=nb_photons[n], d=distances[i], k2=ratios[j]\n", + " )\n", + " # The line above is very slow - use the line below instead when debugging\n", + " # difference[n, i, j] = np.random.rand(1)" + ], + "execution_count": 15, + "outputs": [ + { + "output_type": "stream", + "text": [ + "-------------------------------------\n", + "Error rate for nb_photons = 4, distance = 3, k1 = 100, k2 = 100000: 0.497000. Time elasped: 71.169343 seconds.\n", + "-------------------------------------\n", + "-------------------------------------\n", + "Error rate for nb_photons = 4, distance = 3, k1 = 100, k2 = 1000000: 0.499800. Time elasped: 96.857939 seconds.\n", + "-------------------------------------\n", + "-------------------------------------\n", + "Error rate for nb_photons = 4, distance = 3, k1 = 100, k2 = 10000000: 0.502300. Time elasped: 68.482089 seconds.\n", + "-------------------------------------\n", + "-------------------------------------\n", + "Error rate for nb_photons = 4, distance = 5, k1 = 100, k2 = 100000: 0.499200. Time elasped: 75.164038 seconds.\n", + "-------------------------------------\n", + "-------------------------------------\n", + "Error rate for nb_photons = 4, distance = 5, k1 = 100, k2 = 1000000: 0.508200. Time elasped: 70.321209 seconds.\n", + "-------------------------------------\n", + "-------------------------------------\n", + "Error rate for nb_photons = 4, distance = 5, k1 = 100, k2 = 10000000: 0.505100. Time elasped: 73.873376 seconds.\n", + "-------------------------------------\n", + "-------------------------------------\n", + "Error rate for nb_photons = 4, distance = 7, k1 = 100, k2 = 100000: 0.495200. Time elasped: 73.376681 seconds.\n", + "-------------------------------------\n", + "-------------------------------------\n", + "Error rate for nb_photons = 4, distance = 7, k1 = 100, k2 = 1000000: 0.517500. Time elasped: 72.477691 seconds.\n", + "-------------------------------------\n", + "-------------------------------------\n", + "Error rate for nb_photons = 4, distance = 7, k1 = 100, k2 = 10000000: 0.516800. Time elasped: 96.925179 seconds.\n", + "-------------------------------------\n", + "-------------------------------------\n", + "Error rate for nb_photons = 4, distance = 9, k1 = 100, k2 = 100000: 0.509200. Time elasped: 83.217636 seconds.\n", + "-------------------------------------\n", + "-------------------------------------\n", + "Error rate for nb_photons = 4, distance = 9, k1 = 100, k2 = 1000000: 0.509500. Time elasped: 87.689594 seconds.\n", + "-------------------------------------\n", + "-------------------------------------\n", + "Error rate for nb_photons = 4, distance = 9, k1 = 100, k2 = 10000000: 0.500600. Time elasped: 72.159962 seconds.\n", + "-------------------------------------\n", + "-------------------------------------\n", + "Error rate for nb_photons = 4, distance = 11, k1 = 100, k2 = 100000: 0.511800. Time elasped: 70.809266 seconds.\n", + "-------------------------------------\n", + "-------------------------------------\n", + "Error rate for nb_photons = 4, distance = 11, k1 = 100, k2 = 1000000: 0.518800. Time elasped: 71.153163 seconds.\n", + "-------------------------------------\n", + "-------------------------------------\n", + "Error rate for nb_photons = 4, distance = 11, k1 = 100, k2 = 10000000: 0.506800. Time elasped: 70.793602 seconds.\n", + "-------------------------------------\n", + "-------------------------------------\n", + "Error rate for nb_photons = 4, distance = 13, k1 = 100, k2 = 100000: 0.505500. Time elasped: 70.624506 seconds.\n", + "-------------------------------------\n", + "-------------------------------------\n", + "Error rate for nb_photons = 4, distance = 13, k1 = 100, k2 = 1000000: 0.503500. Time elasped: 70.774193 seconds.\n", + "-------------------------------------\n", + "-------------------------------------\n", + "Error rate for nb_photons = 4, distance = 13, k1 = 100, k2 = 10000000: 0.522700. Time elasped: 72.376953 seconds.\n", + "-------------------------------------\n", + "-------------------------------------\n", + "Error rate for nb_photons = 4, distance = 15, k1 = 100, k2 = 100000: 0.511400. Time elasped: 70.389348 seconds.\n", + "-------------------------------------\n", + "-------------------------------------\n", + "Error rate for nb_photons = 4, distance = 15, k1 = 100, k2 = 1000000: 0.510900. Time elasped: 83.862812 seconds.\n", + "-------------------------------------\n", + "-------------------------------------\n", + "Error rate for nb_photons = 4, distance = 15, k1 = 100, k2 = 10000000: 0.503900. Time elasped: 68.846179 seconds.\n", + "-------------------------------------\n", + "-------------------------------------\n", + "Error rate for nb_photons = 7, distance = 3, k1 = 100, k2 = 100000: 0.493300. Time elasped: 71.930928 seconds.\n", + "-------------------------------------\n", + "-------------------------------------\n", + "Error rate for nb_photons = 7, distance = 3, k1 = 100, k2 = 1000000: 0.492900. Time elasped: 68.949645 seconds.\n", + "-------------------------------------\n", + "-------------------------------------\n", + "Error rate for nb_photons = 7, distance = 3, k1 = 100, k2 = 10000000: 0.125900. Time elasped: 68.546538 seconds.\n", + "-------------------------------------\n", + "-------------------------------------\n", + "Error rate for nb_photons = 7, distance = 5, k1 = 100, k2 = 100000: 0.495600. Time elasped: 68.430804 seconds.\n", + "-------------------------------------\n", + "-------------------------------------\n", + "Error rate for nb_photons = 7, distance = 5, k1 = 100, k2 = 1000000: 0.301500. Time elasped: 68.759815 seconds.\n", + "-------------------------------------\n", + "-------------------------------------\n", + "Error rate for nb_photons = 7, distance = 5, k1 = 100, k2 = 10000000: 0.176200. Time elasped: 68.838088 seconds.\n", + "-------------------------------------\n", + "-------------------------------------\n", + "Error rate for nb_photons = 7, distance = 7, k1 = 100, k2 = 100000: 0.508100. Time elasped: 79.019300 seconds.\n", + "-------------------------------------\n", + "-------------------------------------\n", + "Error rate for nb_photons = 7, distance = 7, k1 = 100, k2 = 1000000: 0.268000. Time elasped: 77.329654 seconds.\n", + "-------------------------------------\n", + "-------------------------------------\n", + "Error rate for nb_photons = 7, distance = 7, k1 = 100, k2 = 10000000: 0.273900. Time elasped: 72.517091 seconds.\n", + "-------------------------------------\n", + "-------------------------------------\n", + "Error rate for nb_photons = 7, distance = 9, k1 = 100, k2 = 100000: 0.499500. Time elasped: 69.234349 seconds.\n", + "-------------------------------------\n", + "-------------------------------------\n", + "Error rate for nb_photons = 7, distance = 9, k1 = 100, k2 = 1000000: 0.345300. Time elasped: 68.999759 seconds.\n", + "-------------------------------------\n", + "-------------------------------------\n", + "Error rate for nb_photons = 7, distance = 9, k1 = 100, k2 = 10000000: 0.342400. Time elasped: 68.691098 seconds.\n", + "-------------------------------------\n", + "-------------------------------------\n", + "Error rate for nb_photons = 7, distance = 11, k1 = 100, k2 = 100000: 0.499700. Time elasped: 68.702952 seconds.\n", + "-------------------------------------\n", + "-------------------------------------\n", + "Error rate for nb_photons = 7, distance = 11, k1 = 100, k2 = 1000000: 0.398300. Time elasped: 69.236237 seconds.\n", + "-------------------------------------\n", + "-------------------------------------\n", + "Error rate for nb_photons = 7, distance = 11, k1 = 100, k2 = 10000000: 0.399100. Time elasped: 68.779391 seconds.\n", + "-------------------------------------\n", + "-------------------------------------\n", + "Error rate for nb_photons = 7, distance = 13, k1 = 100, k2 = 100000: 0.498600. Time elasped: 68.886379 seconds.\n", + "-------------------------------------\n", + "-------------------------------------\n", + "Error rate for nb_photons = 7, distance = 13, k1 = 100, k2 = 1000000: 0.435300. Time elasped: 70.253677 seconds.\n", + "-------------------------------------\n", + "-------------------------------------\n", + "Error rate for nb_photons = 7, distance = 13, k1 = 100, k2 = 10000000: 0.427700. Time elasped: 71.385530 seconds.\n", + "-------------------------------------\n", + "-------------------------------------\n", + "Error rate for nb_photons = 7, distance = 15, k1 = 100, k2 = 100000: 0.502800. Time elasped: 78.550687 seconds.\n", + "-------------------------------------\n", + "-------------------------------------\n", + "Error rate for nb_photons = 7, distance = 15, k1 = 100, k2 = 1000000: 0.459000. Time elasped: 71.288507 seconds.\n", + "-------------------------------------\n", + "-------------------------------------\n", + "Error rate for nb_photons = 7, distance = 15, k1 = 100, k2 = 10000000: 0.447000. Time elasped: 73.258285 seconds.\n", + "-------------------------------------\n", + "-------------------------------------\n", + "Error rate for nb_photons = 10, distance = 3, k1 = 100, k2 = 100000: 0.501700. Time elasped: 70.457285 seconds.\n", + "-------------------------------------\n", + "-------------------------------------\n", + "Error rate for nb_photons = 10, distance = 3, k1 = 100, k2 = 1000000: 0.499500. Time elasped: 70.590181 seconds.\n", + "-------------------------------------\n", + "-------------------------------------\n", + "Error rate for nb_photons = 10, distance = 3, k1 = 100, k2 = 10000000: 0.102700. Time elasped: 70.819256 seconds.\n", + "-------------------------------------\n", + "-------------------------------------\n", + "Error rate for nb_photons = 10, distance = 5, k1 = 100, k2 = 100000: 0.499100. Time elasped: 71.996081 seconds.\n", + "-------------------------------------\n", + "-------------------------------------\n", + "Error rate for nb_photons = 10, distance = 5, k1 = 100, k2 = 1000000: 0.358200. Time elasped: 70.039874 seconds.\n", + "-------------------------------------\n", + "-------------------------------------\n", + "Error rate for nb_photons = 10, distance = 5, k1 = 100, k2 = 10000000: 0.054700. Time elasped: 68.721642 seconds.\n", + "-------------------------------------\n", + "-------------------------------------\n", + "Error rate for nb_photons = 10, distance = 7, k1 = 100, k2 = 100000: 0.511800. Time elasped: 74.377347 seconds.\n", + "-------------------------------------\n", + "-------------------------------------\n", + "Error rate for nb_photons = 10, distance = 7, k1 = 100, k2 = 1000000: 0.096800. Time elasped: 70.419338 seconds.\n", + "-------------------------------------\n", + "-------------------------------------\n", + "Error rate for nb_photons = 10, distance = 7, k1 = 100, k2 = 10000000: 0.052700. Time elasped: 70.292175 seconds.\n", + "-------------------------------------\n", + "-------------------------------------\n", + "Error rate for nb_photons = 10, distance = 9, k1 = 100, k2 = 100000: 0.501600. Time elasped: 69.105949 seconds.\n", + "-------------------------------------\n", + "-------------------------------------\n", + "Error rate for nb_photons = 10, distance = 9, k1 = 100, k2 = 1000000: 0.056000. Time elasped: 68.804265 seconds.\n", + "-------------------------------------\n", + "-------------------------------------\n", + "Error rate for nb_photons = 10, distance = 9, k1 = 100, k2 = 10000000: 0.055300. Time elasped: 72.318183 seconds.\n", + "-------------------------------------\n", + "-------------------------------------\n", + "Error rate for nb_photons = 10, distance = 11, k1 = 100, k2 = 100000: 0.504200. Time elasped: 94.127630 seconds.\n", + "-------------------------------------\n", + "-------------------------------------\n", + "Error rate for nb_photons = 10, distance = 11, k1 = 100, k2 = 1000000: 0.054500. Time elasped: 78.572011 seconds.\n", + "-------------------------------------\n", + "-------------------------------------\n", + "Error rate for nb_photons = 10, distance = 11, k1 = 100, k2 = 10000000: 0.059000. Time elasped: 96.247134 seconds.\n", + "-------------------------------------\n", + "-------------------------------------\n", + "Error rate for nb_photons = 10, distance = 13, k1 = 100, k2 = 100000: 0.504400. Time elasped: 70.746398 seconds.\n", + "-------------------------------------\n", + "-------------------------------------\n", + "Error rate for nb_photons = 10, distance = 13, k1 = 100, k2 = 1000000: 0.056400. Time elasped: 70.327472 seconds.\n", + "-------------------------------------\n", + "-------------------------------------\n", + "Error rate for nb_photons = 10, distance = 13, k1 = 100, k2 = 10000000: 0.053400. Time elasped: 72.075044 seconds.\n", + "-------------------------------------\n", + "-------------------------------------\n", + "Error rate for nb_photons = 10, distance = 15, k1 = 100, k2 = 100000: 0.496300. Time elasped: 70.579632 seconds.\n", + "-------------------------------------\n", + "-------------------------------------\n", + "Error rate for nb_photons = 10, distance = 15, k1 = 100, k2 = 1000000: 0.054400. Time elasped: 70.822054 seconds.\n", + "-------------------------------------\n", + "-------------------------------------\n", + "Error rate for nb_photons = 10, distance = 15, k1 = 100, k2 = 10000000: 0.060200. Time elasped: 72.904309 seconds.\n", + "-------------------------------------\n", + "-------------------------------------\n", + "Error rate for nb_photons = 15, distance = 3, k1 = 100, k2 = 100000: 0.496500. Time elasped: 70.265501 seconds.\n", + "-------------------------------------\n", + "-------------------------------------\n", + "Error rate for nb_photons = 15, distance = 3, k1 = 100, k2 = 1000000: 0.499500. Time elasped: 72.351297 seconds.\n", + "-------------------------------------\n", + "-------------------------------------\n", + "Error rate for nb_photons = 15, distance = 3, k1 = 100, k2 = 10000000: 0.157200. Time elasped: 72.740201 seconds.\n", + "-------------------------------------\n", + "-------------------------------------\n", + "Error rate for nb_photons = 15, distance = 5, k1 = 100, k2 = 100000: 0.504500. Time elasped: 74.459069 seconds.\n", + "-------------------------------------\n", + "-------------------------------------\n", + "Error rate for nb_photons = 15, distance = 5, k1 = 100, k2 = 1000000: 0.471200. Time elasped: 70.855352 seconds.\n", + "-------------------------------------\n", + "-------------------------------------\n", + "Error rate for nb_photons = 15, distance = 5, k1 = 100, k2 = 10000000: 0.057400. Time elasped: 70.983077 seconds.\n", + "-------------------------------------\n", + "-------------------------------------\n", + "Error rate for nb_photons = 15, distance = 7, k1 = 100, k2 = 100000: 0.505700. Time elasped: 71.369307 seconds.\n", + "-------------------------------------\n", + "-------------------------------------\n", + "Error rate for nb_photons = 15, distance = 7, k1 = 100, k2 = 1000000: 0.195500. Time elasped: 72.168745 seconds.\n", + "-------------------------------------\n", + "-------------------------------------\n", + "Error rate for nb_photons = 15, distance = 7, k1 = 100, k2 = 10000000: 0.055300. Time elasped: 70.438114 seconds.\n", + "-------------------------------------\n", + "-------------------------------------\n", + "Error rate for nb_photons = 15, distance = 9, k1 = 100, k2 = 100000: 0.493800. Time elasped: 70.558800 seconds.\n", + "-------------------------------------\n", + "-------------------------------------\n", + "Error rate for nb_photons = 15, distance = 9, k1 = 100, k2 = 1000000: 0.074200. Time elasped: 96.405218 seconds.\n", + "-------------------------------------\n", + "-------------------------------------\n", + "Error rate for nb_photons = 15, distance = 9, k1 = 100, k2 = 10000000: 0.053700. Time elasped: 70.337165 seconds.\n", + "-------------------------------------\n", + "-------------------------------------\n", + "Error rate for nb_photons = 15, distance = 11, k1 = 100, k2 = 100000: 0.497500. Time elasped: 72.830533 seconds.\n", + "-------------------------------------\n", + "-------------------------------------\n", + "Error rate for nb_photons = 15, distance = 11, k1 = 100, k2 = 1000000: 0.055600. Time elasped: 95.748791 seconds.\n", + "-------------------------------------\n", + "-------------------------------------\n", + "Error rate for nb_photons = 15, distance = 11, k1 = 100, k2 = 10000000: 0.051100. Time elasped: 70.500518 seconds.\n", + "-------------------------------------\n", + "-------------------------------------\n", + "Error rate for nb_photons = 15, distance = 13, k1 = 100, k2 = 100000: 0.499000. Time elasped: 96.055168 seconds.\n", + "-------------------------------------\n", + "-------------------------------------\n", + "Error rate for nb_photons = 15, distance = 13, k1 = 100, k2 = 1000000: 0.055900. Time elasped: 73.637201 seconds.\n", + "-------------------------------------\n", + "-------------------------------------\n", + "Error rate for nb_photons = 15, distance = 13, k1 = 100, k2 = 10000000: 0.054500. Time elasped: 70.822516 seconds.\n", + "-------------------------------------\n", + "-------------------------------------\n", + "Error rate for nb_photons = 15, distance = 15, k1 = 100, k2 = 100000: 0.494200. Time elasped: 71.481590 seconds.\n", + "-------------------------------------\n", + "-------------------------------------\n", + "Error rate for nb_photons = 15, distance = 15, k1 = 100, k2 = 1000000: 0.054200. Time elasped: 70.463998 seconds.\n", + "-------------------------------------\n", + "-------------------------------------\n", + "Error rate for nb_photons = 15, distance = 15, k1 = 100, k2 = 10000000: 0.052700. Time elasped: 72.105492 seconds.\n", + "-------------------------------------\n", + "-------------------------------------\n", + "Error rate for nb_photons = 19, distance = 3, k1 = 100, k2 = 100000: 0.496900. Time elasped: 70.332159 seconds.\n", + "-------------------------------------\n", + "-------------------------------------\n", + "Error rate for nb_photons = 19, distance = 3, k1 = 100, k2 = 1000000: 0.513500. Time elasped: 78.706125 seconds.\n", + "-------------------------------------\n", + "-------------------------------------\n", + "Error rate for nb_photons = 19, distance = 3, k1 = 100, k2 = 10000000: 0.201900. Time elasped: 77.739521 seconds.\n", + "-------------------------------------\n", + "-------------------------------------\n", + "Error rate for nb_photons = 19, distance = 5, k1 = 100, k2 = 100000: 0.498000. Time elasped: 70.559857 seconds.\n", + "-------------------------------------\n", + "-------------------------------------\n", + "Error rate for nb_photons = 19, distance = 5, k1 = 100, k2 = 1000000: 0.499000. Time elasped: 82.915350 seconds.\n", + "-------------------------------------\n", + "-------------------------------------\n", + "Error rate for nb_photons = 19, distance = 5, k1 = 100, k2 = 10000000: 0.051700. Time elasped: 73.195369 seconds.\n", + "-------------------------------------\n", + "-------------------------------------\n", + "Error rate for nb_photons = 19, distance = 7, k1 = 100, k2 = 100000: 0.499300. Time elasped: 70.454549 seconds.\n", + "-------------------------------------\n", + "-------------------------------------\n", + "Error rate for nb_photons = 19, distance = 7, k1 = 100, k2 = 1000000: 0.304700. Time elasped: 75.665987 seconds.\n", + "-------------------------------------\n", + "-------------------------------------\n", + "Error rate for nb_photons = 19, distance = 7, k1 = 100, k2 = 10000000: 0.053900. Time elasped: 70.624962 seconds.\n", + "-------------------------------------\n", + "-------------------------------------\n", + "Error rate for nb_photons = 19, distance = 9, k1 = 100, k2 = 100000: 0.502200. Time elasped: 73.715155 seconds.\n", + "-------------------------------------\n", + "-------------------------------------\n", + "Error rate for nb_photons = 19, distance = 9, k1 = 100, k2 = 1000000: 0.096400. Time elasped: 70.765682 seconds.\n", + "-------------------------------------\n", + "-------------------------------------\n", + "Error rate for nb_photons = 19, distance = 9, k1 = 100, k2 = 10000000: 0.052100. Time elasped: 100.187774 seconds.\n", + "-------------------------------------\n", + "-------------------------------------\n", + "Error rate for nb_photons = 19, distance = 11, k1 = 100, k2 = 100000: 0.500100. Time elasped: 74.620972 seconds.\n", + "-------------------------------------\n", + "-------------------------------------\n", + "Error rate for nb_photons = 19, distance = 11, k1 = 100, k2 = 1000000: 0.061700. Time elasped: 72.562406 seconds.\n", + "-------------------------------------\n", + "-------------------------------------\n", + "Error rate for nb_photons = 19, distance = 11, k1 = 100, k2 = 10000000: 0.055300. Time elasped: 69.534153 seconds.\n", + "-------------------------------------\n", + "-------------------------------------\n", + "Error rate for nb_photons = 19, distance = 13, k1 = 100, k2 = 100000: 0.494600. Time elasped: 94.375211 seconds.\n", + "-------------------------------------\n", + "-------------------------------------\n", + "Error rate for nb_photons = 19, distance = 13, k1 = 100, k2 = 1000000: 0.054300. Time elasped: 69.341189 seconds.\n", + "-------------------------------------\n", + "-------------------------------------\n", + "Error rate for nb_photons = 19, distance = 13, k1 = 100, k2 = 10000000: 0.052700. Time elasped: 70.512143 seconds.\n", + "-------------------------------------\n", + "-------------------------------------\n", + "Error rate for nb_photons = 19, distance = 15, k1 = 100, k2 = 100000: 0.499500. Time elasped: 68.640973 seconds.\n", + "-------------------------------------\n", + "-------------------------------------\n", + "Error rate for nb_photons = 19, distance = 15, k1 = 100, k2 = 1000000: 0.055900. Time elasped: 75.023128 seconds.\n", + "-------------------------------------\n", + "-------------------------------------\n", + "Error rate for nb_photons = 19, distance = 15, k1 = 100, k2 = 10000000: 0.054500. Time elasped: 68.573808 seconds.\n", + "-------------------------------------\n" + ] + } + ], + "id": "36" + }, + { + "cell_type": "code", + "metadata": {}, + "source": [ + "def plot_results(ratios, distances, difference, n):\n", + " # Create the meshgrid\n", + " ratios_mesh, distances_mesh = np.meshgrid(ratios, distances)\n", + " ratios_mesh_log = np.log10(ratios_mesh)\n", + "\n", + " # Define the colormap\n", + " colors = [(0, 0.5, 0), (0.9, 0.5, 0), (0.9, 0, 0)]\n", + " n_bins = 100 # Discretizes the interpolation into bins\n", + " cmap_name = \"red_darker_green\"\n", + " cmap = LinearSegmentedColormap.from_list(cmap_name, colors, N=n_bins)\n", + "\n", + " # Plotting\n", + " plt.figure(figsize=(10, 8))\n", + " plt.pcolormesh(\n", + " ratios_mesh_log,\n", + " distances_mesh,\n", + " difference[n, :, :],\n", + " shading=\"auto\",\n", + " cmap=cmap,\n", + " vmin=0.0,\n", + " vmax=0.5,\n", + " )\n", + " plt.xticks(\n", + " np.log10(ratios), labels=[f\"$10^{int(np.log10(r/100))}$\" for r in ratios]\n", + " )\n", + " plt.yticks(distances)\n", + "\n", + " # Adding the value on each pixel\n", + " for i in range(len(distances)):\n", + " for j in range(len(ratios)):\n", + " plt.text(\n", + " np.log10(ratios[j]),\n", + " distances[i],\n", + " f\"{difference[n, i, j]:.3f}\",\n", + " ha=\"center\",\n", + " va=\"center\",\n", + " color=\"white\",\n", + " )\n", + "\n", + " plt.colorbar(label=\"Circuit error rate\")\n", + " plt.xlabel(\"$\\kappa_2/\\kappa_1$\")\n", + " plt.ylabel(\"Distances\")\n", + " plt.title(f\"avg number of photons = {nb_photons[n]}\")\n", + "\n", + " plt.show()" + ], + "execution_count": 16, + "outputs": [], + "id": "37" + }, + { + "cell_type": "code", + "metadata": {}, + "source": [ + "for n in range(len(nb_photons)):\n", + " plot_results(ratios, distances, difference, n)" + ], + "execution_count": 17, + "outputs": [ + { + "output_type": "display_data", + "data": { + "image/png": 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", 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MXhuqz8ZV6jus6XplluJM+ZYuXWonBS5iPsszzzzTTiJcnqysLLVs2dJ+Zz7uuOPseFEz6XGoHPLBiQlMmjdvHupiAAAA4AA2btyoww8/XE4LTFrWq6fyO0ZVr7i4OBtAFGe6bd17770ltqWlpcnn8+3T8mHWV61aVea527dvb1tVjj32WKWnp+uRRx7RCSecYOcoC9XP4ZAPTkyLibHU/HBDXRigtmkQ6gIAtVBEqAsA1D5Zfqnb9r3f25zEtEiYwGSJ+V5Zw9fOlNQ9K8sGbWZsSJHSrSaVZTJrmqWICUyOOuooPfvss7rvvvsUCod8cFLUDGYCE+f9ugMO57yWdcD5qDdApTm5C379EH6XjI+PLxGclKVhw4YKCwvTtm3bSmw362YsSUVERESoa9euWrNmjUKF/4UCAAAAtVxkZKS6deumefPmBbeZcSRmvXjryP6YbmE//PCDmjZtqlA55FtOAAAAgLpgxIgRGjx4sLp3727nNpk0aZKys7ODc5kMGjRIhx12mCZMmGDXx40bp+OPP17t2rXT7t277fwoJpXwtddeG7J7IDgBAAAADgEDBw5UamqqxowZYydh7NKli2bNmhUcJL9hw4YS2dB27dplUw+bY5OSkmzLy4IFC2wa4lA55GeIz8jIUEJCglYz5gQ4eI1CXQCgFmJAPHDQMv1S+62yGaMONLYiZN8l3VL9Gh4SkxmQ2vud+blUF8acAAAAAHAEghMAAAAAjkBwAgAAAMARCE4AAAAAOALBCQAAAABHIJUwAAAAUJFH+jU9gX3AzKSoOoWWEwAAAACOQHACAAAAwBEITgAAAAA4AsEJAAAAAEcgOAEAAADgCGTrAgAAAA4kLETZuryqU2g5AQAAAOAIBCcAAAAAHIHgBAAAAIAjEJwAAAAAcASCEwAAAACOQLYuAAAAoCKP9EORrauOoeUEAAAAgCMQnAAAAABwBIITAAAAAI5AcAIAAADAEQhOAAAAADgCwQkAAAAARyCVMAAAAHAgYaQSrgm0nAAAAABwBIITAAAAAI5AcAIAAADAEQhOAAAAADgCwQkAAAAARyBbFwAAAFCRR/pk66p2tJzgT4kZNkyN1q5VSm6uGixapIgePco9tt7gwWoaCJRYzPtKixs7Vo03b1ZKTo6S58xRWLt2JfYnvf++Gq9fb99rjkt4+WW5mzatlvsDqkPMkGFqtGStUjbkqsHHixTRtfx6U1x0/4Fquj2gpGn/LbE94YmX7PbiS9KbH5c4JrxTVyW//Yma/LpLTValKeGRZ+WKja3S+wKqW8zgYWq0aK1SfstVgw8WKaJLBevOhQPVdFNASS+UrDvFxT/wtD0m5tpbg9sie59qt5W1RHTuXiX3BKAkghNUWvSAAYqfOFFZY8cq7bjj5F2+XMmzZ8vdqFG57/Gnp2tbSkpw2d6yZYn9sXfdpdhbblH69dcrrVcvBbKz7TkVFRU8puCzz7RrwACltm+vXX/5i8LbtlXSO+9U670CVSX6ogGKHztRWY+MVdqZx8n703IlT58td8Py640R1ryl4u99RPkLvyxzf968j7XtmJTgsvu6K4L73E2aqsE7c+Vdu0Zp/Xpp5+X9FN7haCU8MbXK7w+oLtEXDlD8PROVNXGs0vodJ+/Py5X82my5Gxyg7hzeUvFjHlH+orLrjhHVr78ijztevi2bSmwvWLJA27qklFhyXpsi7/rf5Vm+pMruDYBDgpMvv/xSF1xwgZo1ayaXy6UZM2aU2H/VVVfZ7cWXfv36hay8KCl2xAjlTJmi3KlT5V250gYUgZwc1RsypPw3BQLyb9u2d9m+veQ5hw9X1v33K3/mTHl/+EG7Bw1SWLNmiu7fP3hM9qRJ8nzzjXwbNsizcKGyHnhAEccfL4XTSxHOF3v9COW8OkW5b06V95eVSr/zegVyc1Tviv3UG7dbiU+/psyH7pFv/e9lH1OQL//2bcElkL47uCvq7PMV8HqU8c8b5fvtF3mWLbHXrXfBpQpr3bYa7hKoerFDRyjn9SnKfWuqvL+uVPrIwrpz+QHqzlOvKfORe+TbUHbdcac0U8L9T2r3TVfaelKCxyN/6ra9y64diup7kXLfeqmK7w6AI4KT7Oxsde7cWZMnTy73GBOMbNmyJbi88cYbNVpGlCMiQhHduil/7ty92wIBux7Zu3e5b3PFxanRunVqvGGDkmbMUHjHjsF9Ya1bK6xp0xLnDGRkqOCbb8o9pyspSfWuvFKeBQskr7eq7g6ovnrTuZvyvyxVb76cq8ju5debuDvGyJ+2Xbmvv1juMZEn9FHjn7ap0YJVin/o/+RKSg7uc0VGSQUF9lrBy+bt6VIZ2fOkP39fQE3UnWO7Kf+rUnVn/lxFdttP3bmtsO68WU7dcbmU+MQrynr6YXl/+fmAxYg++0K5kxooZzrBCVBdQvqo+ZxzzrHL/kRFRSklJaXGyoSKcTdsKFd4uG39KM6sh3foUOZ7vKtXK33IEHlWrJA7IUGxd9yhBgsWKPXoo+XftEnuwp9zWecs2lek/gMPKOamm+SOjVXBwoXaef75VX6PQFVzJxfWm9RSv+Op2xTerux6E9HrRMX89Rqlnt6l3PPmfzpLef97T74NaxXWqq3qj/6Pkt/4WDvO7S35/SqY/6nc4yYq9sY7lP3c43LFxKr+vx/YU6YmjNdCLao7aWXUnbbl1J0eJyrmimuUelb5dSf2xn/aB1s5LzxRoXLUu/wa5X8+W/5S3b8A1KExJ59//rkaN26s9u3b64YbbtCOHTv2e3x+fr4yMjJKLHAGz6JFyn3lFTs2peDLL7XrkkvkT01VzHXXHfS5sh5+WGldu2rHWWdJPp8SX365WsoMhJIrNk6JT72i9BFDFdhZ/v/78mZMV/7sD+Rd+aPyP35fu/52viKP66nIE/vY/d7VP2v3zYMVe8PtSlmfoyY/brWBjG/7Vingr8E7Amqw7jzxitLvHKrArrLrTnin4xR7za3afdtVFTqnu+lhiurTV7lvvlDFpUWtERaipY5xdCd906XrkksuUevWrfXbb79p9OjRtqVl4cKFCgsr+6c1YcIEjR07tsbLWtf409IU8HrlbtKkxHaz7t+6tWIn8Xrl+f57hRdm4yp6X+lzmHXvsmUl3hrYsUM+s/z6q3atXKkmf/xhx52YAAhwKv/OwnrTqFS9adREfhMolGLGg4S3bK2kVz8odvCeZ0opmz1KPaG9fOv27UfvW79WvrRUhbdup4KvPrXb8t57wy7uRo0VyMm2XWLM+Jey3g84tu40LKPupJZRd1q1VXiL1kqaWkbdWe9R6intFdnrZLkbNlbjxRuCh5jWmfgxjyr22uFKPb51iXPGDLzajjnJ+2Rm1d8ggNrRcnL55ZfrwgsvVKdOndS/f399+OGH+vbbb21rSnlGjRql9PT04LJx48YaLXOd4fHIs3Spos44Y+82l8uum25WFeJ2K6JTJ/m2bLGrvrVr7evi53TVr6/IXr32f87CPziuYhm9AMfWm+VLFXVyqXpz8hkqWLLv77j311VKPeUYpZ3eJbjkz56pgvmf2de+TRvLfcLrTm4g37Y9das4f+p2mwUv+qKBCuTlKf+LOVV7j0B11Z0VSxV1Uqm6c9IZKlhaRt1Zs0qppx+jtLO7BJf8T2aqYMFn9rVv80blvvuK0s48tsQxJltX9tMPa+eVffc5Z70BVyv3nZcZ3wjU5ZaT0tq0aaOGDRtqzZo1OqP4l+JSY1TMguqXPXGiEqdNk2fJEnkWL1bM8OF23oTcl/YMFEyYNs2OJckcPdqux919twoWLZJvzRq5EhMVd+edCmvZUrnPP7/3nJMmKe7f/5b3119tsFL/vvvk27xZeYWZ3CJ69rRzqRTMn6/Arl0Ka9vWHuNds6biQREQQtnPTFTik9NsGlLPd4sVc91wOwYk983CevPUNNufPXP8aNNPVd5VP5V4vz99t32qVLTd1Lm4O+5R3ofv2tYX88Q4fsxD8q1do/zPZgffFzPkRhV8u0CB7CxF9TlL8WMeVsb9IxXISK/hTwConOwpE5X42DR5ViyR5/vFihk6XK56scotHJye8Hhh3XmgsO6sLlV3MgrrTuH2wK6d8u7aWeIYk63Ll7rVZrUrLvKk0xXeso1yXt/79wpA9ahVwckff/xhx5w0ZcI9R8h76y1lNGqkuHHjFJaSIs+yZdrZr18wPXBYixZ2MG7xzFoJU6bYY/27dtmWl7QTTrBpiItkP/SQ/bKV8Nxzcicm2iDEnNP8oTFMquLoSy5R/bFj7XGmpSV/1iybfthmIwIcLu/9t5TRoJHi7hqnsMYp8vy4zM47Ylo0jLDDStabAwn4fIroeKzqDRgsd0KifFs3q+DzT5T54N0l6kTEcT1V/y5Tb+LsU+X0O69T7tuvVss9AtUhb+ZbykhupLg7ximsUYo8Py3Tzr/1s9m4jLBmB1d3DkbM5deo4Nuv5fttdbWcH8BerkCgWG7JGpaVlWVbQYyuXbtq4sSJOu2005ScnGwXM3bkL3/5i83WZcac3HXXXcrMzNQPP/xQ4dYRMyA+ISFB5n8n9av5foBDzv7nNgNQlohQFwCofTL9Uvutsl3y4+Pj5STB75JJUn1XzV47MyC13+XMz+WQbDlZsmSJDUaKjBgxwv47ePBgPf3001qxYoWmTZum3bt324kazz77bN1333102wIAAEDNcodgtLZfdU5Ig5M+ffpofw03s2fv7S8NAAAA4NDm6GxdAAAAAOoOghMAAAAAjkBwAgAAAMARCE4AAAAAOEKtmucEAAAAqDPZuuogPmIAAAAAjkBwAgAAAMARCE4AAAAAOALBCQAAAABHIDgBAAAA4Ahk6wIAAAAOJCwEj/VdqnNoOQEAAADgCAQnAAAAAByB4AQAAACAIxCcAAAAAHAEghMAAAAAjkC2LgAAAKAij/R5rF/t+IgBAAAAOALBCQAAAABHIDgBAAAA4AgEJwAAAAAcgeAEAAAAgCMQnAAAAABwBFIJAwAAAAcSFoLH+i7VObScAAAAAHAEghMAAAAAjkBwAgAAAMARCE4AAAAAOALBCQAAAABHIFsXAAAAUJFH+jzWr3Z8xAAAAAAcgeAEAAAAgCMQnAAAAABwBIITAAAAAI5AcAIAAADAEcjWBQAAABxIWAge67tU59ByAgAAAMARaDkBUL6YUBcAqIUiQl0AoBbyh7oAcApaTgAAAAA4AsEJAAAAAEcgOAEAAADgCIw5AQAAACrySN9k7EK1ouUEAAAAgCMQnAAAAABwBIITAAAAAI5AcAIAAADAEQhOAAAAADgC2boAAACAijzSr+nH+gHVObScAAAAAHAEghMAAAAAjkBwAgAAAMARCE4AAAAAOALBCQAAAABHIFsXAAAAcCBhhQuqFS0nAAAAAByB4AQAAACAIxCcAAAAAHAEghMAAAAAjkBwAgAAAMARCE4AAAAAOAKphAEAAICKPNKv6cf6AdU5tJwAAAAAcASCEwAAAACOQHACAAAAwBEITgAAAAA4AsEJAAAAAEcgWxcAAABwIGGFC6oVLScAAAAAHIHgBAAAADhETJ48Wa1atVJ0dLR69eqlxYsXV+h9b775plwul/r3769QIjgBAAAADgHTp0/XiBEjdM899+i7775T586d1bdvX23fvn2/71u3bp3uuOMOnXzyyQo1ghMAAADgEDBx4kQNHTpUV199tTp27KhnnnlGMTExevHFF8t9j8/n05VXXqmxY8eqTZs2CjWCEwAAAMDBMjIySiz5+fn7HFNQUKClS5fqzDPPDG5zu912feHCheWee9y4cWrcuLGuueYaOQHBCQAAAFDRbF01vUhq3ry5EhISgsuECRP2KV5aWpptBWnSpEmJ7WZ969atZd7S/Pnz9cILL2jKlClyClIJAwAAAA62ceNGxcfHB9ejoqL+9DkzMzP197//3QYmDRs2lFMQnAAAAAAOFh8fXyI4KYsJMMLCwrRt27YS2816SkrKPsf/9ttvdiD8BRdcENzm9/vtv+Hh4Vq9erXatm2rmka3LlRazLBharR2rVJyc9Vg0SJF9OhRofdFDxyopoGAkv773xLb3Y0bK+Gll9R40yalZGcr6eOPFdauXYljwtq0UdJ776nx9u1qkp6uxOnT7fuA2iTm78PUaP5apazOVYMZixTRuYJ154KBarouoKTnStaduOH3qNG8lWryc5aaLN+p5FfnKKJLzxLHmOuZ9xZfYm/4Z5XeF1DdYq4cpkafrVXKj7lq8M4iRRxbwbpz3kA1/TWgpP8rVnfCw1X/zgfU8MMVarI8S43nb1LCQ9Pkbty0xHvDWh2hpKdnqMk3qWryfboavPGVInv1qepbA/60yMhIdevWTfPmzSsRbJj13r1773N8hw4d9MMPP2jZsmXB5cILL9Rpp51mX5uuZKFAcIJKiR4wQPETJypr7FilHXecvMuXK3n2bLkbNdrv+8JatlT8I48o/8sv99mXNGOGDT52XXSRUrt2lW/9eiXPnStXTIzdb/5N/uQTKRDQztNP144TT5QrMlJJH3wguVzVdq9AVYo+f4Di/z1RWY+PVdp5x8n783Ilvzxb7gYHqDuHt1T86EeU/82+dcf7+y9KH3OT0vp20o5LT5Lvj3VKfvkTuZNLNtNnPnq3tvVICS45U5+s8vsDqkv0uQMUP3qisp4aq7T+x8m7crmSX5wtd/IB6s5hLRU/8hHlf1uy7riiYxRx9HHKmnyfPd+umy5ReJv2SnpmZonjkp/70AYyOwadrrT+3eRZtVxJz30od8OS/foBJxgxYoTtpjVt2jStXLlSN9xwg7Kzs232LmPQoEEaNWqUfW3mQTnmmGNKLImJiapfv759bYKdOhecfPnll7YpqVmzZnbSlxkzZpTYf++999qoLjY2VklJSTbbwDfffBOy8mKv2BEjlDNlinKnTpV35UqlX3+9Ajk5qjdkSPlvcruV+NpryrznHvl+/73ErrAjjlBk797KuOEGeZYske+XX+xrV716ir7iCntMxIknKqxVK+2+6ip5f/zRLrsHD1ZE9+6KPP306r5loErEXjtCOW9OUe7bU+Vds1Lp/7pegdwc1RtwgLoz6TVlPnaPfBtL1h0jb+YbKvh6nnwb18r768/KuH+E3PEJCu9wbInj/NmZ8qduCy7mukBtETtkhHKmT1Huu4V1Z0xh3bn0AHXn0deU+fi+dSeQlaGdV52tvI/flm/tL/Is+0YZY29SZKfucjfd88TYldRA4a2PVNazD8i7+gf51q9R5iMj5Y6JVfiRx1T3LQMHbeDAgXrkkUc0ZswYdenSxbaAzJo1KzhIfsOGDdqyZYucLKTBiYnkzOQwZibLshx55JF66qmnbJOTySZgZrs8++yzlZqaWuNlRTEREYro1k35c+fu3RYI2HUTYJQnbswY+bdvV24ZubZdhQO7Anl5Jc6p/HxFnnTS3mMCAQWKpc+zx/v9wWMAx9edY7op/+tSdefruYo8bj9159Yx8u/Yrty3XqzQNWKu+If8GbvlWbm85HluGKkm36ep4f++U+w/7pDCCtPAALWh7hzdTfkLStWdBXMV2XU/deemwrrzTgXqjvk7Uz9BAb9fgczdey6xa4e8v61STP9BctWLsXUm5vLr5EvbJs+PS//8faF2cYdoOUg33XST1q9fb9MNm4f6Zpb4Ip9//rmmTp1a7nvNvtKNBXVqQPw555xjl/L89a9/3WdiGZPubMWKFTrjjDNqoIQoi7thQ7nCw+UvNeDKrId36FDme0yrR8w11yi1S5cy93tXrZJ3/XrVnzBB6dddp0B2tmJvu01hzZsrrOme/r+eRYvs9vgHH1TG6NG2ta3+Aw/YsrgLjwGczJ1UWHfSStWd1G0Kb1tO3el+omIGXKPUc8uuO0WiTj9PiU++ab9A+bdv0c6/nWW/WBXJeekJeX76Tv7dOxXZ7QTVv2uC7Vufef/tVXR3QAjqzo791J1uJyrmsmuUeuH+605QZJTi73xQeR++oUBWZnDzjqvOVNL/zVCTZZn2YZgJdnZe00+BjD0BDIA6OubETCzz3HPP2dzOprWlPCZKLD1RDULLFRenxFdeUfrQoQrs2PtlqQSvV7suuUThRx6plF27lJKTo8jTTlPeRx/Zp1iGPy1Nuy67TFEXXKCUrCw7IN6VmCjP0qX2DwZwqHHFxinxsVeUPmpoiUCjLAULP1PauV204y8nKP+LWUqc/FaJcSzZLzymgkVfyLvqB+W89qwy7r9dsYNvNiMoa+BOgBDUnYdfUfq/Dlx3rPBwJT3xlh2/mH7PDSV2Jdwz2QYkO644WWl/6am8uTOU/OwHcjfaN/sRgDqQSvjDDz/U5ZdfrpycHDVt2lRz5szZby5mMynN2LFja7SMdY0JEgJer9ylJvkx6/4yJvkJa9tW4a1b7xm4Hjx4T1yc4vEotX17OwbF+913SuvaVa74eDvQ3VzHZAEzY1CKFMyZo9R27eRq0MAGNIH0dDXesmWfMSyAE/l3FdadUgNp3Y2ayJ9aRt1p2VbhzVsr6fky6s4aj1JPby/fhj2/+6bvvW/9b3ZJ//4bNfrsF9UbeI2y/++BMsti+te7IiIUdngr+X7/pWpvFKiputOgnLrTorDuPFtG3VnpUWrfvXXHBiaPv6WwZi3toPfirSaRvU9X1Gnna1v3pOD2jHtvVNSJZ6nexYOV/dyD1XTHQN3l+JaTonRmCxYsUL9+/TRgwABt37693ONNBoL09PTgYiatQRXzeGxrRVTxrnUul10vWLiwzC5bqccco7QuXYJL/syZKvjsM/vaV+pnFMjIsIGJSSNsBrvnvf/+Puc0LTAmMDGtKyaVcN7MktlVAMfWnR+XKuqEUnXnhDNU8F0Zdee3VUo9+xjbIlK05M+dGWwl8W3Zz//f3G65IsufpCu8YxcFfD7508r//yngqLrz01JF9S6j7nxfTt059xilXdgluOTPm6mCRZ/Z18G6UxSYtDpCO686U4HdO0ucx44zMUq3zpv1wmAHQB1rOTGZutq1a2eX448/XkcccYQdd1KUBq00M2NmVcyaif3LnjhRidOm2VYNz+LFihk+XK7YWOW+9JLdnzBtmvybNilz9Gg7qN37008l3u/fvdtGxsW3R196qfypqfJt2KDwTp0U//jjypsxw7aWFKlnMnWtXGmPM4PvzTHZjz1ms3sBtUH28xOV+Og0eX5YIs+yxYq5ZrhcMbHKfbuw7jw6Tf5tm5T5UGHd+aVU3ckorDuF282Xp7ib/qW8uTPtWBNXUkPFDrpRYSmHKe9/b9tjIo47XhFdetmgxjz9jTiut+Lvfky5M16l3zxqjewXJyrxoWny/LhEnhWLFXPVcLnqxSr33cK681Bh3Xl0tFSQL++vpepOZmHdKdpuApMn37HphHf+43zJHRZsmfGn77QBkQl8Aum77LmznhqnQF6uYgYOVdjhrZX/+f9q/kMA6gDHByelmclkzLgShFbeW28po1EjxY0bp7CUFHmWLdPOfv1sNi4jrEWLgx4HYga1m7lTTPcw35Ytyn35ZWXdd1+JY8Lbt7eD5t3JyfKtW6es8eNtcALUFnkfvqWM5EaKu22cwhqlyLNymXYO7hdswQg7rIUUqHjdCfh9dkBw0l8G20HD/t075FnxrXZcdrJNK2yPyc9XvQsuV/3h99rWFO/Gtcp+8TEbKAG1Rd5HhXXn1mJ155p+djyIEdbs4OpOWJPDFH3mRfZ1ow9KZrbbcWUfFSz+wo5XMdeoP2K8Grz8qc0aZoKbXTdcJO+qFVV8h3A8E93WdJLDgOocVyBg8rWGRlZWltasWWNfd+3a1WbjMt24kpOT1aBBA40fP97OVGnGmqSlpdmUw6+//rqWLl2qo48+ukLXMAPizSD61ZLqV/P9AIeclqEuAFALRYS6AEDtk+mX2v8u2yU/Pj5eThL8LtlDql/Dj/UzvVL7b535uRySLSdLliyxwUjxWS2NwYMH65lnntGqVavsDJcmMDHBSo8ePfTVV19VODABAAAAUHuENDjp06eP9tdw895779VoeQAAAACEDqkmAAAAADgCwQkAAAAAR6h12boAAACAkDzSr+nH+m7VOXXwlgEAAAA4EcEJAAAAAEcgOAEAAADgCAQnAAAAAByB4AQAAACAIxCcAAAAAHAEUgkDAAAABxJWuNSkgOocWk4AAAAAOALBCQAAAABHIDgBAAAA4AgEJwAAAAAcgeAEAAAAgCOQrQsAAACoyCP9mn6s71adUwdvGQAAAIATEZwAAAAAcASCEwAAAACOQHACAAAAwBEITgAAAAA4Atm6AAAAgAMJK1xqUkB1Di0nAAAAAByB4AQAAACAIxCcAAAAAHAEghMAAAAAjkBwAgAAAMARyNYFAAAAHAjZumoELScAAAAAHIHgBAAAAIAjEJwAAAAAcASCEwAAAACOQHACAAAAwBHI1gUAAABU5JF+TT/Wd6vOqYO3DAAAAMCJCE4AAAAAOALBCQAAAABHYMwJgPI1CnUBAAB1gi/UBYBT0HICAAAAwBFoOQEAAAAq8kg/rIav6VedQ8sJAAAAAEcgOAEAAADgCAQnAAAAAByB4AQAAACAIxCcAAAAAHAEghMAAAAAjkAqYQAAAKAij/Rr+rG+W3VOHbxlAAAAAE5EcAIAAADAEQhOAAAAADgCwQkAAAAARyA4AQAAAOAIZOsCAAAADiSscKlJftU5tJwAAAAAcASCEwAAAACOQHACAAAAwBEITgAAAAA4AsEJAAAAAEcgWxcAAABQkUf6Nf1Y3606pw7eMgAAAAAnIjgBAAAA4AgEJwAAAAAcgeAEAAAAgCMQnAAAAABwBLJ1AQAAAAcSVrjUJL/qHFpOAAAAADgCwQkAAAAARyA4AQAAAOAIBCcAAAAAHIHgBAAAAIAjkK0LAAAAOBCyddUIWk4AAAAAOALBCQAAAABHIDgBAAAA4AgEJwAAAAAcgeAEf0rMsGFqtHatUnJz1WDRIkX06FHusfUGD1bTQKDEYt5XWtzYsWq8ebNScnKUPGeOwtq1K7HflZSkxFdfVZP0dDXZtUsJzz8vV2xstdwfUB1iLhumRu+vVcr8XDV4aZEiOpZfb6JPu1gNpn2rJp/uUpMvs9Twte9V75y/lTjGndxYCfe8pMYfbVLKV9lKeuJjhTUvWW/cDZooYezLajxry57zvLJU0addUm33CBwqdSfssDZKeug9Nf5ku5p8lq7E/0y37wNQPQhOUGnRAwYofuJEZY0dq7TjjpN3+XIlz54td6NG5b7Hn56ubSkpwWV7y5Yl9sfedZdib7lF6ddfr7RevRTIzrbnVFRU8JjE115T+NFHa+dZZ2nn+ecr8pRTlPDcc9V6r0BViT5rgOKHT1TW82OV9vfj5P11uZKfnC13Utn1xp++U1kvjdeOIb2VdsWxyvngJSWMeUmRx58dPCbp4RkKa9ZGu+64SKl/6yrflvVKnjxXruiY4DGJ976s8JbttWvEhUq7opPyPntPiRPeUviRXWrkvoHaWHfMv8lPfSIpoJ03nK4d154oV0SkkiZ+ILlcNXbvcNC35lAsdUxIb/nLL7/UBRdcoGbNmsnlcmnGjBkl9r/33ns6++yz1aBBA7t/2bJlISsr9hU7YoRypkxR7tSp8q5caQOKQE6O6g0ZUv6bAgH5t23bu2zfXvKcw4cr6/77lT9zprw//KDdgwYprFkzRffvb/eHd+ig6HPOUfq118qzeLE8X3+tjJtvVvTll8vdtGl13zLwp8X+dYRyZkxR7gdT5V27UukTrlcgL0f1Liy73hR894XyP58h77pV8m36XTlvPiHvmhWK7HKS3R/W4ghFHttbGQ/eIM/PS+Rb/4syHrhBrqh6iu57RfA8EceeoJzpT8rz87fybVqrrBfHK5C5WxFHdauxewdqW92J6Hyiwpq20u6xV8n724922X3vYEUc1V2RPU6v0fsH6oqQBifZ2dnq3LmzJk+eXO7+k046SQ8++GCNlw0HEBGhiG7dlD937t5tgYBdj+zdu9y3ueLi1GjdOjXesEFJM2YovGPH4L6w1q0V1rRpiXMGMjJU8M03wXNG9O4t/65d8ixdGjzGHu/3K6JXr6q/T6AqhUcookM35S8uVW8Wz1Vkp/LrTXHmC1FYy/Yq+O5Lu+6K2NOqGMjPK3FOefKDX8IMz4oFij5roFzxSfaJr3mtqGgVLP28ym4PONTqjisyym4LFOTvPaQgz/7Niey8t34BOEQmYTznnHPsUp6///3v9t9169bVYKlQEe6GDeUKD7etH8WZddO6URbv6tVKHzJEnhUr5E5IUOwdd6jBggVKPfpo+TdtkjslJXiO0ucs2mf+Ld3aIp9P/p07FVZ4DOBU7sTCerOz1O/4zm0Kb1V2vTFcsfG2T7z9ouTzKf3BYSoo/JJmngp7t6xX/RsnKH3CdQrkZiv2r7cprElzhTXY25q4a9QAJf1nulLm7VTA67FPnHfdebF8f/xWjXcM1O664/lhkQJ52Yq/+UFlTB5te3HUv+kBWxZ3Q1rrgepwyM0Qn5+fb5ciGRkZIS0P9vIsWmSXIgULFqjRypWKue46ZY0ZE9KyAU4WyMlU2pVd5IqJU1SPMxR/20TbTcV0W5HPq113XaLEu19Qyqe7FPB6lf/tXOV9/VGJPvH1r79PrvqJ2jHsDPl3pyn61P5KmvCWdgw92XZVAQ5Ff7bumLqya+RlShj5tFIG3mJbTHI/eUOelUvtawBV75ALTiZMmKCxY8eGuhiHPH9amv0fubtJkxLbzbp/69aKncTrlef77xVemI2r6H2lz2HWvYXjjcx2d+NSWVLCwuROTpavotcFQsR80bH1JrlUvUluIv+O/fz+BgLBFg7vL8sV3uooxV01SjvNFyyzbdV3Sruyq31KbAbrmuuYTEaelUuC2YZiB96s1IFHy/v7z3Zb1q8rFNn1ZMVcdqPtZw84WajqjlHwzRylXtxOroQGNqAJZKXbrHe+T36vrtsF6rRDLgfAqFGjlJ6eHlw2btwY6iIdmjweO+4j6owz9m5zuex6wcKFFTuH262ITp3k27LFrvrWrrWvi5/TVb++Inv1Cp7Ts3Ch3ElJCj/uuOAxkaefbs/l+eabKrs9oFp4PfKsWmqf4JaoNz3OUMEPFaw3htstmW4qpQSyM+yXK5MK1QzYzfvi/T2XKMraVfpJr88nlzkX4HQhqjsljknfYQOTyO6nyZ3UWHlfzaz07aCWMv+7DKvhxa0655BrOYmKirILql/2xIlKnDZNniVLbOasmOHD7XwjuS+9ZPcnTJtmx5Jkjh5t1+PuvlsFixbJt2aNXImJirvzToW1bKnc55/fe85JkxT373/L++uvNlipf9998m3erLzCTG7eVauU9/HHSpwyxWYHMwPzE556Snlvvil/YZADOFn26xOVeM80+2TW89NixVwxXK56scr9oLDe3DtN/tRNypy8p97EXjVyTyahTb/ZAbxRJ56reuf+XenFWjuiz7hU/l2p8m3boPC2nRR/++PK+2KGfeIb7Fu/4VfFj3pWmY/fIX/6DkX36a/IXmdp123nh+iTAJxfd4x6F1xls4OZ40x2r/gRjyv7jcdsdi8AVe+QC05Qc/LeeksZjRopbtw4Oxjds2yZdvbrFxywHtaiRYkntWbyxIQpU+yxRRm30k44waYhLpL90EM2wDHzlrgTE1Uwf749p4qNI9p95ZU2IEmeN8+eP+/dd5Vxyy01fPdA5eTNeUsZiY0Ud904hTVIkeeXZdp5Sz/5dxbWm5QWUqBYvYmOVcI//09hjQ9XID9X3vWrtHvM3+x5ipiBuaYvveni4kvbotyPXlbW8/ftvajPq53Dz7UDec38DKb/vW/jGqXfO1j5Cz6u2Q8AqE11x3xRatneDpp3xyfLt3mdnTsl+/XHavDOgbrFFQiYvHmhkZWVpTVr1tjXXbt21cSJE3XaaacpOTlZLVq00M6dO7VhwwZt3rxZ5513nt588021b99eKSkpdqkIMyA+ISFBq82A0Gq+H+CQ0z3UBQAA1AWZPqn997Jd8uPj4+Ukwe+SA6X6kTV77cwCqf10Z34u1SWkPdmWLFligxKzGCNGjLCvxxRmbpo5c6ZdN4GJcfnll9v1Z555JpTFBgAAAHCodevq06eP9tdwc9VVV9kFAAAAwKGvDuYAAAAAAOBEDIgHAAAAKvJIv6Yf67tV59TBWwYAAADgRAQnAAAAAByB4AQAAACAIxCcAAAAAHAEghMAAAAAjkC2LgAAAOBAwgqXmr5mHUPLCQAAAABHIDgBAAAA4AgEJwAAAAAcgeAEAAAAgCMQnAAAAABwBLJ1AQAAABV5pF/Tj/XdqnPq4C0DAAAAcCKCEwAAAOAQMXnyZLVq1UrR0dHq1auXFi9eXO6x7733nrp3767ExETFxsaqS5cueuWVVxRKBCcAAADAIWD69OkaMWKE7rnnHn333Xfq3Lmz+vbtq+3bt5d5fHJysv71r39p4cKFWrFiha6++mq7zJ49W6FCcAIAAAAcAiZOnKihQ4faAKNjx4565plnFBMToxdffLHM4/v06aOLL75YRx11lNq2batbb71Vxx57rObPn69QITgBAAAAHCwjI6PEkp+fv88xBQUFWrp0qc4888zgNrfbbddNy8iBBAIBzZs3T6tXr9Ypp5yiUCE4AQAAAA4kLESLpObNmyshISG4TJgwYZ/ipaWlyefzqUmTJiW2m/WtW7eWe1vp6emKi4tTZGSkzjvvPD355JM666yzFCqkEgYAAAAcbOPGjYqPjw+uR0VFVdm569evr2XLlikrK8u2nJgxK23atLFdvkKB4AQAAABwsPj4+BLBSVkaNmyosLAwbdu2rcR2s56SklLu+0zXr3bt2tnXJlvXypUrbctMqIITunUBAAAAtVxkZKS6detmWz+K+P1+u967d+8Kn8e8p6wxLTWFlhMAAADgEDBixAgNHjzYzl3Ss2dPTZo0SdnZ2TZ7lzFo0CAddthhwTEr5l9zrMnUZQKSjz76yM5z8vTTT4fsHghOAAAAgEPAwIEDlZqaqjFjxthB8Kab1qxZs4KD5Dds2GC7cRUxgcuwYcP0xx9/qF69eurQoYNeffVVe56DlZeXZyd+/LNcAZM37BBm0q2ZrAarzYCfUBcGqG26h7oAAIC6INMntf9+T+aoA42tCNl3yWul+pE1e+3MAqn98878XIq6gI0fP97Op2LGtvzyyy92MP3dd99tZ6m/5pprDvqcjDkBAAAAcNDuv/9+TZ06VQ899JAd81LkmGOO0fPPP3/wJyQ4AQAAAFAZL7/8sp577jldeeWVNlNYkc6dO2vVqlWVOifBCQAAAICDtmnTpmAa4tLdvTwez8GfkOAEAAAAQGV07NhRX3311T7b33nnHXXt2rVS5yRbFwAAAICDZrKCmdTFpgXFtJa89957Wr16te3u9eGHHx78CWk5AQAAACr4rTkUi4NddNFF+uCDDzR37lzFxsbaYMXMMG+2nXXWWZU6Jy0nAAAAACrl5JNP1pw5c1RVHB6PAQAAAHAiM6fJjh079tm+e/duu68yCE4AAAAAHLR169bJ5/Ptsz0/P9+OQ6kMunUBAAAAqLCZM2cGX8+ePVsJCQnBdROszJs3z84QXxkEJwAAAAAqrH///vZfl8tls3UVFxERYQOTRx99VJVBcAKgfE1DXQCgFto7STKAijLz9X0f6kKgokzaYKN169b69ttv1bBhQ1UVghMAAACgIiO1a/rhg1uOtnbt2io/J8EJAAAAgErJzs7WF198oQ0bNqigoKDEvltuueWgz0dwAgAAAOCgff/99zr33HOVk5Njg5Tk5GSlpaUpJiZGjRs3rlRw4vDGIgAAAABOdNttt+mCCy7Qrl27VK9ePS1atEjr169Xt27d9Mgjj1TqnAQnAAAAAA7asmXLdPvtt8vtdissLMzOb9K8eXM99NBDGj169MGfkOAEAAAAQGWYtMEmMDFMNy4z7sQw855s3LixUudkzAkAAABwIO4QPNZ3y9G6du1qUwkfccQROvXUUzVmzBg75uSVV17RMccccyjeMgAAAAAn+s9//qOmTfdMijZ+/HglJSXphhtuUGpqqp577rlKnZOWEwAAAAAHJRAI2K5cRS0k5vWsWbP0Z9FyAgAAAOCgg5N27dpVemxJeQhOAAAAABwUMxDejDXZsWNH1Z63Ss8GAAAAoE544IEHdOedd+rHH3+ssnNWyZgTn8+nH374QS1btrQDYQAAAIBDSljhUtPXdLBBgwbZ2eE7d+6syMhIOxFjcTt37qyZ4GT48OHq1KmTrrnmGhuYmNRhCxYssFPVf/jhh+rTp09lTgsAAACglpg0aVKVn7NSwck777yjv/3tb/b1Bx98oLVr12rVqlU2p/G//vUvff3111VdTgAAAAAOMnjw4Co/Z6XGnJjJVVJSUuzrjz76SJdddpmOPPJIDRkyxHbvAgAAAIAaCU6aNGmin3/+2XbpMvmMzzrrLLvd9DkLC3N45zgAAAAAjlSpbl1XX321BgwYYGeEdLlcOvPMM+32b775Rh06dKjqMgIAAACoAyoVnNx77712Nkgz6Yrp0hUVFWW3m1aTkSNHVnUZAQAAgND3N6rpSTjcqnMqnUr40ksvtf/m5eVV66AYAAAAAM7i8Xhs6uBly5bZRouQxmNmrMl9992nww47THFxcfr999/t9rvvvlsvvPBClRUOAAAAgPNERESoRYsWNi6oSpUKTsaPH6+pU6fqoYceshOuFDFR0/PPP1+V5QMAAADgQGYKkdGjR1dqssUq7db18ssv67nnntMZZ5yh66+/PrjdzA5p5jsBAAAAcGh76qmntGbNGjVr1kwtW7ZUbGxsif3fffddzQQnmzZtUrt27fbZ7vf7bf8zAAAAAIe2/v37V/k5KxWcdOzYUV999ZWNkErPHN+1a9eqKhsAAADgDGYqv5qezi9MjnbPPfc4IzgZM2aMzcxlWlBMa8l7772n1atX2+5eH374YZUXEgAAAIAzLV26VCtXrrSvjz766D/VWFGp4OSiiy7SBx98oHHjxtm+ZSZYOe644+y2otniAQAAABy6tm/frssvv1yff/65EhMT7bbdu3frtNNO05tvvqlGjRrV3NQuJ598subMmWMLlZOTo/nz5+vss8+u7OkAAAAA1CI333yzMjMz9dNPP9mMXWb58ccflZGRoVtuuaXmWk6+/fZb252rV69eJbZ/8803dpb47t27V6owAAAAAGqHWbNmae7cuTrqqKNKjE2fPHlypRstKtVycuONN2rjxo37bDdjUMw+AAAAAIc2v99vJ2MszWwz+2osOPn555/tGJPSzOAXsw8AAAA4JLN11fTiYKeffrpuvfVWbd68uURjxW233WbnQ6yx4CQqKkrbtm3bZ/uWLVsUHl6pnmIAAAAAatkkjGZ8SatWrdS2bVu7tG7d2m578sknK3XOSkUSpg/ZqFGj9P777yshISE4Mt9MX0+2LgAAAODQ17x5czsLvBl3smrVKrvNjD8588wzK33OSgUnjzzyiE455RQ7CWNRHuNly5apSZMmeuWVVypdGAAAAADO5/F4VK9ePRsDmMaJqmqgqFRwcthhh2nFihV67bXXtHz5cluwq6++WldccUWZg2IAAAAAHDoiIiLUokUL+Xy+Kj1vpQeImMkX//GPf1RpYQAAAADUDv/617/ssA7Tcyo5OTm0wcmvv/6qzz77zE7CWDpVmJkxHgAAAMChPSB+zZo1atasmR3uYRovijPjUWokOJkyZYpuuOEGNWzYUCkpKXK5XMF95jXBSd0RM2yYYu+8U2EpKfIsX66Mm2+W59tvyzy23uDBSpw6tcS2QF6ettarV2Jb3Nixihk6VO7ERBV8/bXSb7hBvjVrgvtdSUlKePJJRV1wgUmwrbx331XGrbcqkJ1dTXcJVK2Yc4cp9uI7FZaUIs/a5cp47mZ5fi273kT3vlixl45WeNN2UniEfJt/VfaMR5X7+atlHh9/w9OKPed6pT8/XDkzHw9ubzRlrcKbtCpxbMa0kcp+98Eqvjug+sScM0yx/e9UWGKKPOuWK+P5/dSd4y9W7F8K605YhHxbflX2+48q94ty6s71Tyu27/VKf2G4cj7cU3fCGrVU3IC7FdnpdHtN367N9v1Z74yXvJ5qvVc4kLuyeW7/5DUdrH///lV+zkoFJ/fff7/Gjx+vf/7zn1VeINQe0QMGKH7iRKVff70833yj2OHDlTx7tlLbt5c/NbXM9/jT0+3+oECgxP7Yu+5S7C23aPfgwfKtXav6992355wdO0r5+faYxNdeU1jTptppBl5FRCjxpZeU8Nxz2n3lldV7w0AViD5pgOKvmaj0/7tenl++UeyFw5U8drZSb2gvf/q+9cafuVNZb4+X749VCngLFNXjfCXc+pJ86dtV8P0nJY6NOr6/ItsfL9+OTWVeO/O1u5Uze0pwPZCbWQ13CFSP6BMHKP7qiUp/prDuXDBcyWNmK/Wm/dSdd8bLt6mw7nQ/Xwk3F9adZaXqTq/+ijxy37oTfngHyeVW+tPXybd1jcJbHKOEYVPkiopV5rQ7q/2eASfzer22UWLIkCE6/PDDQxuP7dq1S5dddplqQmZmpoYPH26biszA+xNOOEHflvNkHjUrdsQI5UyZotypU+VdudIGKYGcHNUbMqT8NwUC8m/btnfZvr3kOYcPV9b99yt/5kx5f/hBuwcNUlizZooujMzDO3RQ9DnnKP3aa+VZvFier7+2rTXRl18ud9Om1X3LwJ8We9EI5XwyRbnzpsq7caUNUgL5Oap3Ztn1puDHL5S/aIa8f6ySb+vvyvngCXnXrVBkx5NKHOdObqaEfzyp3Y9eqUA5T3T9uZny794WXMx1gdoi9sIRypkzRbmfTpX3j5U2SLF154xy6s5PXyj/m2J158PCunNUGXXn2ie1+7ErFfCVrDv5389W+lNDVLB8jnzb1ir/2w+U/f4jij7+kmq9V6A2MHMbPvzwwzZIqUqVCk5MYPLJJyWfOlSXa6+9VnPmzLEDbX744Qc7x4rJnWxmn0QIRUQools35c+du3dbIGDXI3v3Lvdtrrg4NVq3To03bFDSjBkKNy0ihcJat7YtIsXPGcjIUME33wTPGdG7t/y7dsmzdGnwGHu836+IXr2q/j6BqhQeoYh23ZS/rFS9WT5XkR3KrzfFRR57usIOa6+Cn77cu9HlUuKIV5T134fl3fhzue+N+8tINXk1TQ0nfafYi++Q3A6fehgoXnfadrN1pUTdWTFXke0rWHc6Fdadn0vVneGvKOv9/ded4lwxCfJn7TzoWwAORaeffrq++OKL0Hfrateune6++24tWrRInTp12id98C233FIlhcvNzdW7775rJ3s086oY9957rz744AM9/fTTtnsZQsPdsKFc4eG29aM4s25aN8riXb1a6UOGyLNihdwJCYq94w41WLBAqUcfLf+mTXKnpATPUfqcRfvMv6VbW+Tzyb9zpx33AjiZO76hXGHhttWiOLMefljZ9cZwxcSr8Uub5IqIkvw+pT8zTAXFApzYv/xT8nltq0p5zFNjz2/f2S9VkR1OUP1BE+ROaqrMF2+vorsDqo+7fmHdSa9E3Xm+WN15bpgKigU4sRcX1p0Py687xYWltFXsuTcrY9odf+JugEPHOeeco5EjR9oGhG7duu0zIP7CCy+smeDkueeeU1xcnI2USkdLpu9ZVQUnppnI5E6Ojo4usd1075o/f36Z78nPz7dLkYyMjCopC/48z6JFdilSsGCBGq1cqZjrrlMWSRSAcpmxIWnDu8gVHaeozmcofshE203FdPkKb3ucYi+4VWm3Hbffc2S//1jwtXfdD7YPfsKwZ5X58ijJW1ADdwGEqO6MKKw7x55hx6zYuvPTFwpvc5xiz79Vabfvv+4U7/6VPGaW8ha8rdw5z1d72YHaYNiwYfbfiRMn7rPPxASVmQOlUsHJ2rVrVRPq16+v3r1767777tNRRx1lZ6B/4403tHDhQtt6U5YJEyZo7NixNVK+usyflqaA1yt3kyYltpt1/9atFTuJ1yvP998rvPBnWfS+0ucw695ly4LHuBs3LnmesDC5k5Plq+h1gRDxZ6Qp4PPKnViq3iQ2kX/3fn5/AwH5tvxmX3rXLlf44Ucp7tJR2vnjF4o8+mS5Exqr8QsbgoebJ8zxVz9qBwynDm1d5ik9q7+RKzxCYU1aybfpl6q6RaBa+DML605CJerO1sK6s66w7vxllHb+9IUiOxbWnSml6s5VhXXnur11x7QyNrjvMxWsWqD0p5njra7yuSSfu+av6WSlpxOpAwnKZMeaBAIBOyt9VFSUnnjiCTsTvdtddtFHjRql9PT04LJx48YaL3Od4PHYcR9RZ5yxd5vLZdcLFi6s2DncbkV06iTfli121WTnMq+Ln9NVv74ie/UKntOzcKHcSUkKP27vk67I00+35zIZwwBH83rkWbPUtn6UqDfHnqGCVRWsN4b5/5/ppmK6v372itJuOVZpt3YJLibjUPZ/H9bOe/uWe4rwNl0UMF0id5fqJgk4te78ttTWlRJ1p9MZKlhdybrzxStKu+1Y27JStNi68/7D2jm2b4kWkwb3f26vn/7U1ftkmQSwR15enkI6CeMff/yhmTNnasOGDSooKNkloKymncpq27at7TqWnZ1tu2g1bdpUAwcOVJs2bco83gQwZkH1y544UYnTpsmzZInNnBUzfLhcsbHKfekluz9h2jQ7liRz9Gi7Hnf33SpYtMjOWeJKTFScmR+lZUvlPr+3eTx70iTF/fvf8v76azCVsG/zZuXNmGH3e1etUt7HHytxyhSbHcwMzE946inlvfmm/IVBDuBk2e9PVOLwafKsWSLPL4sVc+FwuaJjlTuvsN4Mnyb/zk3KfHlPvYm9dKQ91rScmH7zUd3PVb0+f1f60zfY/YHMnfJmlhyca7J1+XZvDbaIRLQ/XhHte6lgxWe2m0tEh96Kv+YxO19DIHt3jX8GQGVkz5yoxFumyfPbEnl+XayY80vVnVsK686rhXXnkpH2WNNyYuvOceeq3ql/V/qz+6k7Po98u7bKt/mXvYHJfZ/Ll7peGVPvkDu+UfDY0mPHgLrI5/PpP//5j5555hlt27ZNv/zyi/2Obsamt2rVStdcc03NBCfz5s2zA1zMxVetWqVjjjlG69atsy0cxxV7ol2VzAAbs5g0xrNnz9ZDDz1ULddBxeW99ZYyGjVS3LhxeyZhXLZMO/v1Cw5YD2vRwmbRKjF54pQp9tiijFtpJ5xg0xAXyX7oIRvgmHlL7CSM8+fbcxbNcWKY+UxMQJI8b97eSRiraJwTUN3y5r+ljIRGivvruD2TMP6+TDvv7RdswQhr1EIKFKs3UbFKuP7/FNbgcAUKcm1a1N0T/2bPU1EBT77qnXy56l9+r/2S5t22VtkzH1P2jKp7kARUt7yv31JGfCPFXV5Yd9Yu085x/eRPL6fuRMcq4R/F6s6mVdo96W/2PBUV1fkshTc7wi5NXiiZJXTLxQ7vbwPUADPv4bRp0+z38qFDhwa3m9hg0qRJlQpOXAETURyknj172tH5ZmyHGReyfPlyNW7cWFdeeaX69etnZ4+vKiYQMUVs37691qxZozvvvNMOkP/qq6/2yRJWFtPakpCQoNVmDEuVlQqoIy4IdQGAWogMzcBBy/RI7f8n2yU/Pj5eTlL0XfLnkVL9kjmaql1mntTxAWd+LoYZA/7ss8/qjDPOCMYERY0XZty4aVSokTEnK1eu1KBBg4ITsJiUvyZ717hx4/Tggw+qKpkfxo033qgOHTrYa5500kk2YKlIYAIAAACgeph5B8tKUmUGyns8ZU8IXC3dukz3qqJxJmYMyG+//aajjz7arqelpakqDRgwwC4AAABAqJh50L0huKaTdezY0fZmatmyZYnt77zzjrp27Vpzwcnxxx9v5xkx6X3PPfdc3X777Xbylffee8/uAwAAAHBoGzNmjAYPHmxbUExriYkFVq9erZdfflkffvhhzQUnJhtXVlaWfW3GnZjX06dP1xFHHFGlmboAAAAAONNFF12kDz74wA7tMD2rTLBikmOZbWeddVbNBSfF0/iagpj0YQAAAADqlpNPPllz5sypsvO5Kxuc7NixY5/tu3fvLnf+EQAAAACo8uDEzGliJl0pLT8/3/Y5AwAAAIBq7dZlZoQvYtL5mpzPRUywYiZnNLNBAgAAAIcSkznLE4Jr1jUHFZz079/f/utyuezI/OLMvCMmMHn00UertoQAAAAA6oSD6tZlUoSZpUWLFtq+fXtw3SymS5dJHXb++edXX2kBAAAAOILJ0pWTk7PPdjNBu9lXY2NO1q5dq4YNG+4zGB4AAABA3TC2cEqR0kzAYvbVWHDy4IMP2nlNilx22WVKTk7WYYcdpuXLl1eqIAAAAABqj0AgYId7lGbiARMb1FhwYuY1ad68uX1t8hrPnTtXs2bN0jnnnKM777yzUgUBAAAA4HxJSUk2+DCByZFHHmlfFy0mYZaZgHHAgAE1Nwnj1q1bg8GJmZreXPzss8+2A+J79epVqYIAAAAATuUJQbYuj5xp0qRJttVkyJAhtvtW8Qy+kZGRNibo3bt3zQUnJlrauHGjDVBMi8n9999vt5tCljX/CQAAAIBDw+DCrL2tW7fWCSecYLP2VpVKBSeXXHKJ/vrXv+qII46wM8Wb7lzG999/r3bt2lVZ4QAAAAA4R0ZGhuLj4+3rrl272sxcZilL0XHVHpw89thjtrnGtJ489NBDiouLs9u3bNmiYcOGVeaUAAAAABzO9KAy3/kbN26sxMTEMgfEFw2Ur0yPqkoFJ6bp5o477thn+2233VaZ0wEAAACoBT799NNgJq7PPvusys9f4eBk5syZtvuWCUzM6/258MILq6JsAAAAABzk1FNPLfN1jQcn/fv3t1m6TBOOeV2eyjbhAAAAAE7lLVxq+ppO9uWXX+53/ymnnFJ9wYnf7y/zNQAAAIC6p0+fPvtsKz4GpTINFgc9CaMJTF588UWdf/75OuaYY9SpUydddNFFevnll+3gFwAAAACHvl27dpVYtm/fbqcZ6dGjhz755JNKnfOgBsSb4MOMJ/noo4/UuXNnG5iYbStXrtRVV12l9957TzNmzKhUQQAAAADUHsUnXyxiZoc3EzGOGDFCS5curd7gZOrUqbZv2bx583TaaaftM3LfjEUxLSiDBg066IIAAAAAqP2aNGmi1atXV+q9BxWcvPHGGxo9evQ+gYlx+umna+TIkXrttdcITgAAAIBD3IoVK0qsmx5VZg6UBx54QF26dKn+4MQUwEy6WB6TaviJJ56oVEEAAAAA1B4mADED4EuPOz/++OPtGPVqD0527txpm2nKY/aZwTAAAADAocRTuNT0NZ1s7dq1JdbdbrcaNWqk6OjoSp/zoIITkw4sPLz8t4SFhcnrdXpGZgAAAAB/VsuWLVXVDjpbl8nKFRUVVeb+/Pz8qioXAAAAAAe75ZZb1K5dO/tvcU899ZTWrFmjSZMmVe88J4MHD7YzxJu0YWUtZh+D4QEAAIBD37vvvqsTTzxxn+0nnHCC3nnnnepvOXnppZcqdREAAAAAh5YdO3aUOddJfHy80tLSKnXOg54hHgAAAADatWtnZ4Qv7eOPP1abNm2qv+UEAAAAqIu8Icie5ZWzmVngb7rpJqWmpto5Dw0zWfujjz5aqfEmBsEJAAAAgIM2ZMgQmxBr/Pjxuu++++y2Vq1a6emnn670OHSCEwAAAAAHxUwf8vrrr+uSSy7RDTfcYFtP6tWrp7i4OP0ZjDkBAAAAcFDM3IfXX3+98vLy7LqZfPHPBiYGwQkAAACAg9azZ099//33qkp06wIAAABw0IYNG6bbb79df/zxh7p166bY2NgS+4899tiDPifBCQAAAFCBzFk1nT3LK2e7/PLL7b/FZ4h3uVwKBAL2X5/Pd9DnJDgBUL6jQl0AoBbyh7oAQC2UH+oCoDLWrl2rqkZwAgAAAOCgtWzZUlWN4AQAAABAhcycOVPnnHOOIiIi7Ov9ufDCC3WwCE4AAAAAVEj//v21detWNW7c2L4uD2NOAAAAAFQrv99f5uuqQnACAAAAHICncKnpa9Y1TMIIAAAAoMI+/fRTdezYURkZGfvsS09P19FHH60vv/xSlUFwAgAAAKDCJk2apKFDhyo+Pn6ffQkJCbruuuv02GOPqTIITgAAAABU2PLly9WvX79y95999tlaunSpKoPgBAAAAECFbdu2zaYSLk94eLhSU1NVGQQnAAAAACrssMMO048//lju/hUrVqhp06aqDIITAAAAoILZump6caJzzz1Xd999t/Ly8vbZl5ubq3vuuUfnn39+pc5NKmEAAAAAFfbvf/9b7733no488kjddNNNat++vd2+atUqTZ482U6++K9//UuVQcsJAAAAcIiYPHmyWrVqpejoaPXq1UuLFy8u99gpU6bo5JNPVlJSkl3OPPPM/R5fpEmTJlqwYIGOOeYYjRo1ShdffLFdRo8ebbfNnz/fHlMZBCcAAADAIWD69OkaMWKE7Vb13XffqXPnzurbt6+2b99e5vGff/65rrjiCn322WdauHChmjdvbjNtbdq06YDXatmypT766COlpaXpm2++0aJFi+xrs61169aVvgdXIBAI6BBmJocx+ZZXS6of6sIAtc1doS4AUAv5Q10AoPbJzJfaP7lnAr+y5s5wwnfJ90ZKsdE1e+3sPOmSByr+uZiWkh49euipp56y636/3wYcN998s0aOHHnA95vuWKYFxbx/0KBBCgVaTgAAAAAHy8jIKLHk5+fvc0xBQYGdW8R0zSridrvtumkVqYicnBx5PB4lJycrVAhOAAAAgAPwSfLW8OIrvLZp/TCtN0XLhAkT9imf6VJlWj5Kj/Uw61u3bq3QPf7zn/9Us2bNSgQ4NY1sXQAAAICDbdy4sUS3rqioqCq/xgMPPKA333zTjkMxg+lDheAEAAAAcLD4+PgDjjlp2LChwsLC7OztxZn1lJSU/b73kUcescHJ3LlzdeyxxyqU6NYFAAAA1HKRkZHq1q2b5s2bF9xmBsSb9d69e5f7voceekj33XefZs2ape7duyvUaDkBAAAADgEjRozQ4MGDbZDRs2dPTZo0SdnZ2br66qvtfpOB67DDDguOWXnwwQc1ZswYvf7663ZulKKxKXFxcXYJBYITAAAA4BAwcOBApaam2oDDBBpdunSxLSJFg+Q3bNhgM3gVefrpp22Wr0svvbTEecw8Kffee69CgeAEAAAAOABP4VLT1zxYN910k13KYga7F7du3To5DWNOAAAAADgCwQkAAAAARyA4AQAAAOAIBCcAAAAAHIHgBAAAAIAjEJwAAAAAcARSCQMAAAAH4C1cavqadQ0tJwAAAAAcgeAEAAAAgCMQnAAAAABwBIITAAAAAI5AcAIAAADAEcjWBQAAAByAp3Cp6WvWNbScAAAAAHAEghNUWsywYWq0dq1ScnPVYNEiRfToUe6x9QYPVtNAoMRi3lda3Nixarx5s1JycpQ8Z47C2rUrsT/siCOUNGOGmqSmqkl6uhp89ZUi+/SplvsDqktM72Fq9M+1Srk/Vw1uXKSIw/dTd3peqwbXf6km9+y0S/K1c8o8PrxxByUNfl9Nxu5Wk/uy1OCmxXInNg/ud8c1UcLAl9X431vs/oa3LFX0MZdU2z0C1SHmhGFqNGqtUv6TqwY3L1JE8wPUnRu+VJOxO+2S/I85+xzf9OFAmUvsqXfse8KwSDW87Xu7P7xZ5+q4PQAEJ6is6AEDFD9xorLGjlXaccfJu3y5kmfPlrtRo3Lf409P17aUlOCyvWXLEvtj77pLsbfcovTrr1dar14KZGfbcyoqKnhM8ocfSuHh2nH66Urr1k2e5cuV9OGHcjdpUq33C1SV6GMHKP78icqaN1ZpTxwn75blSr5mttyxZdedqDZ9lLvsDe147jSl/V9v+dI3KvnaT+SObxY8Jiy5jRpcP1/e7au049k+SnvsWGXNu0/y5AWPSRz4ssIbtdeuqRcq7bFOyvvxPSVe+ZbCm3WpkfsG/qzozgMUf8FEZc0Zq7RJx8m7ebmSr91P3WlbWHeePU1pT/WWb/dGJQ8tWXe2jUspseyefrUCfr/yfnh3n/PFn/eQfOmbq/UeAdSC4KRVq1ZyuVz7LDfeeGOoi1anxY4YoZwpU5Q7daq8K1fagCKQk6N6Q4aU/6ZAQP5t2/Yu27eXPOfw4cq6/37lz5wp7w8/aPegQQpr1kzR/fvb/a4GDRR+5JHKeuABu9+3Zo0yR46UOzZW4cccU923DFSJ2JNHKGfxFOUumSrv9pVK/+/1CnhyVK9H2XVn95t/U86ip20Q40tdrfR3rpVcbkW1OyN4TP1+45W3+iNlfvxPeTcvk2/n78pf+YH82anBYyJanqCcr5+U549v5du5Vlmfjlcgd7ciDutWI/cN/Fmxp4xQzjfF6s57hXWnZzl1542/KWfh0zaIsXXn7cK6c8TeuuPP3FZiiT76IhX89pmtI8VFte+nqCPPVuaHZbSoAKhbwcm3336rLVu2BJc5c+bY7Zdddlmoi1Z3RUQools35c+du3dbIGDXI3v3Lvdtrrg4NVq3To03bLBds8I7dgzuC2vdWmFNm5Y4ZyAjQwXffBM8Z2DHDnlXrVLMoEFyxcRIYWGKue46+bZtk2fp0uq6W6DqhEXYYCD/11J1Z81cRbYov+4U54qIkSssQv6cnYUbXIrqcJ58ab8o+ZpZanz3NttVLKrjRSXe51m/QNGdB8pVL8m+x7xWRLQKfv+8Sm8RqNG68+tcRbasYN2JLFV3SnHHNVbUUecpZ/EL+2xPuHSKdr/5dxsMAajjwUmjRo2UkpISXD788EO1bdtWp556aqiLVme5GzaUKzzctn4UZ9bdKSllvse7erXShwzRrosu0u6//U1yu9VgwQK5DztszzkL33egc+4480yFd+2qJpmZSsnLsy04O/v1U2D37mq4U6BquWMayhUWLn9Wqd/zzG1y1y+77pRW/9wH5cvYbAMae87YxnJH1Vdsn5HKXz1LO58/W3k//VdJf39Pka1PCb5v12sD7BezlHt3KmV8vhIueVa7Xr5Yvh2/VfFdAlXPHVtO3cmqRN0pHuAUU6/7YAXyM22Xx+ISBk5VzqJn5PmDh2B1nbdYxq6aWryqe2pVKuGCggK9+uqrGjFihO3aVZb8/Hy7FMnIyKjBEqI8nkWL7FKkYMECNVq50rZ8ZI0ZU+HzJEyebLuD7Tj5ZAVycxVz7bVK/uADpfXoIf/WrdVUesAZYvv8U/U6X27Hlchb+P85155nTPk/va/s+ZPsa9MFLLLlCYo5/noVrP3Sbqt/9n1yRSdqx3NnyJ+Tpuij+yvpyre045mT5d36Y+huCqgBsaf9U/W6XK4dzxSrO6XE9Bii3O9eK7E/5sSbbfCf9emEGiwtULc5vuWkuBkzZmj37t266qqryj1mwoQJSkhICC7Nm+/NVoOq4U9LU8Dr3WcQulmvcIDg9crz/fcKL8zGVfS+/Z0z8vTTFXX++dp9+eXyLFgg7/ffK+PGG22QYrKBAU5ngoKAz2szZxXnrt9E/sz9153YU25XXJ+RtmXEu/WHUuf0yLv95xLHmz75YYktggPmY0+8WenvDFHBb5/Ku2WFsuaOk+ePJYrpzfg9OJ8/u5y6E1eBunPq7Yo7baR2Tjlb3i17605xEa1PshnvchY/X2J7VLvTFdGyt1Im5CvlAY8a/XON3d7wliW2RQVAHQ9OXnjhBZ1zzjlq1mxvpo3SRo0apfT09OCycePGGi1jneDx2DEeUWfsHVRo+72fcYYKFi6s2DncbkV06iTfli121bd2rX1d/Jyu+vUV2atX8Jx2nInh95c8l1l316pfZdRVPo88m5aWGMxu6067M1Swofy6E3vqnYo7427tfLGfff8+5/zjW4U1al9ic3jDI+XbtX7PJSIL606gVN0J+OQqbHkBam3dWb+futOnsO4832+/3bJiel6jgo1LbOBeXPr7tyhtYmelPdbFLjtfPNdu3/3aQGXO+ldV3BmA2tqta/369Zo7d67ee69kX9DSoqKi7ILqlT1xohKnTZNnyRJ5Fi9WzPDhcsXGKvell+z+hGnT5N+0SZmjR9v1uLvvVsGiRTbDlisxUXF33qmwli2V+/zep1TZkyYp7t//lvfXX22wUv++++TbvFl5M2bY/SZICezaZc+dNW7cnm5dQ4fawfT5//tfiD4J4OBkfzVRiQOm2VYLzx+LFXPScLkiYpW7pLDuDJgmf8YmZc7aU3diT71L9c8ep91v/FW+neuCT44DBVkKFGTb11lfPKykv063XbhMpqGoI/sp6qgLtOO5PXMAmRTD3rRfFX/xs8r83x3y5+yw3boi252lXVPPD9lnARyM7C8nKnFgYd3ZuFgxJw+XKzJWud8W1p3Lp8mfvkmZHxfWnT53qX7fcdr9+l/l27XOtlAagfy9dcdwRdVX9LGXKfOD2/e5pn/3RhUP6cMKsuy/3h2/2WsBqMPByUsvvaTGjRvrvPPOC3VRICnvrbeU0aiR4saNU1hKijzLltmB6UXpgcNatCjRwuFKSlLClCn2WP+uXbblJe2EE2wa4iLZDz1kA5yE556TOzFRBfPn23OqcAyRydZl1uuPH68Gn35qs4Z5f/rJDrL3rij5tAtwqrwVbykjtpHizh6nsPop8mxeZltE/FmFdcd0xSrWwhFz/A1yhUcp6e8l513InHOvsuaOta/zf5phUxLHnTZKYRc+IW/qau169S/yrPt6z8F+r33iW/+cB5R01QdyRcXJl7ZG6W8NVv7qj2vy9oFKy1teWHf6Fqs7z++n7vQurDuDStWdT+61c6UUie5yuVxy2TlRAISeKxAIBORwfr9frVu31hVXXKEHHnjgoN5rBsSbsSerzYDQaishcIi6K9QFAGqhUr3nABxYZr7U/knZLvnx8fFykqLvkpNHSvWia/bauXnSjQ8483OpLrWis7HpzrVhwwYN2d8EfwAAAABqtVrRrevss89WLWjgAQAAAHCot5wAAAAAOPQRnAAAAABwBIITAAAAAI5QK8acAAAAAKHkCcEXZ4/qHlpOAAAAADgCwQkAAAAARyA4AQAAAOAIBCcAAAAAHIHgBAAAAIAjkK0LAAAAOACyddUMWk4AAAAAOALBCQAAAABHIDgBAAAA4AgEJwAAAAAcgeAEAAAAgCMQnAAAAABwBFIJAwAAAAfgk+QNwTXrGlpOAAAAADgCwQkAAAAARyA4AQAAAOAIBCcAAAAAHIHgBAAAAIAjkK0LAAAAOACPpLAQXLOuoeUEAAAAgCMQnAAAAABwBIITAAAAAI5AcAIAAADAEQhOAAAAADgC2boAAACAAyBbV82g5QQAAACAIxCcAAAAAHAEghMAAAAAjkBwAgAAAMARCE4AAAAAOALZugAAAIAD8BYuNX3NuoaWEwAAAACOQHACAAAAwBHo1gWgfDtDXQCg9pl7eKhLANQ+uXwjRSFaTgAAAAA4AsEJAAAAAEegEQ0AAACoQOYsTwiuWdfQcgIAAADAEQhOAAAAADgCwQkAAAAARyA4AQAAAOAIBCcAAAAAHIFsXQAAAEAFMmeFheCadQ0tJwAAAAAcgeAEAAAAgCMQnAAAAABwBIITAAAAAI5AcAIAAADAEQhOAAAAADgCqYQBAACAA/CE4Km+R3UPLScAAAAAHIHgBAAAAIAjEJwAAAAAcASCEwAAAACOQHACAAAAwBHI1gUAAAAcANm6agYtJwAAAAAcgeAEAAAAgCMQnAAAAABwBIITAAAAAI5AcAIAAADAEcjWBQAAAByAT5I3BNesa2g5AQAAAOAIBCcAAAAAHIHgBAAAAIAjEJwAAAAAcASCEwAAAACOQLYuAAAA4AA8klwhuGZdQ8sJAAAAAEcgOAEAAADgCAQnAAAAAByBMSeotJhhwxR7550KS0mRZ/lyZdx8szzffnvA90UPHKikN99U3owZ2nXxxcHt7saNVf/BBxV19tlyJyYq/8sv7Tl9a9aUeH/E8cer/vjxiujVS/L55Fm2TDv79pXy8qrlPoGqFtNnmGL73qmwhBR5Ni5Xxhs3y7Ou7LoT3fVixZ47WuGN20lhEfJt/1XZnzyq3EWvljgu7sKxijl5qNwxiSpY87XSX7tBvu17607cuaMV1ek8RTTvooCvQNtuTar2+wSq2pE9hunoE+5UvbgU7dq6XIs/vlk7NpdddxIadVTnPuPUoFk3xSW20rezhmvVN4+XOObiW9fafaWt/nayFn90U3C94eHHq+vp49XwsF7yB3zatXWZ5r3aVz4vf3eAqkbLCSolesAAxU+cqKyxY5V23HHyLl+u5Nmz5W7UaL/vC2vZUvGPPGIDj9KSZsxQWJs22nXRRUrt2lW+9euVPHeuXDExJQKT5FmzlP/JJ9rRs6fSevRQzlNPSX5/tdwnUNWiuw9Q/ICJyvpgrNLuO07eP5YrefhsueuXXXf82TuV9dF47ZjQW2ljj1XO1y8p4aqXFHn02cFjYvvdpdgzblH6q9cr7T+9FCjItudUeNTeE4VHKm/p28r+4umauE2gyrU8eoC6nz1RK74Yq/89e5x2bVuuM/42W9ExZded8IgYZe3+Xd/PHamczC1lHvPRlB56+5GU4DLn5TPt9vU/vV0iMDnjylna/Nsn+uj5nvp4Sg+tXvyUAgH+7gB1Mji599575XK5SiwdOnQIdbHqvNgRI5QzZYpyp06Vd+VKpV9/vQI5Oao3ZEj5b3K7lfjaa8q85x75fv+9xK6wI45QZO/eyrjhBnmWLJHvl1/sa1e9eoq+4orgcfGPPabsJ55Q9oMPyvvzz/a4vLfflgoKqvN2gSoTe9YI5Xw1RbkLpsq7ZaUNKAIFOap3Ytl1p+CXL5T//Qx5t66SL/V35cx7Qt4/Viiy3Ul7z3nGcGX9737lL58p76YftPvFQQpLbKborv2Dx2TNvFfZcyfZ/UBt1PH4Efr1uyn6bdlUpaet1KIPr5fPk6O2XcuuOzs2L9F3c+7Sup+my+/LL/OY/Jw05WVvCy6HH3m+Mnau0bb1XwSP6d73Ma1a/IR++vpBpaf+rIwdv2j9z2/L7+PvTl3jCdFS1zg+ODGOPvpobdmyJbjMnz8/1EWq2yIiFNGtm/Lnzt27LRCw6ybAKE/cmDHyb9+u3Bdf3GefK2rPE95A8a5ZgYCUn6/Ik/Z8CTOtMpHHH2/P0eDrr9V461Ylf/65Ik48sUpvD6g2YRGKaNlN+StL1Z2VcxXZtvy6U1xkh9MVltJeBb/saX0Ma9haYYlNS5wzkJuhgt+/UWSbip0TcDq3O0LJzbpp6+/F6o4C2vL7XDU6vHeVXaP1sX/Tb9/v/RtlWmUaHX688rK3q++Qr3Xp7Vt19uDP1ag5f3eAOh2chIeHKyUlJbg0bNgw1EWq09wNG8oVHi7/tm0ltpt1d0pKme8xAUTMNddo99ChZe73rlol7/r1qj9hglyJiTYAir3rLoU1b66wpk3tMabLl1H/3nttq83Ofv3k+e47NZg3T2Ht2lX5fQJVzR3XUK6wcPkzStWdjG1yx5dddwxXvXg1eTJTKU8XKPmW/9kxKgWFwYg7Yc/79jln5rbgPqC2i4ppKLc7XLnZJX/PTWuHGX9SFZp36K/I6ETbMlMkLmnP353Op96rNd9N0bzX+mnn1u901qB5qp/M3x2gzgYnv/76q5o1a6Y2bdroyiuv1IYNG8o9Nj8/XxkZGSUWhJYrLk6Jr7yi9KFDFdixo+yDvF7tuuQShR95pFJ27VJKTo4iTztNeR99pEDReBL3nl/XnGef3dOdbNkyZY4YIe/q1YrZX3cyoJYL5GUqbVwXpf2nhzL/+y87ZiXyyFNDXSzgkNKu6zXa/OvHys3aOz7F5drzd+eXpc/aoMUMhF8ye4QydqxWu3K6kwE4xLN19erVS1OnTlX79u1tl66xY8fq5JNP1o8//qj69evvc/yECRPsMag+/rQ0BbxeuZs0KbHdrPu3bt3n+LC2bRXeurWSPvig2MF7/oef4vEotX17OwbF+913SuvaVa74eLkiI+11GixaZMeg2Otu2fMHw4w1Kc6MeQlr0aI6bhWoUv6sNAV8XrnjS9Wd+CbyZ+xbd4ICAflSf7MvvRuXK7zpUYo7d5R2/vKF/Olb956j8LVdr99E3o3LqutWgBplxob4/V7Viy1Zd6Jjmyg3az91p4JiE1oopc2Z+uKtS0psLwpUzFiT4tJTVyo2nr87QJ1sOTnnnHN02WWX6dhjj1Xfvn310Ucfaffu3XrrrbfKPH7UqFFKT08PLhs3bqzxMh/yPB55li5V1Bln7N3mctn1goULy+yylXrMMUrr0iW45M+cqYLPPrOvfaV+RoGMDBuYmK5aEd27K+/99+1237p18m3apLD27Uscb1pbTGYvwPF8HnnWL1XUUaXqzlFnqOC3fetOuczT3MJMXL60tfLt3qKoDnvP6Yqur8g2vVTw+0GcE3Awv9+jnZuXKqVNsbojl11P/ePP/5637XK1HVey6Zf/ldietXudcjI2Kb5hyb878Q2OVFY6f3eAOtlyUlpiYqKOPPJIrSk190WRqKgou6B6ZU+cqMRp02yrhmfxYsUMHy5XbKxyX3rJ7k+YNk3+TZuUOXq0HdTu/emnEu/3795tI+Pi26MvvVT+1FT5NmxQeKdOin/8cTsXSsGcOcFjsh5+WPXHjrWpi838JvUGD1Z4hw7ademlNXj3QOVlz5moxCHT5Fm3RJ61ixVz5nC5ImOV+3Vh3RkyTf5dm5T539F2PfackfZY03LiCo9SVKdzVe/4v9t5TILnnDdJcef9W97tv9pgpf5F98m3e7Pyvp8RPMad3Fzu2GSFJbeQ3GEKb97ZbjdzoQTys2v8cwAO1s+LJurE/tNsFq60TYt11PHDFR4Rq9+W7ak7J/SfptzMTfp+3ujgAHcz14l9HRapmPjDlNSks7wFWcrctaclcg+XDU5+Xz5NgYBvn+v+tOBhde4z1s6rYrp1tekyWPENO+iLt/m7U9d4Q/BU36u6p9YFJ1lZWfrtt9/097//PdRFqdPy3npLGY0aKW7cuD2TMJqJEPv1s5m0DNvN6iDnHnE3bWrnTjHdw3xbtij35ZeVdd99JY7JefxxuaKjbUphV3KyDVJ2nHXWPqmJAafKW/KWMuo3UtxF4xQWbyZhXKadj/eTP7Ow7pjgodj8Ca6oWCVc+X8KSzpcAU+uvFtWafcLf7PnKZI96yEb4CT8/bk9kzD+Ot+eU9696VPrXzROMSdcFVxvNGZPl68dD/ex6YoBp1v/01s2e5aZWHHPJIzL9Olr/WyLR1HXrOJ1p179Zjr/+r1dG83kjWbZuu5zzZl2WnB70zZnKi6xpdYUy9JVnJm4MSw82qYUjqqXrJ3blmvuK2cpaxd/d4Dq4AoETL5W57rjjjt0wQUXqGXLltq8ebPuueceLVu2TD///LMaHWDCP8MMiE9ISNBq88e5RkoMHEKuDXUBgNpn7uGhLgFQ++TmSdc9INslPz4+Xk5S9F1y4EgpMrpmr12QJ0136OdSZ8ec/PHHH7riiivsgPgBAwaoQYMGWrRoUYUCEwAAAKAumTx5slq1aqXo6GibWGrx4sXlHvvTTz/pL3/5iz3eTHQ+adIkhZrju3W9+eaboS4CAAAA4HjTp0/XiBEj9Mwzz9jAxAQbJqHU6tWr1bhx432Oz8nJsVN1mORTt912m5zA8S0nAAAAAA5s4sSJGjp0qK6++mp17NjRBikxMTF68cWyx1T16NFDDz/8sC6//HLHJJQiOAEAAAAcLKPUBONm0vHSCgoKtHTpUp155pnBbW63264vLGOqB6ciOAEAAAAqkNbXU8OLt/DazZs3t4PyixYz6XhpaWlp8vl8alJqkmyzvrWMSbKdyvFjTgAAAIC6bOPGjSWydTmlC1Z1IDgBAAAAHCw+Pv6AqYQbNmyosLAwbdu2rcR2s56SkqLagm5dAAAAQC0XGRmpbt26ad68ecFtfr/frvfu3Vu1BS0nAAAAwCFgxIgRGjx4sLp3766ePXvaVMLZ2dk2e5cxaNAgHXbYYcExK2YQvZnYvOj1pk2b7GTncXFxateuXUjugeAEAAAAOAQMHDhQqampGjNmjB0E36VLF82aNSs4SH7Dhg02g1eRzZs3q2vXrsH1Rx55xC6nnnqqPv/885DcA8EJAAAAcACeWnLNm266yS5lKR1wmJnhA4GAnIQxJwAAAAAcgeAEAAAAgCMQnAAAAABwBIITAAAAAI5AcAIAAADAEcjWBQAAAByAV5IrBNesa2g5AQAAAOAIBCcAAAAAHIHgBAAAAIAjEJwAAAAAcASCEwAAAACOQLYuAAAA4AA8deSaoUbLCQAAAABHIDgBAAAA4AgEJwAAAAAcgeAEAAAAgCMQnAAAAABwBLJ1AQAAAAfgk+QKwTXrGlpOAAAAADgCwQkAAAAARyA4AQAAAOAIBCcAAAAAHIHgBAAAAIAjkK0LAAAAOACPpEANX9OruoeWEwAAAACOQHACAAAAwBEITgAAAAA4AsEJAAAAAEcIr1NhmCvUhQBqmZdCXQCg9llxd6hLANQ++aEuAByj7gQnAAAAQCWRratm0K0LAAAAgCMQnAAAAABwBIITAAAAAI5AcAIAAADAEQhOAAAAADgCwQkAAAAARyCVMAAAAODAtL5e1T20nAAAAABwBIITAAAAAI5AcAIAAADAEQhOAAAAADgCwQkAAAAARyBbFwAAAFCBzFmBGr6mT3UPLScAAAAAHIHgBAAAAIAjEJwAAAAAcASCEwAAAACOQHACAAAAwBHI1gUAAAAcgEeSv4av6VPdQ8sJAAAAAEcgOAEAAADgCAQnAAAAAByB4AQAAACAIxCcAAAAAHAEsnUBAAAAB+CVFKjha/pU99ByAgAAAMARCE4AAAAAOALBCQAAAABHIDgBAAAA4AgEJwAAAAAcgWxdAAAAwAF4JPlr+Jo+1T20nAAAAABwBIITAAAAAI5AcAIAAADAEQhOAAAAADgCwQkAAAAARyA4QaXF3DBMjdasVUpWrhosWKSIHj0q9L7oAQPV1BtQ0rv/LbHd3bixEl54SY03bFJKRraS/vexwtq1K3FM/P89o0ar1yglM0eNt2xX0nszFNa+fZXeF1DdqDtA5ZzQY5hG3bpW//lXrm6+ZpGaNyu/7jRp1FGDLnvHHv/wPQGd1OvWfY457aSRuuXaxbpvZIbuuWObBg/8rxo1OHKf41oefryuGzRP40dl6b6R6brhqi8UHh5d5fcHZ/MWZuyqycWruofgBJUSfdkAxT8yUVn3jVVaj+PkXb5cyR/NlrtRo/2+L6xlS8U/9Ijyv/pyn332y1KbNtp1yUVK7d5VvvXrlTx7rlwxMcFjPN8tVfq1Vyv1mKO089y+ksulBh9/Irn5VUbtQN0BKqfz0QN0wdkTNeeLsZr07HHavG25rv3bbMXGlF13IiJitGP37/po7khlZG4p85i2LU/Vgm8n66kXjtdzr5ylMHeEhv7tE/ve4oHJNVfO0i+/faInnu+pJ6b00NeLn1IgUNNJZYG6wfF/lZ5++mkde+yxio+Pt0vv3r318ccfh7pYdV7sbSOU8/wU5U6bKu/KlUofdr0COTmqd/WQ8t/kdivxldeUOfYe+X7/vcSusCOOUOTxvZVx4w3yLFki3y+/2NeuevUUffkVweNyn5+igq++sl++vN9/r8wx/1ZYixYKa9WqOm8XqDLUHaByTjl+hL75boqWLJuq7Wkr9d6H18vjyVHPrmXXnT82L9H/5tyl5T9Nl9eXX+Yxz792jpYsn6ZtqT9ry7YVmv7+VUpKbKnDm3YLHnNB38f09eIn9NnXD9rjUnf8ohU/vy2fr6Da7hWoyxwfnBx++OF64IEHtHTpUi1ZskSnn366LrroIv3000+hLlrdFRGhiOO6KX/e3L3bAgG7br4klSfu7jHyb9+u3Jde3GefKypqz2ny8kqcU/n5ijzxpDLPZ54K17vqanl//12+jRv/1C0BNYK6A1SKadE4rFk3/fr73roTUMCutzy8/LpzsKKjEuy/Obk77b+mVca0nGRlb9eNQ77WmNu36vrBn6tV8xOr7JoAallwcsEFF+jcc8/VEUccoSOPPFLjx49XXFycFi1aFOqi1Vnuhg3lCg+Xf/u2EtvNujslpcz3RJx4omKuvka7rxta5n7vqlXyrl+v+uMnyJWYaL/Exd55l8KaN1dY06Yljo25/gY12Z1p+9ZH9z1HO/udJXlMz0zA2ag7QOXExjRUmDtcWdkl645Zrx9Xdt05WC65dGG/SVq7Yb62pe55ANogqY3996xT77WtNs+/1k+btn5nx580TC45rgtAHQlOivP5fHrzzTeVnZ1tu3eVJT8/XxkZGSUWhJYrLk6JU19R+vVDFdixo+yDvF7tuuwShR9xpFLSdtlBu5F9TlPexx8p4C/Zrzf39deU1r2rdpx2iry//qKkN96SCp8eA4cS6g5Qcy4+b7JSGh+j1965PLjN5drzNWnR0mdtd7LNW5fpg9kjlLpjtXqU050MwJ8Trlrghx9+sMFIXl6ebTX573//q44dO5Z57IQJEzR27NgaL2Nd4k9LU8DrlbtxkxLbzbp/69Z9jg9r21bhrVsracYHxQ7e8z/8lDyPUju2t/3ovd99Z784ueLj5YqMtNcxmYxMP/riAhkZ8pllzRoVLFqkJmm7FN3/YuVNf7O6bhmoEtQdoHKyc9Lk83sVF1uy7pj1zKx9687B6n/OkzrqiPP1f1NPUXrmpuD2jKw9A+m3p/5c4vhtqSuVGN/iT18XQC1tOWnfvr2WLVumb775RjfccIMGDx6sn38u+T+KIqNGjVJ6enpw2Uh/6qrn8djMP1Gnn7F3m8tl1wsWLSyz20lq52OU1q1LcMn/YKYKPv/Mvi7d5918gTJfrkwq1Ihu3ZX3wfvll8XlksssPP1FbUDdASrF5/do0+alatfmjBLdsMz6+j/2rTsHG5gc0+FiPfvy6dq1e12JfWY9PWOTGjUsmXbbpBvelb7+T10XtY83REtdUytaTiIjI9WuMGd/t27d9O233+rxxx/Xs88+u8+xUVFRdkH1yn5sohJfmibP0iXyfLtYMbcMlys2VrlTX7L7E16aJv/mTcr812g7MNdbKoGBf/duGxkX3x79l0vlT0uVb8MGhR/TSfGPPa6892eoYM4cuz+sdWs7z0P+nE/kT01V2OGHK+6ukQrk5ir/449q+BMAKoe6A1TOl4smamD/aTYL18ZNi3Xy8cMVGRGrb5ftqTuX959mWz0+njc6OIjezHViX4dFKiH+MDVr0ln5BVnases3u/3icyera6e/auqbFyk/P1P1C1tmcvPT5fXuSTLx+YKHdXafsdq8dbnt1tW9y2A1bthBr7x9aYg+CeDQViuCk9L8fr8dW4LQyXv7LWU0aqS4e8cpLCVFnuXLtPO8fjajkGFSlKpUf/cDcTdtaud/cDdpIt+WLcp99WVl3X9fcL/JRhR50smKvWW43ElJ8m/bpoKvvlTaySfYL1xAbUDdASpn+U9v2exZffuMs4PgTaBgBqibTFpGYkKLEnOPxNdvptuuXxZc73PCnXb5bd3nembaacFJHQ0zqWJx02dcZVMMG/O/eVwR4dG6sO9jiqmXbOdXMXOi7NhVMq03gKrhCgRMzknnMt20zjnnHLVo0UKZmZl6/fXX9eCDD2r27Nk666yzDvh+MyA+ISFBq91SfVeNFBkAUIdNvDvUJQBqn/w86ckHZLvkm3ntnKTou2SzkZI7umav7c+TNjv0c6mzLSfbt2/XoEGDtGXLFvuLYSZkrGhgAgAAAKD2cHxw8sILL4S6CAAAAABqgOODEwAAACDUPCFIc+tX3VMrUgkDAAAAOPQRnAAAAABwBIITAAAAAI5AcAIAAADAEQhOAAAAADgC2boAAACAA/CSratG0HICAAAAwBEITgAAAAA4AsEJAAAAAEcgOAEAAADgCAQnAAAAAByBbF0AAABABbJ1uWr4mgHVPbScAAAAAHAEghMAAAAAjkBwAgAAAMARCE4AAAAAOALBCQAAAABHIFsXAAAAcAAesnXVCFpOAAAAADgCwQkAAAAARyA4AQAAAOAIBCcAAAAAHIHgBAAAAIAjkK0LAAAAOAAv2bpqBC0nAAAAAByB4AQAAACAIxCcAAAAAHAEghMAAAAAjkBwAgAAAMARCE4AAAAAOAKphAEAAIAKpBJG9aPlBAAAAIAjEJwAAAAAh4jJkyerVatWio6OVq9evbR48eL9Hv/222+rQ4cO9vhOnTrpo48+UigRnAAAAACHgOnTp2vEiBG655579N1336lz587q27evtm/fXubxCxYs0BVXXKFrrrlG33//vfr372+XH3/8UaFCcAIAAAAcAiZOnKihQ4fq6quvVseOHfXMM88oJiZGL774YpnHP/744+rXr5/uvPNOHXXUUbrvvvt03HHH6amnnlKoHPID4gOBgP03a88/AABUq/y8UJcAqH0K8kt+b3Ok/NBdMyMjo8TmqKgouxRXUFCgpUuXatSoUcFtbrdbZ555phYuXFjm6c1209JSnGlpmTFjhkLlkA9OMjMz7b/dzO+6g3/fAQCHiAdCXQCgdn9vS0hIkJNERkYqJSVFWx/bGpLrx8XFqXnz5iW2mW5b9957b4ltaWlp8vl8atKkSYntZn3VqlVlnnvr1q1lHm+2h8ohH5w0a9ZMGzduVP369eVyuUJdHBRjngKYymZ+PvHx8aEuDlBrUHeAyqHuOJdpMTGBifne5jRmoPjatWtty0SoPhtXqe+wpVtNDiWHfHBimrMOP/zwUBcD+2H+QPBHAjh41B2gcqg7zuS0FpPSAYpZnKxhw4YKCwvTtm3bSmw366blpyxm+8EcXxMYEA8AAADUcpGRkerWrZvmzZsX3Ob3++167969y3yP2V78eGPOnDnlHl8TDvmWEwAAAKAuGDFihAYPHqzu3burZ8+emjRpkrKzs232LmPQoEE67LDDNGHCBLt+66236tRTT9Wjjz6q8847T2+++aaWLFmi5557LmT3QHCCkDH9Jc2ArkO53yRQHag7QOVQd3CoGzhwoFJTUzVmzBg7qL1Lly6aNWtWcND7hg0b7JCHIieccIJef/11/fvf/9bo0aN1xBFH2ExdxxxzTMjuwRVwdM42AAAAAHUFY04AAAAAOALBCQAAAABHIDgBAAAA4AgEJwAAAAAcgeAEAAAAgCMQnMCRdu/ebXN0mxR4Jp3dlClTQl0koNbIyclRy5Ytdccdd4S6KECt0apVKx177LH2785pp50W6uIAdRbznMCR6tevry+//FIxMTF28iAToFxyySVq0KBBqIsGON748eN1/PHHh7oYQK2zYMECxcXFhboYQJ1GywkcKSwszAYmRn5+vsx0PEzJAxzYr7/+qlWrVumcc84JdVEAADhoBCeoFqbV44ILLlCzZs3kcrnsbKOlTZ482TajR0dHq1evXlq8ePE+Xbs6d+6sww8/XHfeeacaNmxYg3cA1M56Y7pyTZgwoQZLDRwadce879RTT1WPHj302muv1WDpARRHcIJqYbpimcDC/DEoy/Tp0zVixAjdc889+u677+yxffv21fbt24PHJCYmavny5Vq7dq1ef/11bdu2rQbvAKh99eb999/XkUceaRegLqmKvznz58/X0qVLNXPmTP3nP//RihUravAOABRxBegrg2pmnkb997//Vf/+/YPbzFMr83Tqqaeesut+v1/NmzfXzTffrJEjR+5zjmHDhun000/XpZdeWqNlB2pTvRk1apReffVV2y0yKytLHo9Ht99+u8aMGRPCOwFq398c01p/9NFH66qrrqrRsgOg5QQhUFBQYJ9OnXnmmcFtbrfbri9cuNCum1aSzMxM+zo9Pd022bdv3z5kZQZqQ70x3bk2btyodevW6ZFHHtHQoUMJTFDnVaTumJaXor85JrD/9NNPbXACoOaRrQs1Li0tTT6fT02aNCmx3ay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", 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", 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" + ] + } + } + ], + "id": "38" + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "These results deserve some comments.\n", + "\n", + "We are looking at the impact of three parameters here:\n", + "- Qubit quality ($\\kappa_2/\\kappa_1$)\n", + "- Number of photons in the cat qubit (`average_nb_photons`)\n", + "- Code distance (`distance`)\n", + "\n", + "The impact of qubit quality is as you would expect: when the other two parameters are fixed, improving qubit quality always improves the results.\n", + "\n", + "There is however a clear threshold somewhere between $\\kappa_2/\\kappa_1 = 10^3$ and $\\kappa_2/\\kappa_1 = 10^4$. This threshold corresponds to the repetition code's threshold: when physical qubits aren't good enough, error correction adds errors and makes results unusable.\n", + "\n", + "As for the number of photons, there is also some threshold, although this one depends on the specific circuit you're running. Here, we see that at 4 photons, the bit-flip performance is simply too low for the results to be usable, no matter what the other two settings are.\n", + "\n", + "No amount of error correction can fix this - if anything, it makes things worse because increasing distance further decreases bit-flip performance. Remember, while the repetition code used by cat qubits exponentially removes phase-flips, it also linearly increases bit-flips. This is why you want the bit-flip performance to be excellent to begin with, meaning you want to use a fairly high number of photons.\n", + "\n", + "At 7 photons and $\\kappa_2/\\kappa_1 = 10^4$, an interesting phenomenon can be witnessed: results get better as distance increases from 3 to 7, but further increasing the distance actually makes them worse. This is because as distance increases, the dominant source of error changes: up to distance 7, phase-flips are the limiting factor, so increasing distance improves the results. But beyond distance 7, bit-flips start to become the limiting factor and it only gets worse as you further increase the distance.\n", + "\n", + "This analysis shows us that in order to run an algorithm on logical qubits, there is a sweet spot to be found. For a given chip (with a fixed $\\kappa_2/\\kappa_1$ ratio), you'll need to find the right combination of distance and number of photons.\n", + "\n", + "While the number of photons is easy to change, it is still unclear to what extent a real chip will let you pick different code distances. If architectures aren't modular enough, then different chips implementing different distances might be needed for different applications. One thing is for sure though: a longer distance means a higher number of qubits and slower operations, so you'll always want to favor the regime requiring the shortest possible distance." + ], + "id": "39" + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Conclusion" + ], + "id": "40" + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We hope this notebook gave you a clearer view of some of the challenges involved in using logical qubits.\n", + "\n", + "You may now reuse the principles showcased in this notebook to study the behavior of your own algorithms on logical backends, and discover what specs and settings will be required to obtain reliable results.\n", + "\n", + "The principles of this notebook are however limited to circuits which can be classically emulated. If you wish to study what happens with bigger circuits, beyond the capability of current emulators, then you'll need to switch to a different approach: resource estimation.\n", + "\n", + "Resource estimation computes how many qubits and how much time will be required to run a given circuit, but without actually running the circuit. You may check out the Microsoft Resource Estimator at https://learn.microsoft.com/en-us/azure/quantum/intro-to-resource-estimation, or Alice & Bob's variant, specifically adapted to cat qubits, at https://github.com/Alice-Bob-SW/qsharp-alice-bob-resource-estimator." + ], + "id": "41" + } + ], + "metadata": { + "colab": { + "provenance": [] + }, + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.11.9" } - ], - "source": [ - "for n in range(len(nb_photons)):\n", - " plot_results(ratios, distances, difference, n)" - ] - }, - { - "cell_type": "markdown", - "id": "39", - "metadata": {}, - "source": [ - "These results deserve some comments.\n", - "\n", - "We are looking at the impact of three parameters here:\n", - "- Qubit quality ($\\kappa_2/\\kappa_1$)\n", - "- Number of photons in the cat qubit (`average_nb_photons`)\n", - "- Code distance (`distance`)\n", - "\n", - "The impact of qubit quality is as you would expect: when the other two parameters are fixed, improving qubit quality always improves the results.\n", - "\n", - "There is however a clear threshold somewhere between $\\kappa_2/\\kappa_1 = 10^3$ and $\\kappa_2/\\kappa_1 = 10^4$. This threshold corresponds to the repetition code's threshold: when physical qubits aren't good enough, error correction adds errors and makes results unusable.\n", - "\n", - "As for the number of photons, there is also some threshold, although this one depends on the specific circuit you're running. Here, we see that at 4 photons, the bit-flip performance is simply too low for the results to be usable, no matter what the other two settings are.\n", - "\n", - "No amount of error correction can fix this - if anything, it makes things worse because increasing distance further decreases bit-flip performance. Remember, while the repetition code used by cat qubits exponentially removes phase-flips, it also linearly increases bit-flips. This is why you want the bit-flip performance to be excellent to begin with, meaning you want to use a fairly high number of photons.\n", - "\n", - "At 7 photons and $\\kappa_2/\\kappa_1 = 10^4$, an interesting phenomenon can be witnessed: results get better as distance increases from 3 to 7, but further increasing the distance actually makes them worse. This is because as distance increases, the dominant source of error changes: up to distance 7, phase-flips are the limiting factor, so increasing distance improves the results. But beyond distance 7, bit-flips start to become the limiting factor and it only gets worse as you further increase the distance.\n", - "\n", - "This analysis shows us that in order to run an algorithm on logical qubits, there is a sweet spot to be found. For a given chip (with a fixed $\\kappa_2/\\kappa_1$ ratio), you'll need to find the right combination of distance and number of photons.\n", - "\n", - "While the number of photons is easy to change, it is still unclear to what extent a real chip will let you pick different code distances. If architectures aren't modular enough, then different chips implementing different distances might be needed for different applications. One thing is for sure though: a longer distance means a higher number of qubits and slower operations, so you'll always want to favor the regime requiring the shortest possible distance." - ] - }, - { - "cell_type": "markdown", - "id": "40", - "metadata": {}, - "source": [ - "## Conclusion" - ] - }, - { - "cell_type": "markdown", - "id": "41", - "metadata": {}, - "source": [ - "We hope this notebook gave you a clearer view of some of the challenges involved in using logical qubits.\n", - "\n", - "You may now reuse the principles showcased in this notebook to study the behavior of your own algorithms on logical backends, and discover what specs and settings will be required to obtain reliable results.\n", - "\n", - "The principles of this notebook are however limited to circuits which can be classically emulated. If you wish to study what happens with bigger circuits, beyond the capability of current emulators, then you'll need to switch to a different approach: resource estimation.\n", - "\n", - "Resource estimation computes how many qubits and how much time will be required to run a given circuit, but without actually running the circuit. You may check out the Microsoft Resource Estimator at https://learn.microsoft.com/en-us/azure/quantum/intro-to-resource-estimation, or Alice & Bob's variant, specifically adapted to cat qubits, at https://github.com/Alice-Bob-SW/qsharp-alice-bob-resource-estimator." - ] - } - ], - "metadata": { - "colab": { - "provenance": [] - }, - "kernelspec": { - "display_name": "Python 3", - "language": "python", - "name": "python3" }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.11.9" - } - }, - "nbformat": 4, - "nbformat_minor": 9 -} + "nbformat": 4, + "nbformat_minor": 9 +} \ No newline at end of file diff --git a/tutorials/basic_tutorials/qml_with_classiq_guide/qml_with_classiq_guide.ipynb b/tutorials/basic_tutorials/qml_with_classiq_guide/qml_with_classiq_guide.ipynb index 5e708237e..39a24bc15 100644 --- a/tutorials/basic_tutorials/qml_with_classiq_guide/qml_with_classiq_guide.ipynb +++ b/tutorials/basic_tutorials/qml_with_classiq_guide/qml_with_classiq_guide.ipynb @@ -1,1147 +1,1138 @@ { - "cells": [ - { - "cell_type": "markdown", - "id": "0", - "metadata": {}, - "source": [ - "# Quantum Machine Learning with Classiq" - ] - }, - { - "cell_type": "markdown", - "id": "1", - "metadata": {}, - "source": [ - "Welcome to the \"Quantum Machine Learning with Classiq\" tutorial. This guide is designed for users already familiar with the fundamentals of the Classiq platform and Quantum Machine Learning (QML) concepts. The aim is to showcase how to implement QML using Classiq. It covers three main methods to implement QML with Classiq:\n", - "\n", - "1. **Using the VQE Primitive**\n", - "2. **Using the PyTorch Integration**\n", - "3. **Using the QSVM Built-in App**\n", - "\n", - "Each section briefly explains the method, followed by an illustrative example that demonstrates the integration. These examples are intended to be straightforward to help you get started quickly." - ] - }, - { - "cell_type": "markdown", - "id": "2", - "metadata": {}, - "source": [ - "## In This Tutorial\n", - "\n", - "1. [Using the VQE Primitive](#Using-the-VQE-Primitive)\n", - " * [Example Using Classiq](#Example-Using-Classiq)\n", - " * [Summary and Exercise](#summary-exercise-vqe)\n", - " * [Read More](#read-more-vqe)\n", - "2. [Using the PyTorch Integration](#Using-the-PyTorch-Integration)\n", - " * [Workflow](#Workflow)\n", - " * [Example - Demonstrate PyTorch Integration with Classiq](#example-code-demonstrating-pytorch-integration-with-classiq)\n", - " * [Step 1.1 - Define the Quantum Model and Synthesize It into a Quantum Program](#step-11---define-the-quantum-model-and-synthesize-it-into-a-quantum-program)\n", - " * [Step 1.2 - Define the Execute and Post-process Callables](#step-12---define-the-execute-and-post-process-callables)\n", - " * [Step 1.3 - Create a torch.nn.Module Network](#step-13---create-a-torchnnmodule-network)\n", - " * [Step 2 - Choose a Dataset, Loss Function, and Optimizer](#step-2---choose-a-dataset-loss-function-and-optimizer)\n", - " * [Step 3 - Train and Evaluate](#step-3-train)\n", - " * [Summary and Exercise](#summary-exercise-pytorch)\n", - " * [Read More](#read-more-pytorch)\n", - "3. [Using QSVM Primitive](#Using-QSVM-Primitive)\n" - ] - }, - { - "cell_type": "markdown", - "id": "3", - "metadata": {}, - "source": [ - "## Using the VQE Primitive" - ] - }, - { - "cell_type": "markdown", - "id": "4", - "metadata": {}, - "source": [ - "The Variational Quantum Eigensolver (VQE) is an algorithm for finding the ground state energy of a Hamiltonian operator, often described by Pauli operators or in the equivalent matrix form. The VQE was proposed in 2014 [[1](#eigenvaluesolver)]. \n", - "\n", - "The algorithm follows these steps:\n", - "\n", - "1. **Create a Parameterized Quantum Model**: Design a quantum model, also known as an ansatz, that captures the problem.\n", - "2. **Synthesize, Execute, and Estimate Expectation Values**: Synthesize the quantum model into a quantum program. Run the quantum program, then measure and calculate the expected value of the Hamiltonian based on this generated program.\n", - "3. **Optimize Parameters**: Use a classical optimizer to adjust the quantum program's parameters for better results.\n", - "4. **Repeat**: Continue this process until the algorithm converges to a solution or reaches a specified number of iterations.\n", - "\n", - "For more details, refer to this review article [[2](#vqa)] and the corresponding preprint [[3](#preprint)]." - ] - }, - { - "cell_type": "markdown", - "id": "5", - "metadata": {}, - "source": [ - "### Example Using Classiq" - ] - }, - { - "cell_type": "markdown", - "id": "6", - "metadata": {}, - "source": [ - "Start with this example, creating a VQE algorithm that estimates the minimal eigenvalue of the following 2x2 Hamiltonian:\n", - "\n", - "\\begin{equation}\n", - "H = \\frac{1}{2}I + \\frac{1}{2}Z - X = \\begin{bmatrix} 1 & -1 \\\\ -1 & 0 \\end{bmatrix}\n", - "\\end{equation}" - ] - }, - { - "cell_type": "markdown", - "id": "7", - "metadata": {}, - "source": [ - "Define the Hamiltonian using `Pauli` terms:" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "8", - "metadata": {}, - "outputs": [], - "source": [ - "!pip install -qq -U \"classiq[qml]\"" - ] - }, - { - "cell_type": "code", - "execution_count": 1, - "id": "9", - "metadata": {}, - "outputs": [], - "source": [ - "from typing import List\n", - "\n", - "from classiq import *\n", - "\n", - "HAMILTONIAN = 0.5 * Pauli.I(0) + 0.5 * Pauli.Z(0) + (-1) * Pauli.X(0)" - ] - }, - { - "cell_type": "markdown", - "id": "10", - "metadata": {}, - "source": [ - "For a single qubit problem, to capture any rotation on the Bloch sphere, use the U-gate (also known as the U3-gate). This includes the state with the minimal energy with respect to the Hamiltonian." - ] - }, - { - "cell_type": "markdown", - "id": "11", - "metadata": {}, - "source": [ - "
\n", - " NOTE on U-gate\n", - " \n", - "The single-qubit gate applies phase and rotation with three Euler angles.\n", - "\n", - "Matrix representation:\n", - "\n", - "\\begin{equation}\n", - "U(\\gamma,\\phi,\\theta,\\lambda) = e^{i\\gamma}\\begin{pmatrix}\n", - "\\cos(\\frac{\\theta}{2}) & -e^{i\\lambda}\\sin(\\frac{\\theta}{2}) \\\\\n", - "e^{i\\phi}\\sin(\\frac{\\theta}{2}) & e^{i(\\phi+\\lambda)}\\cos(\\frac{\\theta}{2}) \\\\\n", - "\\end{pmatrix}\n", - "\\end{equation}\n", - "\n", - "Parameters:\n", - "\n", - "- `theta`: `CReal`\n", - "- `phi`: `CReal`\n", - "- `lam`: `CReal`\n", - "- `gam`: `CReal`\n", - "- `target`: `QBit`\n", - "\n", - "
" - ] - }, - { - "cell_type": "code", - "execution_count": 2, - "id": "12", - "metadata": {}, - "outputs": [], - "source": [ - "@qfunc\n", - "def main(q: Output[QBit], angles: CArray[CReal, 3]) -> None:\n", - " allocate(q)\n", - " U(angles[0], angles[1], angles[2], 0, q)" - ] - }, - { - "cell_type": "markdown", - "id": "13", - "metadata": {}, - "source": [ - "To seamlessly harness the power of VQE, synthesize the ansatz `main`, and use the `minimize` attribute from `ExecutionSession` to optimize it." - ] - }, - { - "cell_type": "code", - "execution_count": 3, - "id": "14", - "metadata": {}, - "outputs": [], - "source": [ - "qprog_1 = synthesize(main)\n", - "\n", - "\n", - "with ExecutionSession(qprog_1) as es:\n", - " result = es.minimize(\n", - " cost_function=HAMILTONIAN,\n", - " initial_params={\"angles\": [0.0] * 3},\n", - " max_iteration=200,\n", - " )" - ] - }, - { - "cell_type": "markdown", - "id": "15", - "metadata": {}, - "source": [ - "
\n", - "Description of ExecutionSession Minimize Parameters\n", - "\n", - "Configure the `minimize` function in the `ExecutionSession` workflow with these parameters:\n", - "\n", - "- **cost_function**: The cost function to minimize, it can be either a quantum a quantum cost function specified by a Hamiltonian or a classical function that is represented as a callable and returns a Qmod expression.\n", - "\n", - "- **initial_params**: Initial parameters for the optimization routine. It accepts only a single parameter and should be formatted as a dict in the form {\"parameter\": list}.\n", - "\n", - "- **max_iteration**: The maximum number of iterations for the optimizer.\n", - "\n", - "- **quantile**: The quantile-based cutoff for which outcomes to consider when estimating the cost function.\n", - "\n", - "\n", - "The output will be a list of dicts, containing the `float` values of the cost function and its respective parameters.\n", - "
\n" - ] - }, - { - "cell_type": "markdown", - "id": "16", - "metadata": {}, - "source": [ - "At this stage, it is possible to visualize the results of the quantum algorithm. For instance, a graph of Energy versus Iterations can be plotted to illustrate the convergence behavior of the algorithm." - ] - }, - { - "cell_type": "code", - "execution_count": 4, - "id": "17", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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++KFGjx6t6dOna/DgwSotLdWqVav0/vvvq7S0tEOvCQB+EaKuhgDQ6X3//ffG9OnTjfz8fMNutxvJycnGSSedZDzxxBNGbW2t97yGhgZj3rx5Ru/evY3Y2FgjLy/PmD17ts85q1atMi677DKjZ8+ehsPhMLp06WKce+65xsqVK31e8/PPPzcKCgoMu91+2HbubbVwNwzDePfdd40hQ4YYdrvdGDBggPH3v/+9zRbu119/fYvre/Xq5dP+2zAMY9u2bcaUKVOM7Oxsw+FwGH369DGuv/56o66uznvOM888Y/Tp08ew2Ww+7dwPbuFuGIZRXFxsTJs2zcjKyjLsdrsxdOhQ4y9/+Uu73+Phfj6mffv2GTNnzjS6d+9u2O12o0ePHsbUqVN9WooHqpZnnnnGkGQkJycbNTU1rdb31VdfGRdeeKGRmZlpOBwOo1evXsYll1xiLF261HuO+dnt3bu3xfWNjY3G3XffbeTm5hrx8fHGGWecYaxbt87IzMw0rr32Wp9zKyoqjNmzZxv9+vUz7Ha7kZWVZYwdO9Z4+OGHjfr6+iN6n2vXrjUuuOACIy0tzYiLizMGDBhg3H333T7nFBcXG9dff72Rl5dnxMbGGrm5uca4ceOMp59+utWfCQAEmsUwwmjlMQAACHtlZWVKT0/XfffdpzvvvDPU5QBA2GFNFgAAaFNNTU2LY+YawdNOOy24xQBAhGBNFgAAaNPixYv13HPP6ZxzzlFSUpI+/fRT/fOf/9SECRN00kknhbo8AAhLhCwAANCmYcOGKSYmRg899JCcTqe3GcZ9990X6tIAIGyxJgsAAAAA/Ig1WQAAAADgR4QsAAAAAPAj1mQdhtvt1q5du5ScnOyz6SIAAACAzsUwDFVUVKhbt26yWtseryJkHcauXbuUl5cX6jIAAAAAhIkdO3aoR48ebT5OyDqM5ORkSZ4fZEpKSoirAQAAABAqTqdTeXl53ozQFkLWYZhTBFNSUghZAAAAAA67jIjGFwAAAADgR4QsAAAAAPAjQhYAAAAA+BEhCwAAAAD8iJAFAAAAAH5EyAIAAAAAPyJkAQAAAIAfEbIAAAAAwI8IWQAAAADgR4QsAAAAAPAjQhYAAAAA+BEhCwAAAAD8iJAFAAAAAH5EyAIAAAAAP4qokPXJJ59o0qRJ6tatmywWi15//fXDXvPRRx/puOOOk8PhUL9+/fTcc88FvE4AAAAAnVdEhayqqioNHz5cTz31VLvO37Jli37605/q9NNP1+rVq3XTTTfpmmuu0TvvvBPgSgEAAAB0VjGhLqAjzj77bJ199tntPn/hwoXq3bu3HnnkEUnSoEGD9Omnn+r3v/+9Jk6c2Oo1dXV1qqur8953Op1HV7Qf/feHvdpXWa+Jx+Yq3m4LdTkAAAAAWhFRI1kdtWzZMo0fP97n2MSJE7Vs2bI2r5k/f75SU1O9t7y8vECX2W6/+Mcq3bR4tXaV14S6FAAAAABtiOqQVVRUpJycHJ9jOTk5cjqdqqlpPajMnj1b5eXl3tuOHTuCUWq7ZCU5JEn7KutDXAkAAACAtkTUdMFgcDgccjgcoS6jVZmJdm0pqdK+yrrDnwwAAAAgJKJ6JCs3N1fFxcU+x4qLi5WSkqL4+PgQVXXkMhLtkqR9VYxkAQAAAOEqqkPWmDFjtHTpUp9j7733nsaMGROiio5OJtMFAQAAgLAXUSGrsrJSq1ev1urVqyV5WrSvXr1a27dvl+RZTzVlyhTv+ddee602b96s2267TevXr9cf/vAHvfjii7r55ptDUf5Ry0oyR7KYLggAAACEq4gKWStXrtTIkSM1cuRISdKsWbM0cuRI3XPPPZKk3bt3ewOXJPXu3VtvvfWW3nvvPQ0fPlyPPPKI/vSnP7XZvj3cZZrTBRnJAgAAAMJWRDW+OO2002QYRpuPP/fcc61e89VXXwWwquDJMKcLMpIFAAAAhK2IGsnq7LIYyQIAAADCHiErgngbX9BdEAAAAAhbhKwIktnU+GJ/db1c7ranTQIAAAAIHUJWBElPsMtikQzDE7QAAAAAhB9CVgSxWS1KT2BdFgAAABDOCFkR5kAbdzoMAgAAAOGIkBVhzHVZJTS/AAAAAMISISvCZCZ6OgyWMpIFAAAAhCVCVoQxR7Jo4w4AAACEJ0JWhDFHskpofAEAAACEJUJWhPGOZDFdEAAAAAhLhKwIY3YXLGW6IAAAABCWCFkRJjPJM12QNVkAAABAeCJkRRhvC3emCwIAAABhiZAVYbKaGl9U1DaqrtEV4moAAAAAHIyQFWFS4mMUY7VIkvZXNYS4GgAAAAAHI2RFGIvFooxEpgwCAAAA4YqQFYFofgEAAACEL0JWBMpirywAAAAgbBGyIlAGe2UBAAAAYYuQFYEymzoMllQSsgAAAIBwQ8iKQJlMFwQAAADCFiErAnnXZDFdEAAAAAg7hKwIlJFId0EAAAAgXBGyIhDTBQEAAIDwRciKQFnmSBaNLwAAAICwQ8iKQOZIVk2DS9X1jSGuBgAAAEBzhKwIlGC3yRHj+egYzQIAAADCCyErAlksFmUl0fwCAAAACEeErAhF8wsAAAAgPBGyIlRmohmyGMkCAAAAwgkhK0KxVxYAAAAQnghZESqL6YIAAABAWCJkRSjvmixGsgAAAICwQsiKUJlN0wVLGMkCAAAAwgohK0JlNI1klTKSBQAAAIQVQlaEyjIbX9BdEAAAAAgrhKwIdWBNVp0MwwhxNQAAAABMhKwIldG0T1aDy5CztjHE1QAAAAAwEbIiVFysTUmOGEmsywIAAADCCSErgmWyVxYAAAAQdiIuZD311FPKz89XXFycRo8ereXLlx/y/AULFmjAgAGKj49XXl6ebr75ZtXW1gap2sDKbJoyWELzCwAAACBsRFTIWrx4sWbNmqU5c+Zo1apVGj58uCZOnKg9e/a0ev6iRYt0++23a86cOVq3bp3+/Oc/a/HixbrjjjuCXHlgZJgdBqsYyQIAAADCRUSFrEcffVTTp0/XtGnTNHjwYC1cuFAJCQl69tlnWz3/888/10knnaSf/exnys/P14QJE3TZZZcdcvSrrq5OTqfT5xaussy9shjJAgAAAMJGxISs+vp6FRYWavz48d5jVqtV48eP17Jly1q9ZuzYsSosLPSGqs2bN+vtt9/WOeec0+brzJ8/X6mpqd5bXl6ef9+IHx1o407IAgAAAMJFTKgLaK+SkhK5XC7l5OT4HM/JydH69etbveZnP/uZSkpK9JOf/ESGYaixsVHXXnvtIacLzp49W7NmzfLedzqdYRu0MpumC5bQ+AIAAAAIGxEzknUkPvroIz3wwAP6wx/+oFWrVunVV1/VW2+9pXvvvbfNaxwOh1JSUnxu4epAd0FGsgAAAIBwETEjWVlZWbLZbCouLvY5XlxcrNzc3Favufvuu3XFFVfommuukSQNHTpUVVVVmjFjhu68805ZrZGdMc2RLPbJAgAAAMJHxKQMu92ugoICLV261HvM7XZr6dKlGjNmTKvXVFdXtwhSNptNkmQYRuCKDZIDa7KYLggAAACEi4gZyZKkWbNmaerUqRo1apROOOEELViwQFVVVZo2bZokacqUKerevbvmz58vSZo0aZIeffRRjRw5UqNHj9bGjRt19913a9KkSd6wFcnMkFVaVS+X25DNaglxRQAAAAAiKmRNnjxZe/fu1T333KOioiKNGDFCS5Ys8TbD2L59u8/I1V133SWLxaK77rpLO3fuVHZ2tiZNmqT7778/VG/Br9ITPCHLbUhl1fXKTHKEuCIAAAAAFiMa5s0FkNPpVGpqqsrLy8OyCcaI37yrsuoGvXfzKTomJznU5QAAAABRq73ZIGLWZKF1mYme0awSOgwCAAAAYYGQFeHMKYI0vwAAAADCAyErwpkjWeyVBQAAAIQHQlaEO9DGnZAFAAAAhANCVoQzNyTeV8l0QQAAACAcELIiXFYS0wUBAACAcELIinAZiTS+AAAAAMIJISvCsSYLAAAACC+ErAjHdEEAAAAgvBCyIpzZ+KK8pkH1je4QVwMAAACAkBXhUuNjZbNaJEn7qxnNAgAAAEKNkBXhrFaL0hOYMggAAACEC0JWFPCuy6LDIAAAABByhKwokEnzCwAAACBsELKigLlXVkklI1kAAABAqBGyokBmomckq5S9sgAAAICQI2RFAfbKAgAAAMIHISsKZCZ5pgvS+AIAAAAIPUJWFMhomi5YwkgWAAAAEHKErChgThdkTRYAAAAQeoSsKJDZ1F1wH90FAQAAgJAjZEUBc5+sqnqXaupdIa4GAAAA6NwIWVEgyREju83zUdL8AgAAAAgtQlYUsFgs3tEs1mUBAAAAoUXIihKZ7JUFAAAAhAVCVpQwm1+U0PwCAAAACClCVpTITGS6IAAAABAOCFlRwjtdkJAFAAAAhBQhK0pkJjFdEAAAAAgHhKwoYU4XpPEFAAAAEFqErChBC3cAAAAgPBCyooTZXXAf0wUBAACAkCJkRQlzJKukql6GYYS4GgAAAKDzImRFCXMkq77Rrcq6xhBXAwAAAHRehKwoEW+3KcFuk8S6LAAAACCUCFlRxDtlkA6DAAAAQMgQsqIIzS8AAACA0CNkRZGsppGsfUwXBAAAAEKGkBVFMhLZKwsAAAAINUJWFMlM8kwXLGG6IAAAABAyhKwoktk0krWPxhcAAABAyERcyHrqqaeUn5+vuLg4jR49WsuXLz/k+WVlZbr++uvVtWtXORwO9e/fX2+//XaQqg2urKaRrH1VjGQBAAAAoRIT6gI6YvHixZo1a5YWLlyo0aNHa8GCBZo4caI2bNigLl26tDi/vr5eZ555prp06aKXX35Z3bt317Zt25SWlhb84oMgg5EsAAAAIOQiKmQ9+uijmj59uqZNmyZJWrhwod566y09++yzuv3221uc/+yzz6q0tFSff/65YmNjJUn5+fnBLDmoMukuCAAAAIRcxEwXrK+vV2FhocaPH+89ZrVaNX78eC1btqzVa/79739rzJgxuv7665WTk6MhQ4bogQcekMvlavN16urq5HQ6fW6RwpwuWFpVL7fbCHE1AAAAQOcUMSGrpKRELpdLOTk5PsdzcnJUVFTU6jWbN2/Wyy+/LJfLpbffflt33323HnnkEd13331tvs78+fOVmprqveXl5fn1fQRSeoJnJMvlNlRe0xDiagAAAIDOKWJC1pFwu93q0qWLnn76aRUUFGjy5Mm68847tXDhwjavmT17tsrLy723HTt2BLHio2OPsSolzjMDlCmDAAAAQGhEzJqsrKws2Ww2FRcX+xwvLi5Wbm5uq9d07dpVsbGxstls3mODBg1SUVGR6uvrZbfbW1zjcDjkcDj8W3wQZSU55Kxt1L7KOvXrkhTqcgAAAIBOJ2JGsux2uwoKCrR06VLvMbfbraVLl2rMmDGtXnPSSSdp48aNcrvd3mPff/+9unbt2mrAigY0vwAAAABCK2JCliTNmjVLzzzzjJ5//nmtW7dO1113naqqqrzdBqdMmaLZs2d7z7/uuutUWlqqG2+8Ud9//73eeustPfDAA7r++utD9RYC7kAbd/bKAgAAAEIhYqYLStLkyZO1d+9e3XPPPSoqKtKIESO0ZMkSbzOM7du3y2o9kBvz8vL0zjvv6Oabb9awYcPUvXt33Xjjjfr1r38dqrcQcJneDYkZyQIAAABCwWIYBr2+D8HpdCo1NVXl5eVKSUkJdTmH9ei7G/T4Bxt1xYm9dO/5Q0JdDgAAABA12psNImq6IA7vwEgW0wUBAACAUCBkRRlzTVZJJdMFAQAAgFAgZEUZs7tgKWuyAAAAgJAgZEWZLHO6IN0FAQAAgJAgZEWZzKbpgvurG9Toch/mbAAAAAD+RsiKMmkJdlksnu9Lq5kyCAAAAAQbISvK2KwWZSSwLgsAAAAIFUJWFDKbX+yjwyAAAAAQdISsKJSZ6Gl+UULzCwAAACDoCFlRKIORLAAAACBkCFlRKCuRNVkAAABAqBCyolCmuVdWFdMFAQAAgGAjZEUhs/FFCdMFAQAAgKAjZEUhc0PifTS+AAAAAIKOkBWFzOmCrMkCAAAAgo+QFYUOjGQRsgAAAIBgI2RFIXMkq6KuUbUNrhBXAwAAAHQuhKwolBIXo1ibRRJTBgEAAIBgI2RFIYvFogz2ygIAAABCgpAVpTITPVMGS+gwCAAAAAQVIStKmXtl0fwCAAAACC5CVpTydhisYiQLAAAACCZCVpQyOwzuY00WAAAAEFSErCjFdEEAAAAgNAhZUSqrqfHFPhpfAAAAAEFFyIpSGd41WYxkAQAAAMFEyIpSTBcEAAAAQoOQFaWyvI0v6mQYRoirAQAAADoPQlaUMkeyahvcqq53hbgaAAAAoPMgZEWpBHuM4mI9Hy9TBgEAAIDgIWRFsczEA1MGAQAAAAQHISuKZdH8AgAAAAg6QlYUy0xiJAsAAAAINkJWFDP3yiphJAsAAAAImiMKWZs2bdJdd92lyy67THv27JEk/ec//9G3337r1+JwdMwOg6VsSAwAAAAETYdD1scff6yhQ4fqyy+/1KuvvqrKykpJ0po1azRnzhy/F4gjl2U2vqhkuiAAAAAQLB0OWbfffrvuu+8+vffee7Lb7d7jZ5xxhr744gu/FoejY45k7WMkCwAAAAiaDoesb775RhdccEGL4126dFFJSYlfioJ/sCYLAAAACL4Oh6y0tDTt3r27xfGvvvpK3bt390tR8I+spu6CpXQXBAAAAIKmwyHr0ksv1a9//WsVFRXJYrHI7Xbrs88+069+9StNmTIlEDXiCGU22yfLMIwQVwMAAAB0Dh0OWQ888IAGDhyovLw8VVZWavDgwTrllFM0duxY3XXXXYGoEUfInC7Y6DbkrGkMcTUAAABA59DhkGW32/XMM89o06ZNevPNN/X3v/9d69ev19/+9jfZbLZA1OjjqaeeUn5+vuLi4jR69GgtX768Xde98MILslgsOv/88wNbYBhxxNiU7IiRJJUwZRAAAAAIipgjvbBnz57q2bOnP2s5rMWLF2vWrFlauHChRo8erQULFmjixInasGGDunTp0uZ1W7du1a9+9SudfPLJQaw2PGQm2VVR16jSqnr1zQ51NQAAAED063DIuuqqqw75+LPPPnvExRzOo48+qunTp2vatGmSpIULF+qtt97Ss88+q9tvv73Va1wuly6//HLNmzdP//3vf1VWVhaw+sJRZpJDW/dVs1cWAAAAECQdDln79+/3ud/Q0KC1a9eqrKxMZ5xxht8KO1h9fb0KCws1e/Zs7zGr1arx48dr2bJlbV73m9/8Rl26dNHVV1+t//73v4d9nbq6OtXVHQgkTqfz6AoPsUzauAMAAABB1eGQ9dprr7U45na7dd1116lv375+Kao1JSUlcrlcysnJ8Tmek5Oj9evXt3rNp59+qj//+c9avXp1u19n/vz5mjdv3tGUGlaadxgEAAAAEHgdbnzR6pNYrZo1a5Z+//vf++Pp/KKiokJXXHGFnnnmGWVlZbX7utmzZ6u8vNx727FjRwCrDLzMRPbKAgAAAILpiBtfHGzTpk1qbAxcm/CsrCzZbDYVFxf7HC8uLlZubm6r9WzdulWTJk3yHnO73ZKkmJgYbdiwodWRN4fDIYfD4efqQ8ccySqpYiQLAAAACIYOh6xZs2b53DcMQ7t379Zbb72lqVOn+q2wg9ntdhUUFGjp0qXeNuxut1tLly7VzJkzW5w/cOBAffPNNz7H7rrrLlVUVOixxx5TXl5ewGoNJ5lJnsBI4wsAAAAgODocsr766iuf+1arVdnZ2XrkkUcO23nwaM2aNUtTp07VqFGjdMIJJ2jBggWqqqrydhucMmWKunfvrvnz5ysuLk5DhgzxuT4tLU2SWhyPZmbjC9ZkAQAAAMHR4ZD14YcfBqKOdpk8ebL27t2re+65R0VFRRoxYoSWLFnibYaxfft2Wa1+WWYWNczpgqVMFwQAAACCwmIYhhHqIsKZ0+lUamqqysvLlZKSEupyOmxvRZ2Ov/99WSzSxvvPkc1qCXVJAAAAQERqbzZo10jWyJEjZbG07z/OV61a1b4KERTpCbGyWCTDkPZX1ysrKXqaegAAAADhqF0hy2w0gcgTY7MqLT5W+6sbtK+SkAUAAAAEWrtC1pw5cwJdBwIoM8nhCVlVdZKSQ10OAAAAENXoEtEJ0GEQAAAACJ4Odxd0uVz6/e9/rxdffFHbt29Xfb3vf7iXlpb6rTj4h9lhkL2yAAAAgMDr8EjWvHnz9Oijj2ry5MkqLy/XrFmzdOGFF8pqtWru3LkBKBFHKzPRsw6LNu4AAABA4HU4ZP3jH//QM888o1tuuUUxMTG67LLL9Kc//Un33HOPvvjii0DUiKNkjmSVELIAAACAgOtwyCoqKtLQoUMlSUlJSSovL5cknXvuuXrrrbf8Wx38IrOpoyDTBQEAAIDA63DI6tGjh3bv3i1J6tu3r959911J0ooVK+Rw0B48HNH4AgAAAAieDoesCy64QEuXLpUk3XDDDbr77rt1zDHHaMqUKbrqqqv8XiCOnhmyWJMFAAAABF6Huwv+9re/9X4/efJk9erVS59//rmOOeYYTZo0ya/FwT/M6YIlIZwuWNvgksttKNHR4V85AAAAIKJ0+L94a2trFRcX571/4okn6sQTT/RrUfCvrKbGF87aRtU3umWPCe72aIZh6LJnvtCO0mq9P+tUpSXYg/r6AAAAQDB1+L+2u3TpoqlTp+q9996T2+0ORE3ws5S4WNmsFkmhmTK4s6xGX20vU0llvb7YzD5qAAAAiG4dDlnPP/+8qqurdd5556l79+666aabtHLlykDUBj+xWi3KMJtfVAV/ymDhtv3NvidkAQAAILodUeOLl156ScXFxXrggQf03Xff6cQTT1T//v31m9/8JhA1wg9C2WFw5dYDIWtls8AFAAAARKMjXpyTnJysadOm6d1339XXX3+txMREzZs3z5+1wY+yzL2yQjCStWLrgdGrtTvLVdvgCnoNAAAAQLAccciqra3Viy++qPPPP1/HHXecSktLdeutt/qzNvhRRohGspy1DdpQXCFJSo6LUYPL0JodZUGtAQAAAAimDncXfOedd7Ro0SK9/vrriomJ0f/+7//q3Xff1SmnnBKI+uAnmUnmmqzghqyvtpfJMKSeGQka2j1Vb32zWyu37dfoPplBrQMAAAAIliNak1VTU6O//vWvKioq0v/7f/+PgBUBvNMFg7xX1sqmqYKjeqWroFe6zzEAAAAgGnV4JKu4uFjJycmBqAUBFKrGF2bTi1H5GRraPVWSp9ug223I2tRWHgAAAIgmHR7JImBFJnNNVkkQpws2uNxa3bT+alR+ugZ1TVaC3SZnbaM27q0MWh0AAABAMB1x4wtElsym6YKlQewu+N0up2oaXEqJi1G/7CTF2KwakZcmybfjIAAAABBNCFmdRFZS8KcLmntijcrP8E4NHJWfIUkq3Mp+WQAAAIhOhKxOwhzJqq53qbq+MSivWbjNM1plNryQPA0wJDYlBgAAQPQiZHUSiXab7DGejzsYo1mGYWiF2fSiWcga2TNNVou0vbRae5y1Aa8DAAAACLYOh6yqqirdfffdGjt2rPr166c+ffr43BCeLBaLspqaX5QGofnFjtIa7a2oU6zNouFN67AkKTkuVgNzUyQxmgUAAIDo1OEW7tdcc40+/vhjXXHFFeratassFtpwR4rMJId2lddqXxCaX6xsmio4pHuq4mJtPo+Nyk/Xd7udWrl1v84Z2jXgtQAAAADB1OGQ9Z///EdvvfWWTjrppEDUgwDKbGp+URKE6YKtTRU0FfRK11+XbfMGMQAAACCadHi6YHp6ujIyMgJRCwIsI4gbEptNL8xugs0d33Ts213OoDXhAAAAAIKlwyHr3nvv1T333KPq6upA1IMAygrSXlnl1Q36vtiz2XBBKyNZ3dLi1S01Ti634d2sGAAAAIgWHZ4u+Mgjj2jTpk3KyclRfn6+YmNjfR5ftWqV34qDf2UGaSSrcLtnFKt3VqI32B2sID9Du9bs0sqt+zW2b1ZA6wEAAACCqcMh6/zzzw9AGQgGc6+skgB3F1x5iPVYplG90vXGml10GAQAAEDU6XDImjNnTiDqQBAcGMkK7HRBMziNyj9EyGp67Ktt++VyG7JZ6VIJAACA6NDhkGUqLCzUunXrJEnHHnusRo4c6beiEBhmd8FA7pNV3+jWmqZ1VgW92m6QMjA3RUmOGFXUNWpDUYUGd0sJWE0AAABAMHU4ZO3Zs0eXXnqpPvroI6WlpUmSysrKdPrpp+uFF15Qdna2v2uEn5jTBfdV1sswjIDscbZ2V7nqGt1KT4hV3+zENs+zWS0a2TNN//2hRIXbSglZAAAAiBod7i54ww03qKKiQt9++61KS0tVWlqqtWvXyul06pe//GUgaoSfmNMF611uVdQFpnV6YdN6rIJeGYcNcaOaRrpYlwUAAIBo0uGRrCVLluj999/XoEGDvMcGDx6sp556ShMmTPBrcfCvuFibEu02VdW7tK+yXilxsYe/qINWevfHans9lsk8x2yUAQAAAESDDo9kud3uFm3bJSk2NlZut9svRSFwMgO4V5ZhGN7AdHw7QtaIvDTZrBbtLKvR7vIav9cDAAAAhEKHQ9YZZ5yhG2+8Ubt27fIe27lzp26++WaNGzfOr8XB/8zmFyUB2Ctr675q7auqlz3GqiHdUw97fqIjRoO7etZiMZoFAACAaNHhkPXkk0/K6XQqPz9fffv2Vd++fdW7d285nU498cQTgagRfpSZeKD5hb+t3OqZKjise6ocMbZ2XVPQy5wyWOr3egAAAIBQ6PCarLy8PK1atUrvv/++1q9fL0kaNGiQxo8f7/fi4H+B3CvLuwlxftut2w82Kj9dz32+leYXAAAAiBodHsmSJIvFojPPPFM33HCDbrjhhqAGrKeeekr5+fmKi4vT6NGjtXz58jbPfeaZZ3TyyScrPT1d6enpGj9+/CHP7wzM6YL7ArBXlrfpRa/Dr8cymR0G1+12qjJAHQ8BAACAYGrXSNbjjz+uGTNmKC4uTo8//vghzw1kG/fFixdr1qxZWrhwoUaPHq0FCxZo4sSJ2rBhg7p06dLi/I8++kiXXXaZxo4dq7i4OD344IOaMGGCvv32W3Xv3j1gdYYz715Zfg5ZpVX12rS3StKBKYDtkZsapx7p8fpxf42+2r5fJx/DPmsAAACIbBbDMIzDndS7d2+tXLlSmZmZ6t27d9tPZrFo8+bNfi2wudGjR+v444/Xk08+KcnT6TAvL0833HCDbr/99sNe73K5lJ6erieffFJTpkxp12s6nU6lpqaqvLxcKSmRv2Huv1bv1I0vrNbYvplaNP1Evz3ve98Va/pfV6pflyS9P+vUDl170wtf6fXVu3TjuGN085n9/VYTAAAA4E/tzQbtGsnasmVLq98HU319vQoLCzV79mzvMavVqvHjx2vZsmXteo7q6mo1NDQoI6PtNUN1dXWqqzuwXsnpdB550WEow7smy78jWUcyVdA0Kj9Dr6/epULWZQEAACAKdHhN1m9+8xtVV1e3OF5TU6Pf/OY3fimqNSUlJXK5XMrJyfE5npOTo6KionY9x69//Wt169btkGvI5s+fr9TUVO8tLy/vqOoON97ugn6eLljY1PSiI1MFTeamxKu271eji73WAAAAENk6HLLmzZunysrKFserq6s1b948vxQVCL/97W/1wgsv6LXXXlNcXFyb582ePVvl5eXe244dO4JYZeBlNTW+KK2qk9t92Jmi7VLb4NLXP5ZLko7vQGdBU/8uyUqOi1F1vUvriyr8UhMAAAAQKh0OWYZhyGKxtDi+Zs2aQ07DO1pZWVmy2WwqLi72OV5cXKzc3NxDXvvwww/rt7/9rd59910NGzbskOc6HA6lpKT43KJJetN0QbchldU0+OU51+4sV73Lrawku3plJnT4eqvVouN6sl8WAAAAokO7Q1Z6eroyMjJksVjUv39/ZWRkeG+pqak688wzdckllwSsULvdroKCAi1dutR7zO12a+nSpRozZkyb1z300EO69957tWTJEo0aNSpg9UWKWJtVqfGxkvy3V5a5x1VBr/RWA3h7HN80ZXAF67IAAAAQ4dq9GfGCBQtkGIauuuoqzZs3T6mpqd7H7Ha78vPzDxl2/GHWrFmaOnWqRo0apRNOOEELFixQVVWVpk2bJkmaMmWKunfvrvnz50uSHnzwQd1zzz1atGiR8vPzvWu3kpKSlJSUFNBaw1lmkl3lNQ3aV1WvY/zwfObo05FMFTQVNO2XVbh1f5ujpQAAAEAkaHfImjp1qiRPO/eTTjpJMTHtvtRvJk+erL179+qee+5RUVGRRowYoSVLlnibYWzfvl1W64HBuT/+8Y+qr6/X//7v//o8z5w5czR37txglh5WshId2ry3yi8dBg3D8HYFPJKmF6YReWmKsVpU5KzVzrIa9Ujv+LRDAAAAIBx0OClVVVVp6dKlmjhxos/xd955R263W2effbbfimvNzJkzNXPmzFYf++ijj3zub926NaC1RKrMpuYX+6qOfrrgpr1V2l/dIEeMVcd2Sz38BW2It9t0bPdUrdlRpsJt+wlZAAAAiFgdbnxx++23y+VytThuGEa7NgRG6Jl7ZZX4YSTLnCo4Ii9N9pgO/zr5MPfYWkHzCwAAAESwDv9X8Q8//KDBgwe3OD5w4EBt3LjRL0UhsDKTPHtllfphJMtsemHudXU0zJC1civNLwAAABC5OhyyUlNTtXnz5hbHN27cqMTERL8UhcAy98ryx5oscz3WqF5H376/oCmobSiukLPWP+3lAQAAgGDrcMg677zzdNNNN2nTpk3eYxs3btQtt9yi//mf//FrcQiMzETPSNbRhqy9FXXaUlIlSd59ro5Gl+Q49cpMkGFIq2jlDgAAgAjV4ZD10EMPKTExUQMHDlTv3r3Vu3dvDRo0SJmZmXr44YcDUSP8zLsm6yinC5qjWANykpWaEHvUdUkHOhQWErIAAAAQoTrcXTA1NVWff/653nvvPa1Zs0bx8fEaNmyYTjnllEDUhwAwpwuWVh3dSFbhNk+DigI/rMcyHZ+foVdX7WRdFgAAACLWEW12ZbFYNGHCBE2YMMHf9SAIzMYXZdUNanC5FWs7sq6AK7aa67H8F7LM5/pqx/6jqg0AAAAIlSMKWUuXLtXSpUu1Z88eud1un8eeffZZvxSGwEmLj5XVIrkNaX9VvbqkxHX4OWobXPp2V7kkz+iTv/TNTlJqfKzKaxr03S6nhuel+e25AQAAgGDo8DDBvHnzNGHCBC1dulQlJSXav3+/zw3hz2q1HPVeWWt2lKnBZahLskM90uP9Wpu5Lmsl67IAAAAQgTo8krVw4UI999xzuuKKKwJRD4IkM9Ghksr6I16X1Xx/LIvF4s/SNCo/XR+s36OVW0t19U96+/W5AQAAgEDr8EhWfX29xo4dG4haEESZ5l5ZR9hhcOVWT9MLf+yPdTDzOVdu2y/DMPz+/AAAAEAgdThkXXPNNVq0aFEgakEQHc10QbfbOLAJsR87C5qG9UhVrM2ivRV12lFa4/fnBwAAAAKpw9MFa2tr9fTTT+v999/XsGHDFBvruz/So48+6rfiEDhZSeaGxB0fydq4t1LO2kbFx9o0qGuKv0tTXKxNQ7unatX2Mq3YWqqemQl+fw0AAAAgUDocsr7++muNGDFCkrR27Vqfx/y9NgeBk5l45HtlrWiaKjiyZ1rAWqyPys/Qqu1lWrltvy4q6BGQ1wAAAAACocMh68MPPwxEHQgyc6+sI5kuWBiA/bEOZnYYNDc8BgAAACIFO712UuaarCNpfGF2Fizw4/5YBzMD3PfFlSqrPrIOiAAAAEAodHgk6/TTTz/ktMAPPvjgqApCcGSZ3QU7OJK1x1mr7aXVslqk43qmBaAyj8wkh/pkJWpzSZVWbd+vMwbmBOy1AAAAAH/qcMgy12OZGhoatHr1aq1du1ZTp071V10IMHO6YEfXZJmjWANyU5QcF3uYs49OQa90bS6p0sqthCwAAABEjg6HrN///vetHp87d64qKyuPuiAEh7lPVmVdo2obXIqLtbXrupVBWI9lOj4/Qy8V/uh9TQAAACAS+G1N1v/93//p2Wef9dfTIcCSHTGKtXmmfe7rwGjWyqZGFIHYH+tgBU2vsebHMtU3ugP+egAAAIA/+C1kLVu2THFxcf56OgSYxWJRZmLH9sqqrm/Ut7uckjwt1gOtT1aiMhLtqmt0a+2u8oC/HgAAAOAPHZ4ueOGFF/rcNwxDu3fv1sqVK3X33Xf7rTAEXmaSXUXO2naPZK3eUSaX21DX1Dh1T4sPcHWeIFjQK13vfVeslVtLdVzPwI+eAQAAAEerwyNZqampPreMjAyddtppevvttzVnzpxA1IgAMZtftLfDoHc9VhBGsUzm2i/WZQEAACBStGsk6/HHH9eMGTMUFxenefPmqUePHrJa2WIr0mWae2W1c7qg2VkwGE0vTObar8Jt+2UYxiG3DwAAAADCQbuS0qxZs+R0etbi9O7dWyUlJQEtCsHhDVntmC7ochv6ytyEOIgha0j3VNljrNpXVa8tJVVBe10AAADgSLVrJKtbt2565ZVXdM4558gwDP3444+qra1t9dyePXv6tUAETkemC24oqlBFXaOSHDEamJsc6NK8HDE2De+RqhVb92vltv3qk50UtNcGAAAAjkS7QtZdd92lG264QTNnzpTFYtHxxx/f4hxzKpfL5fJ7kQgMc6+sfVWHny5Y2NS6fWTPNMXYgjtVtKBXhlZs3a/Crft1yai8oL42AAAA0FHtClkzZszQZZddpm3btmnYsGF6//33lZmZGejaEGAH1mQdfiRrZQimCprMNWArmoIeAAAAEM7a3cI9OTlZQ4YM0V/+8heddNJJcjgcgawLQXBguuDhR7LM7n7HB7GzoMkMdpv3Vqm0ql4ZTeEQAAAACEcdnvc1depUAlaUaN74wjCMNs/bXV6jnWU1slktGpGXFqTqDkhPtKtfF89arMJttHIHAABAeKMPeydmrsmqa3Srqr7ttXTmKNagrslKdHR4/2q/OLBfFlMGAQAAEN4IWZ1Ygj1G8bE2SYeeMmgGm1G9gj9V0GRugLySkSwAAACEOUJWJ2eOZpUcovmFdxPi/OA3vTCZI1nf/Fiu2gY6WAIAACB8dThk/eY3v1F1dXWL4zU1NfrNb37jl6IQPGbzi9I2NiSurGvUut2ejahDOZLVKzNBWUl21bvc+mZnecjqAAAAAA6nwyFr3rx5qqysbHG8urpa8+bN80tRCJ4sbxv31qcLfrV9v9yG1CM9XrmpccEszYfFYvGGPHONGAAAABCOOhyyzE2HD7ZmzRplZIRupANHJqNZh8HWmIFmVAj2xzqYOV2xkP2yAAAAEMba3SouPT1dFotFFotF/fv39wlaLpdLlZWVuvbaawNSJALHnC5Y0sZIltkyvSAE+2MdzNwva+W2/XK7DVmtLcM+AAAAEGrtDlkLFiyQYRi66qqrNG/ePKWmpnofs9vtys/P15gxYwJSJAInq6nxRWtrshpdbq3abm5CHPqRrGO7pSou1qqy6gZtLqlUvy7JoS4JAAAAaKHdIWvq1KmSpN69e+ukk05STExo9kuCf5ndBfe10l1wfVGFqutdSo6LUf8wCDT2GKuG90jTl1tKtXLrfkIWAAAAwlKH12QlJydr3bp13vv/+te/dP755+uOO+5QfX3bbcARnjIS254uaO6PdVzP9LCZmmeuy1pB8wsAAACEqQ6HrJ///Of6/vvvJUmbN2/W5MmTlZCQoJdeekm33Xab3wtEYGUmtj1d0NwfKxymCprMDoM0vwAAAEC46nDI+v777zVixAhJ0ksvvaRTTz1VixYt0nPPPadXXnnF3/W18NRTTyk/P19xcXEaPXq0li9ffsjzX3rpJQ0cOFBxcXEaOnSo3n777YDXGEmymu2T5XYb3uOGYXg7CxaEcH+sgx3XM10Wi7R1X7X2VrTerAMAAAAIpSNq4e52uyVJ77//vs455xxJUl5enkpKSvxb3UEWL16sWbNmac6cOVq1apWGDx+uiRMnas+ePa2e//nnn+uyyy7T1Vdfra+++krnn3++zj//fK1duzagdUYSs4V7o9uQs7bBe3xnWY2KnLWKsVo0Ii8tRNW1lJoQ610fxmgWAAAAwlGHQ9aoUaN033336W9/+5s+/vhj/fSnP5UkbdmyRTk5OX4vsLlHH31U06dP17Rp0zR48GAtXLhQCQkJevbZZ1s9/7HHHtNZZ52lW2+9VYMGDdK9996r4447Tk8++WRA64wk9hirkuM8TUxKmjW/MFu3H9s9VfF2W0hqa0tB0/RFNiUGAABAOOpwyFqwYIFWrVqlmTNn6s4771S/fv0kSS+//LLGjh3r9wJN9fX1Kiws1Pjx473HrFarxo8fr2XLlrV6zbJly3zOl6SJEye2eb4k1dXVyel0+tyiXfMpg6YVTU0vwmET4oOZa8TMNWMAAABAOOlwH/Zhw4bpm2++aXH8d7/7nWy2wI14lJSUyOVytRgty8nJ0fr161u9pqioqNXzi4qK2nyd+fPna968eUdfcATJTLRrS0mV9jXrMGiOEoVjyDKbX6zdWa6aelfYjbQBAACgc+vwSJapsLBQf//73/X3v/9dq1atUlxcnGJjY/1ZW0jMnj1b5eXl3tuOHTtCXVLAmXtllTSNZDlrG7ShuELSgal54aRHery6JDvU6Da05seyUJcDAAAA+OjwSNaePXs0efJkffzxx0pLS5MklZWV6fTTT9cLL7yg7Oxsf9coScrKypLNZlNxcbHP8eLiYuXm5rZ6TW5ubofOlySHwyGHw3H0BUcQc68scyRr1bb9MgypV2aCuiTHhbK0VlksFh2fn6G3vtmtwm37dWKfzFCXBAAAAHh1eCTrhhtuUGVlpb799luVlpaqtLRUa9euldPp1C9/+ctA1ChJstvtKigo0NKlS73H3G63li5dqjFjxrR6zZgxY3zOl6T33nuvzfM7q6wk372yzKYXBWE4VdBk1mZumAwAAACEiw6PZC1ZskTvv/++Bg0a5D02ePBgPfXUU5owYYJfizvYrFmzNHXqVI0aNUonnHCCFixYoKqqKk2bNk2SNGXKFHXv3l3z58+XJN1444069dRT9cgjj+inP/2pXnjhBa1cuVJPP/10QOuMNOaGxPuaugseWI8VPvtjHWxU0zTGwm375XYbslotIa4IAAAA8OhwyHK73a2uvYqNjfXunxUokydP1t69e3XPPfeoqKhII0aM0JIlS7zNLbZv3y6r9cDg3NixY7Vo0SLddddduuOOO3TMMcfo9ddf15AhQwJaZ6TJbOouWFJZpwaXW1/t8ISs48NwPZZpcNcUJdhtctY26oc9lRqQmxzqkgAAAABJRxCyzjjjDN1444365z//qW7dukmSdu7cqZtvvlnjxo3ze4EHmzlzpmbOnNnqYx999FGLYxdffLEuvvjiAFcV2bwjWVX1+m6XU7UNbqXGx6pvdlKIK2tbjM2qEXlp+nzTPq3cVkrIAgAAQNjo8JqsJ598Uk6nU/n5+erbt6/69u2r3r17y+l06oknnghEjQiwzGb7ZK1sth4r3KfgjerFpsQAAAAIPx0eycrLy9OqVav0/vvve/enGjRoUItNfxE5zBbu+6vr9eXmfZIOrHkKZ6PyPWvGVm6j+QUAAADCR4dDluRpoX3mmWfqzDPP9Hc9CIH0BLssFskwpP/+UCIpvJtemEb2TJPVIu0orVGxs1Y5KeHXbh4AAACdT7unC37wwQcaPHiwnE5ni8fKy8t17LHH6r///a9fi0Nw2KwWpSd4RrNqGlyKtVk0rEdqiKs6vOS4WA3ITZHElEEAAACEj3aHrAULFmj69OlKSUlp8Vhqaqp+/vOf69FHH/VrcQges/mFJA3tnqq4WFsIq2k/77ospgwCAAAgTLQ7ZK1Zs0ZnnXVWm49PmDBBhYWFfikKwWeuy5IOrHWKBM33ywIAAADCQbtDVnFxcav7Y5liYmK0d+9evxSF4DM7DEqezoKRwgyE3+5yqqquMcTVAAAAAB0IWd27d9fatWvbfPzrr79W165d/VIUgq/5dMFRERSyuqfFq2tqnFxuQ2t2lIW6HAAAAKD9Ieucc87R3Xffrdra2haP1dTUaM6cOTr33HP9WhyCJzPRM5LVJyvRZ1QrEpijWStofgEAAIAw0O4W7nfddZdeffVV9e/fXzNnztSAAQMkSevXr9dTTz0ll8ulO++8M2CFIrAGdU2WJJ0xsEuIK+m443qm6Y01u/TNzrJQlwIAAAC0P2Tl5OTo888/13XXXafZs2fLMAxJnj2zJk6cqKeeeko5OTkBKxSBNeHYXC295VT1zEgIdSkdNqirp+Plut0VIa4EAAAA6OBmxL169dLbb7+t/fv3a+PGjTIMQ8ccc4zS0yNnDQ/a1jc7KdQlHJFBTXtl7SyrUXlNg1Lj227QAgAAAARah0KWKT09Xccff7y/awGOSGpCrLqlxmlXea02FFXohN6R04IeAAAA0afdjS+AcGZOGVxf5AxxJQAAAOjsCFmICgObGnes203IAgAAQGgRshAVBubS/AIAAADhgZCFqGBOF9xQVCGX2whxNQAAAOjMCFmICvmZCXLEWFXT4NL20upQlwMAAIBOjJCFqBBjs6p/jmdd1nrWZQEAACCECFmIGoNofgEAAIAwQMhC1PA2vyii+QUAAABCh5CFqGG2cWevLAAAAIQSIQtRY1DTSNaO0hpV1DaEuBoAAAB0VoQsRI30RLtyU+IkeVq5AwAAAKFAyEJU8Ta/IGQBAAAgRAhZiCoDmzYlpsMgAAAAQoWQhagyMJe9sgAAABBahCxElcFNI1nriyrkdhshrgYAAACdESELUaV3VqLsNquq613asb861OUAAACgEyJkIarE2Kw6JidJkrRuN80vAAAAEHyELESdQTS/AAAAQAgRshB1vM0vighZAAAACD5CFqLOoGbNLwAAAIBgI2Qh6pgjWdv2VauyrjHE1QAAAKCzIWQh6mQmOdQl2SFJ2sBoFgAAAIKMkIWodGDKIOuyAAAAEFyELESlgV09UwbpMAgAAIBgI2QhKg3KbRrJYq8sAAAABBkhC1GpeYdBt9sIcTVtc9Y26Pfvfa/d5TWhLgUAAAB+QshCVOqTnahYm0WVdY3aWRa+AWbhR5v02NIf9PA734e6FAAAAPgJIQtRKdZmVb8u4b8u64vN+yRJq7bvD3ElAAAA8JeICVmlpaW6/PLLlZKSorS0NF199dWqrKw85Pk33HCDBgwYoPj4ePXs2VO//OUvVV5eHsSqEUqDvM0vwnNdVm2DS9/s9Pw+bimpUll1fYgrAgAAgD9ETMi6/PLL9e233+q9997Tm2++qU8++UQzZsxo8/xdu3Zp165devjhh7V27Vo999xzWrJkia6++uogVo1Q8ja/CNM27qt3lKnBZfjcBwAAQOSLCXUB7bFu3TotWbJEK1as0KhRoyRJTzzxhM455xw9/PDD6tatW4trhgwZoldeecV7v2/fvrr//vv1f//3f2psbFRMTES8dRwFs437+jDdkHjl1lKf+19tL9NpA7qEqBoAAAD4S0SMZC1btkxpaWnegCVJ48ePl9Vq1Zdfftnu5ykvL1dKSsohA1ZdXZ2cTqfPDZHJ7DC4dV+VqusbQ1xNSyu2etZh9clOlMRIFgAAQLSIiJBVVFSkLl18/4U/JiZGGRkZKioqatdzlJSU6N577z3kFENJmj9/vlJTU723vLy8I64boZWV5FBWkkOGIW0Is9Esl9vQqm2ekDX95D6SpDU/lskwwrfdPAAAANonpCHr9ttvl8ViOeRt/fr1R/06TqdTP/3pTzV48GDNnTv3kOfOnj1b5eXl3tuOHTuO+vUROoPCdMrg+iKnKuoaleSI0QUju8seY1VZdYO27qsOdWkAAAA4SiFdmHTLLbfoyiuvPOQ5ffr0UW5urvbs2eNzvLGxUaWlpcrNzT3k9RUVFTrrrLOUnJys1157TbGxsYc83+FwyOFwtKt+hL9BXVP03x9Kwq6N+4otnvVYx/VKV1ysTUO6pWjV9jKt3rFfvbMSQ1wdAAAAjkZIQ1Z2drays7MPe96YMWNUVlamwsJCFRQUSJI++OADud1ujR49us3rnE6nJk6cKIfDoX//+9+Ki4vzW+2IDANzm0aywqyN+4qmqYIn5KdLkkbkpWvV9jJ9tb1MF4zsEcrSAAAAcJQiYk3WoEGDdNZZZ2n69Olavny5PvvsM82cOVOXXnqpt7Pgzp07NXDgQC1fvlySJ2BNmDBBVVVV+vOf/yyn06mioiIVFRXJ5XKF8u0giMzmF+uKnGGz3skwDO9I1qj8DEnSiJ5pkmh+AQAAEA0ipo/5P/7xD82cOVPjxo2T1WrVRRddpMcff9z7eENDgzZs2KDqas+allWrVnk7D/br18/nubZs2aL8/Pyg1Y7Q6ZudpBirRRW1jdpZVqMe6QmhLkk7Smu0p6JOsTaLRuSlSZJGNn1dt9up2gaX4mJtoSsQAAAARyViQlZGRoYWLVrU5uP5+fk+IxWnnXZa2IxcIHTsMVb165Kk9UUVWr+7IixC1vKm/bGGdk/1hqke6fHKSrKrpLJe3+5yqqBXeihLBAAAwFGIiOmCwNHwThkMk+YX5ibExzdNFZQki+XAqNZX2/eHoiwAAAD4CSELUc/b/CJM2rgvbyVkSfKGLNZlAQAARDZCFqLewGbNL0JtX2WdNu+tkqQWUwJH5HnuE7IAAAAiGyELUc/ckHhrSZVq6kPbWXJlU+v2/jlJSk+0+zw2LC9VFov04/4a7a2oC0V5AAAA8ANCFqJedpJDmYl2uQ3p++LQThk8uHV7cylxseqXnSSJ0SwAAIBIRshC1LNYLN7mF+tDPGXwwCbELUOW1HxdFs0vAAAAIhUhC52C2fxi3e7QjWRV1zfq253lkqRR+a23aGdTYgAAgMhHyEKnMDAM2riv3l6mRrehbqlxbe7XZY5kfb2jXG43+7wBAABEIkIWOgWz+cX6ooqQbVJttm5vbT2WaUBOsuJjbaqoa9SmvZXBKg0AAAB+RMhCp9CvS5JsVovKaxq0u7w2JDWs3OpZZ3V877ZDVozNqqE9UiVJX20vC0ZZAAAA8DNCFjoFR4xNfbMTJYWm+UWjy61V25tCVhvrsUwjm6YMfsW6LAAAgIhEyEKnMci7Liv4zS++2+1Udb1LKXEx6t8l+ZDnHugwWBb4wgAAAOB3hCx0GgNzQ9f8Ynmz/bGsVsshzx3Z0zPStaHIqer6xoDXBgAAAP8iZKHTGNis+UWwmeux2mrd3lxuapxyU+LkNqSvfywPdGkAAADwM0IWOo3BTdMFN++tVG2DK2ivaxiGVm7zjGS1tQnxwZgyCAAAELkIWeg0uiQ7lJ4QK7ch/VAcvPboW0qqVFJZL3vMgc6Bh+PdlJgOgwAAABGHkIVOw2KxHGh+EcQOg+ZUwRE90uSIsbXrmpGMZAEAAEQsQhY6lVA0vziwCfHh12OZhvZIlc1qUZGzVrvLawJVGgAAAAKAkIVOxdv8Ioht3Fc2haxDbUJ8sAR7jPrneGplyiAAAEBkIWShUzGbX6wvcsowjIC/3p6KWm3dVy2LRTquZ/tHsiSaXwAAAEQqQhY6lX5dkmS1SPurG1TsrAv465nrsQbmpig1PrZD15rrsr4iZAEAAEQUQhY6lbhYm/pkJ0kKTvMLcxPi4zuwHss0sqnD4Dc/lqvR5fZnWQAAAAggQhY6HW+HwSA0vzD3xzq+nftjNdc3O0nJjhjVNLi0oTj4GygDAADgyBCy0OkMzA1O84uK2gZ9t8sT5I4kZFmtFg3L8+yrxbosAACAyEHIQqczyOwwGODpgl9tL5PbkPIy4pWbGndEz+FtfkGHQQAAgIhByEKnY04X3LS3SrUNroC9jrd1e6+Oj2KZRuZ51nIxkgUAABA5CFnodHJT4pQaHyuX29DGPZUBe50DmxAfecga0dT8YuPeSjlrG/xRFgAAAAKMkIVOx2KxNJsyGJh1WfWNbu/o0wm9O95Z0JSV5FCP9HgZhvT1jnI/VQcAAIBAImShUxqYG9gOg2t3lau2wa30hFj1bWoZf6QObEq83w+VAQAAINAIWeiUAt38YmWzqYIWi+WonmtkT9ZlAQAARBJCFjqlA3tlVcgwDL8///ItnlGnI9mE+GDmSNZX28sCUisAAAD8i5CFTumYLsmyWqTSqnrtrajz63O73YYKj2IT4oMd2y1FsTaL9lXV68f9NUf9fAAAAAgsQhY6pXi7TflZiZKkdX5ufrFpb6X2VzcoLtaqY7ulHvXzxcXavCNvXzFlEAAAIOwRstBpmcFlvZ+bX6zY6pkqODIvXfYY//yJjWRTYgAAgIhByEKnNSjX0/zC3x0GV5ibEPthPZbJ3C+LDoMAAADhj5CFTss7kuXn6YLekNX76NdjmUbkeQLb2l1O1Te6/fa8AAAA8D9CFjqtgU0ha+OeStU1uvzynLvLa/Tj/hpZLQdar/tDfmaC0hJiVd/oDtjeXgAAAPAPQhY6rW6pcUqJi1Gj29CmPVV+eU5zPdbgbilKcsT45TklyWKxaHiPNEnslwUAABDuCFnotCwWi3c0y1+bEq/c6r/W7Qcb6V2XVeb35wYAAID/ELLQqfm7+cXyLYELWQc2Jab5BQAAQDgjZKFTG+jH5hflNQ3aUOx5nlF+7CxoMkPW1n3V2l9V7/fnBwAAgH9ETMgqLS3V5ZdfrpSUFKWlpenqq69WZWVlu641DENnn322LBaLXn/99cAWiohidhhct/voQ9aqbftlGJ4mFV2S4476+Q6WlmBX76YNlFf/WOb35wcAAIB/REzIuvzyy/Xtt9/qvffe05tvvqlPPvlEM2bMaNe1CxYskMViCXCFiET9c5JksUgllXXaW1F3VM+1IoDrsUxsSgwAABD+IiJkrVu3TkuWLNGf/vQnjR49Wj/5yU/0xBNP6IUXXtCuXbsOee3q1av1yCOP6Nlnnw1StYgkCfYY5Wd6RoeOtvlFMEKWuSnxVzS/AAAACFsREbKWLVumtLQ0jRo1ynts/Pjxslqt+vLLL9u8rrq6Wj/72c/01FNPKTc3t12vVVdXJ6fT6XNDdBvU1dP8Yv1RTBmsbXBpzY5ySf7dhPhg5rqsNTvKZBhGwF4HAAAARy4iQlZRUZG6dOnicywmJkYZGRkqKipq87qbb75ZY8eO1Xnnndfu15o/f75SU1O9t7y8vCOuG5FhYK65LuvIA/U3O8tV73IrK8mu/MwEf5XWwsDcFNljrCqvadCWEv/s7QUAAAD/CmnIuv3222WxWA55W79+/RE997///W998MEHWrBgQYeumz17tsrLy723HTt2HNHrI3J4m18cRYfB5lMFA7n+zx5j1dDuqZLYLwsAACBcxYTyxW+55RZdeeWVhzynT58+ys3N1Z49e3yONzY2qrS0tM1pgB988IE2bdqktLQ0n+MXXXSRTj75ZH300UetXudwOORwONr7FhAFBjbtlbVxT4XqG92yx3T83x5WbvXsXTUqgOuxTCPy0lS4bb9W7yjThcf1CPjrAQAAoGNCGrKys7OVnZ192PPGjBmjsrIyFRYWqqCgQJInRLndbo0ePbrVa26//XZdc801PseGDh2q3//+95o0adLRF4+o0SM9XsmOGFXUNWpzSaV3+mB7ud2GVjaNZJ0QpJAlSV/RYRAAACAsRcSarEGDBumss87S9OnTtXz5cn322WeaOXOmLr30UnXr1k2StHPnTg0cOFDLly+XJOXm5mrIkCE+N0nq2bOnevfuHbL3gvBjsVg08CiaX3y/p0LO2kYl2G3eJhqBZIasdbudqm1wBfz1AAAA0DEREbIk6R//+IcGDhyocePG6ZxzztFPfvITPf30097HGxoatGHDBlVXV4ewSkSqo2l+sWKLZxTruJ7pirEF/k+qR3q8spIcanQb+nZXecBfDwAAAB0T0umCHZGRkaFFixa1+Xh+fv5hW1rT8hptMUeyjqT5xYqm9ViB3B+rOYvFohF5aXp/XbG+2l6mgl7BeV0AAAC0T8SMZAGBZHYYXN/BkSzDMJp1Fkz3e11tGcmmxAAAAGGLkAVIGpDjGcnaU1GnfZV17b5uZ1mNdpfXKsZq0Yim4BMM5rqs1TS/AAAACDuELEBSoiNGvZo2EV7fgSmD5ijWsd1TlWAP3uzbYT1SZbF4Qt7eivaHQgAAAAQeIQtoMugIml+Y67FOCOJUQUlKjovVMV2SJLEpMQAAQLghZAFNvM0vOtDG3ewsGIxNiA/mnTK4Y3/QXxsAAABtI2QBTbzNL4raN5K1v6peP+yplCSN6hXckSxJGpHneU02JQYAAAgvhCygiTld8IfiSjW43Ic9v3CbZwSpb3aiMpMcAa2tNeZI1tc/lsvlZnsCAACAcEHIApr0SI9Xot2mepdbW0qqDnu+2fTihN6h2aeqf06SEuw2VdY1atPeypDUAAAAgJYIWUATq9WigV3b3/zCDFmjQrQZcIzNqqHdUyXRyh0AACCcELKAZgbmtq/5RW2DS9/sLJckHR+CphemEd5NiWl+AQAAEC4IWUAzA9vZ/GL1jjI1uAzlpDiUlxEfjNJaNbJpXRbNLwAAAMIHIQtoZnBTG/f1hxnJat663WKxBLyutozs6ekw+H1xharqGkNWBwAAAA4gZAHN9M/xhKwiZ632V9W3ed6KbeYmxKGbKihJOSlx6poaJ7ch7/RFAAAAhBYhC2gmOS7WO/1vXRtTBl1uQ6uaQtao/ODvj3WwEUwZBAAACCuELOAg5n5ZbU0ZXLfbqcq6RiU7YjSw6dxQMkPWappfAAAAhAVCFnCQw7VxN1u3H9crXTZr6NZjmcx1Wat3lIW2EAAAAEgiZAEteJtfFLU+krVya9N6rBBtQnywod1TZbNaVOys0+7ymlCXAwAA0OkRsoCDmFMAvy+uUKPL7fOYYRjNNiEO/XosSYq32zSgqWEHmxIDAACEHiELOEjPjAQl2G2qa3Rr674qn8e2l1ZrT0Wd7DarhjethQoHBzYlLgtpHQAAACBkAS1YrRYNyPWMDK07qPnFiqapgkN7pCou1hb02tribX7BSBYAAEDIEbKAVphTBg9ufmFuQnx8iPfHOthxTSNZ3+wsbzHFEQAAAMFFyAJaMaiN5hcrtpkhKzzWY5n6ZCUpOS5GNQ0ubShuvWEHAAAAgoOQBbRiUFdzr6wDI1kllXXavNezRqsgTJpemKxWi4b3SJPEpsQAAAChRsgCWmGuydpVXquy6npJB1q3D8hJVlqCPWS1teXApsRlIa0DAACgsyNkAa1IiYtV97R4SQemDHpbt4fZVEHTyKZ1WYQsAACA0CJkAW04eMrgyqaQFS6bEB/MHMnauKdS5TUNoS0GAACgEyNkAW0wm1+s212hqrpGrd3lCVujwqyzoCkzyaG8DM/o29c/loW2GAAAgE6MkAW0wTuSVeTU6h1lcrkNdU+L904jDEcj8jxTGdkvCwAAIHQIWUAbBjY1v9hQXKEvN++TFL7rsUwjaX4BAAAQcoQsoA29MhMVF2tVbYNbr6zaKSn8NiE+2IhmzS8MwwhtMQAAAJ0UIQtog81q0YBcz5TBnWU1ksI/ZA3umqJYm0X7qur14/6aUJcDAADQKRGygEMY1DRlUJJS42N1TJekEFZzeHGxNg1uWku2avv+EFcDAADQORGygEMY2CxkjeqVLqvVEsJq2mdkz6bmF6zLAgAACAlCFnAIZodBKXxbtx9sBM0vAAAAQoqQBRzCwNwDIeuE3uHdWdBkhqxvdzlV1+gKbTEAAACdECELOITUhFhdOTZfZx2bq+E90kJdTrv0ykxQekKs6hvdWre7ItTlAAAAdDoxoS4ACHdz/+fYUJfQIRaLRcPz0vTRhr1avX2/d2QLAAAAwcFIFhCFRubR/AIAACBUCFlAFGq+KTEAAACCi5AFRKERTevHtu6rVmlVfWiLAQAA6GQIWUAUSk2IVZ+sREnSGkazWjAMg86LAAAgYCKm8UVpaaluuOEGvfHGG7Jarbrooov02GOPKSkp6ZDXLVu2THfeeae+/PJL2Ww2jRgxQu+8847i4+ODVDkQGiN6pmlzSZW+2lGm0wd2CXU5QVFV16i9FXUqqazz+bq3sr7pa51Kmr7WN7rVJytRx/VKV0HTrV92UkRsOA0AAMJbxISsyy+/XLt379Z7772nhoYGTZs2TTNmzNCiRYvavGbZsmU666yzNHv2bD3xxBOKiYnRmjVrZLUygIfoNzIvTa+u2hnx67Jq6l2esHRQcPIGqIo6lTSFqJqGjo1ObS6p0uaSKr1c+KMkKTkuRsf19ASuUb3SNTwvTYmOiPmfSQAAECYshmEYoS7icNatW6fBgwdrxYoVGjVqlCRpyZIlOuecc/Tjjz+qW7durV534okn6swzz9S99957xK/tdDqVmpqq8vJypaSkHP4CIEx882O5Jj35qeJjbTprSK6ykuzKTnYoK8nh8zU9wS5bkEdvDMNQeU2D9lTUaY+zTnsqalt8bwaoyrrGDj13fKxN2cnme2z9PWcnORQXa9PaXeVatW2/Crft1+odZaqu9w1pVos0qGuKd6TruJ7p6pEeL4uF0S4AADqj9maDiPgn2mXLliktLc0bsCRp/Pjxslqt+vLLL3XBBRe0uGbPnj368ssvdfnll2vs2LHatGmTBg4cqPvvv18/+clP2nyturo61dXVee87nU7/vhkgSAZ2TVZGol2lVfV67audbZ5ntUiZSZ7gkZVsfrUru1kgMQNKWkLsIQOGy21oX2WdJzBV1DaFJt/vzfBU73K3+704YqytBCV7szB14GtHRp5OH9BFpw/wTKVsdLm1vqhChU2hq3Dbfu0sq9G3u5z6dpdTf122TZLUJdnhDV0FvdJ1bLdU2WMYHT8cwzBUVe9SdV2jUuJjFRdrC3VJAAAETESErKKiInXp4rumJCYmRhkZGSoqKmr1ms2bN0uS5s6dq4cfflgjRozQX//6V40bN05r167VMccc0+p18+fP17x58/z7BoAQiLVZ9fovTtLKbaXNptjVN5tiV6fS6nq5DXmPaffhntOizMQDo0RpCXaVVdc3Bak67ausk7sDY+NpCbHq0hSUuiTHHfg+5cD32ckOJTtiAj56FGOzakj3VA3pnqqpY/MlSUXltQdC1/b9+nZnufZU1Ok/a4v0n7We/+2xx1g1vEeqZ21Xz3Qd1ytdWUmOgNYaSm63oYraRpXV1KusukFlNQ0qq65XeU2D5351g8pq6lXeymONzX45Euw2ZSTalZloV0aiXene7x3KbLrvfTzJHpTfAQAA/CWkIev222/Xgw8+eMhz1q1bd0TP7XZ7/pX85z//uaZNmyZJGjlypJYuXapnn31W8+fPb/W62bNna9asWd77TqdTeXl5R1QDEGo9MxPUMzOhzccbXW6VVnlC0sFB7EDTCM/3ZdUNanAZKnLWqshZ2+ZzmiNjXZLNW5y6pDiaQlPz7x1yxIT3aEZuapx+OqyrfjqsqySptsGlr38s9wavVdv3q7SqXiu27teKrfu91+VnJqhfl2SlxMUoOS5GKfGxSo6LUXKc52tK3IH7KU2PO2KsAQ8RLreh6vpGVdW5VFXfqKq6pu/rGlVV36jqes/3zhpPQPIGp5oGlVfXe48dzSRzi0UyDKm63qXq+hr9uL+mXdfF2ixKT2gKXkmeMJaREOv5muQJY+kJdiU5YmSzWhRjs3i+Ws2vVsXYfO+bjwer2YlhGHK5DbkMQ2635DbM7z3HbVaL7DFW2W1Wxdiie3TUMAw1ug3VNbpV2+BSXaNbdU1fvfebvm90GXLEWOWItSou1ub5Psbz1Xs/1nMs2FOfAaAtIQ1Zt9xyi6688spDntOnTx/l5uZqz549PscbGxtVWlqq3NzcVq/r2tXzH0WDBw/2OT5o0CBt3769zddzOBxyOKL3X6GB5mJsVs+oUUrcYc+tb3RrX5Vv04my6oam0ai4phEohzITHVH7HzpxsTad0DtDJ/TOkOT5D8UtJVXewFW4bb++L67U1n3V2rqvukPPHWuztBLCzCB24H5KXKwSHDbV1LtUXe9SZV3jgeBU1+hzrLLO1fSY5/GONgY5lES7TWkJdqXGxyotwXNLjbd7vo8/6H5CrNKavnfEWFVR16jSynrtq6pXaVW99leZ39dpX9P90qoDj1fXu9TgMrwjpv5msUixzUKXzdYynNmsFtksFm8ochue0OpuCk5uo9kxM0g1hSlX0zkdYbXIG7jsTYHiwP0D38c2fW318eb3bVYZ8tRoGJ6AJ3l+h5sfMzwHPceanW/I8Hw1Wn+OepdnW4S6Brfnq094cqu2lcc6+CNpl1ibRY4Ym+JiDwQxu08Ysymu6asnrFlltVi8789Tk+dza37MkCE1+xkZPt+bPxvfx80l72boj7FaD/xe2VqGfc+xZuc0+xpjO/haz33pwOfjNprV0rz2g+tUU50+jzU7pgO1B0qLGpv9frV6rFnNLT6PVs6X5P1HK6vFIovF8zdlsVhkaXrMe0ye783HzPMtkvcfYHyOWXzP9zzPgcct3u8tTa/p+7reY4d4XQbtW5eV5NCo/IxQl9FuIQ1Z2dnZys7OPux5Y8aMUVlZmQoLC1VQUCBJ+uCDD+R2uzV69OhWr8nPz1e3bt20YcMGn+Pff/+9zj777KMvHuhk7DFWdU2NV9dUtj8wWSwW9clOUp/sJF08yjPiXV7doK927NeuslpV1DaoorZRFbUNcvp89YwWVdQ2qLKuUW5DanAZKm0KFYFms1qUaLcpyRGjBEeMEu02JTpilGCPUZLDpqS4GKV7A5TdG5rM4JQaH3tU69BSmoJjftNebodT2+Dy/mzMMFZa1dD0tV77Kuu1v9rzWG29S41uzyhJo8stV9P35tfWGIY8awTDaOs0tyHVNrhV2+CW1LHmL5HIbjswGuUZoWr6PtaqWKtVda4DI111DS7VNhv5av65NrgMNbgaVen/LA4gxE7pn62/XnVCqMtot4hYkzVo0CCdddZZmj59uhYuXKiGhgbNnDlTl156qbez4M6dOzVu3Dj99a9/1QknnCCLxaJbb71Vc+bM0fDhwzVixAg9//zzWr9+vV5++eUQvyMA0So1IVanDWj/vmRmQwhP6Gr0BjNns2B2IJR57lfXuxRvtynRHqOEpoCU6Gj6ao9p+tr68QS7LShTE/0pLtambmnx6pZ2dAHfnK7XPHR5vrrV6Gp+zN0U0prdd3lGp6wWz2iCtelfpM3vbVbzuHzPaRoBs1rl+Woea3bcajkwSlbf6PbcXJ6vdc3uNzQd8x5vdr++0XXgvqv587hU3+hWg8vw+ddz81/wPTuatPxXfWvT74f3X+nl+Vd9i+d07zHzOe1No0Le0aLYVqb0NR9hirUqrumr3WY9qimbjS63d3phXaNLteaIWUPLqYfmOeboWm2DWzKMtkcfDjp24OfSdMzn52I58HO1HBiN8P6eHfQ71tDK75zLbTQdd/v8nrb4BwOX5/fWrOXgEZVW62x6TAe9n4NHVczzA/2/Eb6jPs1HiFp5T2r987AcVL/585eajWypadTV/N7tO3onNR/FOzBS29aIpu/oWsuRwuaja1KzY83Ob/6aB48ghn/P79Dp3+XQe+OGm4gIWZL0j3/8QzNnztS4ceO8mxE//vjj3scbGhq0YcMGVVcfmKJz0003qba2VjfffLNKS0s1fPhwvffee+rbt28o3gIAtGCxWJTkiFES+3EFnMXSNG0rTJcCWmVRrM2qRGasd0hM0xo2fm4AwklE7JMVSuyTBQAAAEBqfzaI7vZFAAAAABBkhCwAAAAA8CNCFgAAAAD4ESELAAAAAPyIkAUAAAAAfkTIAgAAAAA/ImQBAAAAgB8RsgAAAADAjwhZAAAAAOBHhCwAAAAA8CNCFgAAAAD4ESELAAAAAPyIkAUAAAAAfkTIAgAAAAA/ImQBAAAAgB8RsgAAAADAjwhZAAAAAOBHMaEuINwZhiFJcjqdIa4EAAAAQCiZmcDMCG0hZB1GRUWFJCkvLy/ElQAAAAAIBxUVFUpNTW3zcYtxuBjWybndbu3atUvJycmyWCwhrcXpdCovL087duxQSkpKSGuB//C5Rh8+0+jDZxqd+FyjD59pdAqnz9UwDFVUVKhbt26yWtteecVI1mFYrVb16NEj1GX4SElJCfkvGPyPzzX68JlGHz7T6MTnGn34TKNTuHyuhxrBMtH4AgAAAAD8iJAFAAAAAH5EyIogDodDc+bMkcPhCHUp8CM+1+jDZxp9+EyjE59r9OEzjU6R+LnS+AIAAAAA/IiRLAAAAADwI0IWAAAAAPgRIQsAAAAA/IiQBQAAAAB+RMiKIE899ZTy8/MVFxen0aNHa/ny5aEuCUdo7ty5slgsPreBAweGuix00CeffKJJkyapW7duslgsev31130eNwxD99xzj7p27ar4+HiNHz9eP/zwQ2iKRbsc7jO98sorW/ztnnXWWaEpFu0yf/58HX/88UpOTlaXLl10/vnna8OGDT7n1NbW6vrrr1dmZqaSkpJ00UUXqbi4OEQVoz3a87medtppLf5er7322hBVjMP54x//qGHDhnk3HB4zZoz+85//eB+PtL9TQlaEWLx4sWbNmqU5c+Zo1apVGj58uCZOnKg9e/aEujQcoWOPPVa7d+/23j799NNQl4QOqqqq0vDhw/XUU0+1+vhDDz2kxx9/XAsXLtSXX36pxMRETZw4UbW1tUGuFO11uM9Uks466yyfv91//vOfQawQHfXxxx/r+uuv1xdffKH33ntPDQ0NmjBhgqqqqrzn3HzzzXrjjTf00ksv6eOPP9auXbt04YUXhrBqHE57PldJmj59us/f60MPPRSiinE4PXr00G9/+1sVFhZq5cqVOuOMM3Teeefp22+/lRSBf6cGIsIJJ5xgXH/99d77LpfL6NatmzF//vwQVoUjNWfOHGP48OGhLgN+JMl47bXXvPfdbreRm5tr/O53v/MeKysrMxwOh/HPf/4zBBWiow7+TA3DMKZOnWqcd955IakH/rFnzx5DkvHxxx8bhuH5u4yNjTVeeukl7znr1q0zJBnLli0LVZnooIM/V8MwjFNPPdW48cYbQ1cUjlp6errxpz/9KSL/ThnJigD19fUqLCzU+PHjvcesVqvGjx+vZcuWhbAyHI0ffvhB3bp1U58+fXT55Zdr+/btoS4JfrRlyxYVFRX5/N2mpqZq9OjR/N1GuI8++khdunTRgAEDdN1112nfvn2hLgkdUF5eLknKyMiQJBUWFqqhocHnb3XgwIHq2bMnf6sR5ODP1fSPf/xDWVlZGjJkiGbPnq3q6upQlIcOcrlceuGFF1RVVaUxY8ZE5N9pTKgLwOGVlJTI5XIpJyfH53hOTo7Wr18foqpwNEaPHq3nnntOAwYM0O7duzVv3jydfPLJWrt2rZKTk0NdHvygqKhIklr9uzUfQ+Q566yzdOGFF6p3797atGmT7rjjDp199tlatmyZbDZbqMvDYbjdbt1000066aSTNGTIEEmev1W73a60tDSfc/lbjRytfa6S9LOf/Uy9evVSt27d9PXXX+vXv/61NmzYoFdffTWE1eJQvvnmG40ZM0a1tbVKSkrSa6+9psGDB2v16tUR93dKyAJC4Oyzz/Z+P2zYMI0ePVq9evXSiy++qKuvvjqElQE4lEsvvdT7/dChQzVs2DD17dtXH330kcaNGxfCytAe119/vdauXcsa2CjT1uc6Y8YM7/dDhw5V165dNW7cOG3atEl9+/YNdplohwEDBmj16tUqLy/Xyy+/rKlTp+rjjz8OdVlHhOmCESArK0s2m61FB5Xi4mLl5uaGqCr4U1pamvr376+NGzeGuhT4ifm3yd9tdOvTp4+ysrL4240AM2fO1JtvvqkPP/xQPXr08B7Pzc1VfX29ysrKfM7nbzUytPW5tmb06NGSxN9rGLPb7erXr58KCgo0f/58DR8+XI899lhE/p0SsiKA3W5XQUGBli5d6j3mdru1dOlSjRkzJoSVwV8qKyu1adMmde3aNdSlwE969+6t3Nxcn79bp9OpL7/8kr/bKPLjjz9q3759/O2GMcMwNHPmTL322mv64IMP1Lt3b5/HCwoKFBsb6/O3umHDBm3fvp2/1TB2uM+1NatXr5Yk/l4jiNvtVl1dXUT+nTJdMELMmjVLU6dO1ahRo3TCCSdowYIFqqqq0rRp00JdGo7Ar371K02aNEm9evXSrl27NGfOHNlsNl122WWhLg0dUFlZ6fMvolu2bNHq1auVkZGhnj176qabbtJ9992nY445Rr1799bdd9+tbt266fzzzw9d0TikQ32mGRkZmjdvni666CLl5uZq06ZNuu2229SvXz9NnDgxhFXjUK6//notWrRI//rXv5ScnOxdv5Gamqr4+Hilpqbq6quv1qxZs5SRkaGUlBTdcMMNGjNmjE488cQQV4+2HO5z3bRpkxYtWqRzzjlHmZmZ+vrrr3XzzTfrlFNO0bBhw0JcPVoze/ZsnX322erZs6cqKiq0aNEiffTRR3rnnXci8+801O0N0X5PPPGE0bNnT8NutxsnnHCC8cUXX4S6JByhyZMnG127djXsdrvRvXt3Y/LkycbGjRtDXRY66MMPPzQktbhNnTrVMAxPG/e7777byMnJMRwOhzFu3Dhjw4YNoS0ah3Soz7S6utqYMGGCkZ2dbcTGxhq9evUypk+fbhQVFYW6bBxCa5+nJOMvf/mL95yamhrjF7/4hZGenm4kJCQYF1xwgbF79+7QFY3DOtznun37duOUU04xMjIyDIfDYfTr18+49dZbjfLy8tAWjjZdddVVRq9evQy73W5kZ2cb48aNM959913v45H2d2oxDMMIZqgDAAAAgGjGmiwAAAAA8CNCFgAAAAD4ESELAAAAAPyIkAUAAAAAfkTIAgAAAAA/ImQBAAAAgB8RsgAAAADAjwhZAAAAAOBHhCwAAPwkPz9fCxYsCHUZAIAQI2QBACLSlVdeqfPPP1+SdNppp+mmm24K2ms/99xzSktLa3F8xYoVmjFjRtDqAACEp5hQFwAAQLior6+X3W4/4uuzs7P9WA0AIFIxkgUAiGhXXnmlPv74Yz322GOyWCyyWCzaunWrJGnt2rU6++yzlZSUpJycHF1xxRUqKSnxXnvaaadp5syZuummm5SVlaWJEydKkh599FENHTpUiYmJysvL0y9+8QtVVlZKkj766CNNmzZN5eXl3tebO3eupJbTBbdv367zzjtPSUlJSklJ0SWXXKLi4mLv43PnztWIESP0t7/9Tfn5+UpNTdWll16qioqKwP7QAAABRcgCAES0xx57TGPGjNH06dO1e/du7d69W3l5eSorK9MZZ5yhkSNHauXKlVqyZImKi4t1ySWX+Fz//PPPy26367PPPtPChQslSVarVY8//ri+/fZbPf/88/rggw902223SZLGjh2rBQsWKCUlxft6v/rVr1rU5Xa7dd5556m0tFQff/yx3nvvPW3evFmTJ0/2OW/Tpk16/fXX9eabb+rNN9/Uxx9/rN/+9rcB+mkBAIKB6YIAgIiWmpoqu92uhIQE5ebmeo8/+eSTGjlypB544AHvsWeffVZ5eXn6/vvv1b9/f0nSMccco4ceesjnOZuv78rPz9d9992na6+9Vn/4wx9kt9uVmpoqi8Xi83oHW7p0qb755htt2bJFeXl5kqS//vWvOvbYY7VixQodf/zxkjxh7LnnnlNycrIk6YorrtDSpUt1//33H90PBgAQMoxkAQCi0po1a/Thhx8qKSnJexs4cKAkz+iRqaCgoMW177//vsaNG6fu3bsrOTlZV1xxhfbt26fq6up2v/66deuUl5fnDViSNHjwYKWlpWndunXeY/n5+d6AJUldu3bVnj17OvReAQDhhZEsAEBUqqys1KRJk/Tggw+2eKxr167e7xMTE30e27p1q84991xdd911uv/++5WRkaFPP/1UV199terr65WQkODXOmNjY33uWywWud1uv74GACC4CFkAgIhnt9vlcrl8jh133HF65ZVXlJ+fr5iY9v/fXWFhodxutx555BFZrZ4JHy+++OJhX+9ggwYN0o4dO7Rjxw7vaNZ3332nsrIyDR48uN31AAAiD9MFAQARLz8/X19++aW2bt2qkpISud1uXX/99SotLdVll12mFStWaNOmTXrnnXc0bdq0Qwakfv36qaGhQU888YQ2b96sv/3tb96GGM1fr7KyUkuXLlVJSUmr0wjHjx+voUOH6vLLL9eqVau0fPlyTZkyRaeeeqpGjRrl958BACB8ELIAABHvV7/6lWw2mwYPHqzs7Gxt375d3bp102effSaXy6UJEyZo6NChuummm5SWluYdoWrN8OHD9eijj+rBBx/UkCFD9I9//EPz58/3OWfs2LG69tprNXnyZGVnZ7donCF5pv3961//Unp6uk455RSNHz9effr00eLFi/3+/gEA4cViGIYR6iIAAAAAIFowkgUAAAAAfkTIAgAAAAA/ImQBAAAAgB8RsgAAAADAjwhZAAAAAOBHhCwAAAAA8CNCFgAAAAD4ESELAAAAAPyIkAUAAAAAfkTIAgAAAAA/ImQBAAAAgB/9f5DZL6qSVhHlAAAAAElFTkSuQmCC", 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" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "import matplotlib.pyplot as plt\n", - "\n", - "cost_list = [term[0] for term in result]\n", - "\n", - "plt.figure(figsize=(10, 6))\n", - "\n", - "plt.plot(range(len(cost_list)), cost_list)\n", - "\n", - "plt.title(\"Cost function convergence\")\n", - "plt.xlabel(\"Iteration\")\n", - "plt.ylabel(\"Cost function value\")\n", - "plt.show()" - ] - }, - { - "cell_type": "markdown", - "id": "18", - "metadata": {}, - "source": [ - "When this is not necessary, it is possible to print only the final results:" - ] - }, - { - "cell_type": "code", - "execution_count": 5, - "id": "19", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Optimal energy: -0.61572265625\n", - "Optimal parameters: {'angles': [2.1377203480076377, 0.004060541282730399, -0.3165621830160506]}\n" - ] - } - ], - "source": [ - "optimal_energy = result[-1][0]\n", - "optimal_parameters = result[-1][1]\n", - "\n", - "print(f\"Optimal energy: {optimal_energy}\")\n", - "print(f\"Optimal parameters: {optimal_parameters}\")" - ] - }, - { - "cell_type": "markdown", - "id": "20", - "metadata": {}, - "source": [ - "The VQE algorithm outputs these key results:\n", - "\n", - "- **Optimal energy**: The lowest energy found for the Hamiltonian, representing the ground state energy (minimal eigenvalue).\n", - "- **Optimal parameters**: The parameters of the quantum program that achieve the optimal energy, corresponding to rotation angles in the U-gate.\n", - "- **Eigenstate**: The quantum state associated with the optimal energy, given as probability amplitudes for the basis states." - ] - }, - { - "cell_type": "markdown", - "id": "21", - "metadata": {}, - "source": [ - "### Summary and Exercise " - ] - }, - { - "cell_type": "markdown", - "id": "22", - "metadata": {}, - "source": [ - "You designed a parameterized quantum circuit capable of capturing a simple Hamiltonian. You initialized an `ExecutionSession` and used `minimize` to execute it, visualizing the results.\n" - ] - }, - { - "cell_type": "markdown", - "id": "23", - "metadata": {}, - "source": [ - "
\n", - "Exercise - Two Qubits VQE\n", - "\n", - "Now, practice the implementation of a similar case to the previous example, but this time for two qubits, following the Hamiltonian:\n", - "\n", - "$$ H = \\frac{1}{2}I \\otimes I + \\frac{1}{2}Z \\otimes Z - X \\otimes X $$\n", - "\n", - "**Use the last example to implement and execute VQE for this Hamiltonian.**\n", - "\n", - "Code skeleton:\n", - "\n", - "```python\n", - "HAMILTONIAN = QConstant(\"HAMILTONIAN\", List[PauliTerm], [...]) #TODO: Complete Hamiltonian\n", - "\n", - "@qfunc\n", - "def main(...) -> None:\n", - " #TODO: Complete the function according to the instructions, choosing simple ansatz.\n", - "\n", - "qprog = synthesize(synthesize)\n", - "show(qprog)\n", - "\n", - "with ExecutionSession(qprog_1) as es:\n", - " result = es.minimize(\n", - " cost_function=HAMILTONIAN,\n", - " initial_params={\"params\": [0.0] * n_params},\n", - " max_iteration=200,\n", - " )\n", - "\n", - "\n", - "```\n", - "
" - ] - }, - { - "cell_type": "markdown", - "id": "24", - "metadata": {}, - "source": [ - "### Read More " - ] - }, - { - "cell_type": "markdown", - "id": "25", - "metadata": {}, - "source": [ - "Further reading from the reference manual:\n", - " - [Execution Primitives](https://docs.classiq.io/latest/user-guide/execution/ExecutionSession/)" - ] - }, - { - "cell_type": "markdown", - "id": "26", - "metadata": {}, - "source": [ - "## Using the PyTorch Integration" - ] - }, - { - "cell_type": "markdown", - "id": "27", - "metadata": {}, - "source": [ - "Classiq integrates with PyTorch, enabling the seamless development of quantum machine learning and hybrid classical quantum machine learning models. This integration leverages PyTorch's powerful machine learning capabilities alongside quantum computing." - ] - }, - { - "cell_type": "markdown", - "id": "28", - "metadata": {}, - "source": [ - "
\n", - "Note on PyTorch Installation:\n", - "\n", - "To properly install and run PyTorch locally, check [this page](https://pytorch.org/get-started/locally/).\n", - "\n", - "
\n" - ] - }, - { - "cell_type": "markdown", - "id": "29", - "metadata": {}, - "source": [ - "### Workflow" - ] - }, - { - "cell_type": "markdown", - "id": "30", - "metadata": {}, - "source": [ - "1. **Defining the Model**\n", - " - **1.1**: Define the quantum model and synthesize it into a quantum program.\n", - " - **1.2**: Define the execute and post-process callables.\n", - " - **1.3**: Create a `torch.nn.Module` network.\n", - "2. **Choosing the Dataset, Loss Function, and Optimizer**\n", - "3. **Training the Model**\n", - "4. **Testing the Model**\n" - ] - }, - { - "cell_type": "markdown", - "id": "31", - "metadata": {}, - "source": [ - "If you are not familiar with PyTorch, read the following documentation:\n", - "\n", - "
\n", - "PyTorch Documentation\n", - "\n", - "- [Creating Models](https://pytorch.org/tutorials/beginner/basics/quickstart_tutorial.html#creating-models)\n", - "- [Building Neural Networks](https://pytorch.org/tutorials/beginner/basics/buildmodel_tutorial.html)\n", - "- [Optimizing Model Parameters](https://pytorch.org/tutorials/beginner/basics/quickstart_tutorial.html#optimizing-the-model-parameters)\n", - "- [Tensors](https://pytorch.org/tutorials/beginner/basics/tensorqs_tutorial.html)\n", - "- [Datasets and DataLoaders](https://pytorch.org/tutorials/beginner/basics/data_tutorial.html)\n", - "\n", - "
\n" - ] - }, - { - "cell_type": "markdown", - "id": "32", - "metadata": {}, - "source": [ - "### Example - Demonstrate PyTorch Integration with Classiq " - ] - }, - { - "cell_type": "markdown", - "id": "33", - "metadata": {}, - "source": [ - "This example demonstrates PyTorch integration using a simple parameterized quantum model.\n", - "\n", - "It utilizes one input from the user and one weight, while using one qubit in the model. The goal of the learning process is to determine the correct angle for an RX gate to perform a \"NOT\" operation. (Spoiler alert: The correct answer is $\\pi$.)\n" - ] - }, - { - "cell_type": "markdown", - "id": "34", - "metadata": {}, - "source": [ - "The dataset `DATALOADER_NOT` is used, as defined [here](https://docs.classiq.io/latest/user-guide/applications/qml/qnn/datasets/). \n", - "`DatasetXor` is also available from the link for further practice." - ] - }, - { - "cell_type": "code", - "execution_count": 7, - "id": "35", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "--> Data for training:\n", - "tensor([[3.1416],\n", - " [0.0000]])\n", - "--> Corresponding labels:\n", - "tensor([1., 0.])\n" - ] - } - ], - "source": [ - "from classiq import *\n", - "from classiq.applications.qnn.datasets import DATALOADER_NOT\n", - "\n", - "for data, label in DATALOADER_NOT:\n", - " print(f\"--> Data for training:\\n{data}\")\n", - " print(f\"--> Corresponding labels:\\n{label}\")" - ] - }, - { - "cell_type": "markdown", - "id": "36", - "metadata": {}, - "source": [ - "This dataset contains two items. The first item indicates no rotation (`0.0000`) and is labeled as 0, indicating the state $|0\\rangle$. The second item indicates a rotation of `3.1416` and is labeled as 1, indicating the state $|1\\rangle$." - ] - }, - { - "cell_type": "markdown", - "id": "37", - "metadata": {}, - "source": [ - "Read an explanation on creating PyTorch datasets here: \n", - "- [Creating a custom dataset for your files](https://pytorch.org/tutorials/beginner/basics/data_tutorial.html#creating-a-custom-dataset-for-your-files)\n", - "- [Writing custom datasets, dataLoaders, and transforms](https://pytorch.org/tutorials/beginner/data_loading_tutorial.html)" - ] - }, - { - "cell_type": "markdown", - "id": "38", - "metadata": {}, - "source": [ - "#### Step 1.1 - Define the Quantum Model and Synthesize It into a Quantum Program\n", - "" - ] - }, - { - "cell_type": "markdown", - "id": "39", - "metadata": {}, - "source": [ - "The first part of the parameterized quantum model has an encoding section, which loads input data ($|0\\rangle$ or $|1\\rangle$) into the parameterized quantum model:\n" - ] - }, - { - "cell_type": "code", - "execution_count": 8, - "id": "40", - "metadata": {}, - "outputs": [], - "source": [ - "@qfunc\n", - "def encoding(theta: CReal, q: QArray) -> None:\n", - " RX(theta=theta, target=q[0])" - ] - }, - { - "cell_type": "markdown", - "id": "41", - "metadata": {}, - "source": [ - "The second part is the `mixing` function, which includes an adjustable parameter for training the RX gate to act later as a NOT gate:" - ] - }, - { - "cell_type": "code", - "execution_count": 9, - "id": "42", - "metadata": {}, - "outputs": [], - "source": [ - "@qfunc\n", - "def mixing(theta: CReal, q: QArray) -> None:\n", - " RX(theta=theta, target=q[0])" - ] - }, - { - "cell_type": "markdown", - "id": "43", - "metadata": {}, - "source": [ - "Combining the two functions into the `main` function:" - ] - }, - { - "cell_type": "code", - "execution_count": 10, - "id": "44", - "metadata": {}, - "outputs": [], - "source": [ - "@qfunc\n", - "def main(input_0: CReal, weight_0: CReal, res: Output[QArray]) -> None:\n", - " allocate(1, res)\n", - " encoding(theta=input_0, q=res) # Loading input\n", - " mixing(theta=weight_0, q=res) # Adjustable parameter" - ] - }, - { - "cell_type": "markdown", - "id": "45", - "metadata": {}, - "source": [ - "Finally, create a model, synthesize it, and display it in the IDE:" - ] - }, - { - "cell_type": "code", - "execution_count": 11, - "id": "46", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Quantum program link: https://platform.classiq.io/circuit/2zPLS8EIKI59yhuhNxg7NFlKTRn\n" - ] - } - ], - "source": [ - "qprog_2 = synthesize(main)\n", - "show(qprog_2)" - ] - }, - { - "cell_type": "markdown", - "id": "47", - "metadata": {}, - "source": [ - "#### Step 1.2 - Define the Execute and Postprocess Callables" - ] - }, - { - "cell_type": "markdown", - "id": "48", - "metadata": {}, - "source": [ - "Before using the quantum layer (QLayer), define the `execute` and `post-processing` functions. These functions are essential for integrating the quantum layer in a PyTorch neural network, as classical layers require classical data as input. This means that only after executing the QLayer (the ansatz) and post-processing the results the data can be further used in other layers of the neural network or be output." - ] - }, - { - "cell_type": "markdown", - "id": "49", - "metadata": {}, - "source": [ - "The `execute` function is straightforward. It takes the quantum program (here, the QLayer) and its parameters, and executes it:" - ] - }, - { - "cell_type": "code", - "execution_count": 12, - "id": "50", - "metadata": {}, - "outputs": [ - { - "name": "stderr", - "output_type": "stream", - "text": [ - "gio: https://platform.classiq.io/circuit/2zPLS8EIKI59yhuhNxg7NFlKTRn?login=True&version=0.85.0: Operation not supported\n" - ] - } - ], - "source": [ - "from classiq.applications.qnn.types import (\n", - " MultipleArguments,\n", - " ResultsCollection,\n", - " SavedResult,\n", - ")\n", - "\n", - "\n", - "def execute(\n", - " quantum_program: QuantumProgram, arguments: MultipleArguments\n", - ") -> ResultsCollection:\n", - " return execute_qnn(quantum_program, arguments)" - ] - }, - { - "cell_type": "markdown", - "id": "51", - "metadata": {}, - "source": [ - "In general, the `post_process` function is needed to prepare the execution results for output or for loss calculation during the training phase.\n", - "\n", - "In this specific example, it returns the probability of measuring $|0\\rangle$. This function assumes that only the differentiation between the single state $|0\\rangle$ and all other states is relevant. If a different differentiation is needed, modify this function accordingly." - ] - }, - { - "cell_type": "code", - "execution_count": 13, - "id": "52", - "metadata": {}, - "outputs": [], - "source": [ - "import torch\n", - "\n", - "\n", - "def post_process(result: SavedResult) -> torch.Tensor:\n", - " \"\"\"\n", - " Take in a `SavedResult` with `ExecutionDetails` value type, and return the\n", - " probability of measuring |0> which equals the amount of `|0>` measurements\n", - " divided by the total number of measurements.\n", - " \"\"\"\n", - " counts: dict = result.value.counts\n", - " # The probability of measuring |0>\n", - " p_zero: float = counts.get(\"0\", 0.0) / sum(counts.values())\n", - " return torch.tensor(p_zero)" - ] - }, - { - "cell_type": "markdown", - "id": "53", - "metadata": {}, - "source": [ - "Using these functions allows QLayers and PyTorch layers to be properly integrated into the same neural network." - ] - }, - { - "cell_type": "markdown", - "id": "54", - "metadata": {}, - "source": [ - "#### Step 1.3 - Create a torch.nn.Module Network" - ] - }, - { - "cell_type": "markdown", - "id": "55", - "metadata": {}, - "source": [ - "Define the `torch.nn.Module` class with a single `QLayer` as follows:" - ] - }, - { - "cell_type": "code", - "execution_count": 14, - "id": "56", - "metadata": {}, - "outputs": [], - "source": [ - "from classiq.applications.qnn import QLayer\n", - "\n", - "\n", - "class Net(torch.nn.Module):\n", - " def __init__(self, *args, **kwargs) -> None:\n", - " super().__init__()\n", - " self.qlayer = QLayer(\n", - " qprog_2, # the quantum program, the result of `synthesize()`\n", - " execute, # a callable that takes\n", - " # - a quantum program\n", - " # - parameters to that program (a tuple of dictionaries)\n", - " # and returns a `ResultsCollection`\n", - " post_process, # a callable that takes\n", - " # - a single `SavedResult`\n", - " # and returns a `torch.Tensor`\n", - " *args,\n", - " **kwargs\n", - " )\n", - "\n", - " def forward(self, x: torch.Tensor) -> torch.Tensor:\n", - " x = self.qlayer(x)\n", - " return x\n", - "\n", - "\n", - "model = Net()" - ] - }, - { - "cell_type": "markdown", - "id": "57", - "metadata": {}, - "source": [ - "In `self.qlayer = QLayer(...)`, define the only layer in the neural network as a single QLayer. Specify the previously defined `quantum_program`, `execute`, and `post_process` as arguments for the layer. Finally, create the neural network and assign it to the variable `model`." - ] - }, - { - "cell_type": "markdown", - "id": "58", - "metadata": {}, - "source": [ - "#### Step 2 - Choose a Dataset, Loss Function, and Optimizer" - ] - }, - { - "cell_type": "markdown", - "id": "59", - "metadata": {}, - "source": [ - "For the loss function and optimizer, use [L1Loss](https://pytorch.org/docs/stable/generated/torch.nn.L1Loss.html) and [SGD](https://pytorch.org/docs/stable/generated/torch.optim.SGD.html), respectively." - ] - }, - { - "cell_type": "code", - "execution_count": 15, - "id": "60", - "metadata": {}, - "outputs": [], - "source": [ - "import torch.nn as nn\n", - "import torch.optim as optim\n", - "\n", - "_LEARNING_RATE = 1\n", - "\n", - "# choosing the data\n", - "data_loader = DATALOADER_NOT\n", - "\n", - "# choosing the loss function\n", - "loss_func = nn.L1Loss() # Mean Absolute Error (MAE)\n", - "\n", - "# choosing the optimizer\n", - "optimizer = optim.SGD(model.parameters(), lr=_LEARNING_RATE)" - ] - }, - { - "cell_type": "markdown", - "id": "61", - "metadata": {}, - "source": [ - "
\n", - "Available Optimization Algorithms and Loss Functions\n", - "\n", - "For details of the optimization algorithms and a comprehensive list of loss functions in PyTorch, refer to the official documentation:\n", - "\n", - "- [Optimization Algorithms](https://pytorch.org/docs/stable/optim.html#algorithms)\n", - "- [Loss Functions](https://pytorch.org/docs/stable/nn.html#loss-functions)\n", - "\n", - "
\n" - ] - }, - { - "cell_type": "markdown", - "id": "62", - "metadata": {}, - "source": [ - "#### Step 3 - Train and Evaluate " - ] - }, - { - "cell_type": "markdown", - "id": "63", - "metadata": {}, - "source": [ - "Import `DataLoader`:" - ] - }, - { - "cell_type": "code", - "execution_count": 16, - "id": "64", - "metadata": {}, - "outputs": [], - "source": [ - "from torch.utils.data import DataLoader" - ] - }, - { - "cell_type": "markdown", - "id": "65", - "metadata": {}, - "source": [ - "A `DataLoader` in PyTorch efficiently iterates over datasets, handling batching, shuffling, and parallel data loading. It streamlines the process of training and evaluating models by managing data efficiently." - ] - }, - { - "cell_type": "markdown", - "id": "66", - "metadata": {}, - "source": [ - "Now you are ready to define the training function. \\\n", - "This simple example follows a loop similar to that recommended by PyTorch [here](https://pytorch.org/tutorials/beginner/blitz/neural_networks_tutorial.html#update-the-weights).\n" - ] - }, - { - "cell_type": "code", - "execution_count": 17, - "id": "67", - "metadata": {}, - "outputs": [], - "source": [ - "def train(\n", - " model: nn.Module,\n", - " data_loader: DataLoader,\n", - " loss_func: nn.modules.loss._Loss,\n", - " optimizer: optim.Optimizer,\n", - " epoch: int = 5, # About 40 epochs needed for full training\n", - ") -> None:\n", - " for index in range(epoch):\n", - " print(index, model.qlayer.weight)\n", - " for data, label in data_loader:\n", - " optimizer.zero_grad()\n", - "\n", - " output = model(data)\n", - "\n", - " loss = loss_func(output, label)\n", - " loss.backward()\n", - " optimizer.step()" - ] - }, - { - "cell_type": "markdown", - "id": "68", - "metadata": {}, - "source": [ - "Here, trained parameters are loaded for demonstration, and only one epoch is performed.\\\n", - "You may comment on the following cell, change the number of epochs above, and expect about 40 epochs for full training for non-trained parameters." - ] - }, - { - "cell_type": "code", - "execution_count": 18, - "id": "69", - "metadata": {}, - "outputs": [], - "source": [ - "with torch.no_grad():\n", - " model.qlayer.weight.copy_(\n", - " torch.tensor([3])\n", - " ) # The value from the last step of the training" - ] - }, - { - "cell_type": "code", - "execution_count": 19, - "id": "70", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "0 Parameter containing:\n", - "tensor([3.], requires_grad=True)\n", - "1 Parameter containing:\n", - "tensor([3.0488], requires_grad=True)\n", - "2 Parameter containing:\n", - "tensor([3.1465], requires_grad=True)\n", - "3 Parameter containing:\n", - "tensor([3.1465], requires_grad=True)\n", - "4 Parameter containing:\n", - "tensor([3.1465], requires_grad=True)\n" - ] + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Quantum Machine Learning with Classiq" + ], + "id": "0" + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Welcome to the \"Quantum Machine Learning with Classiq\" tutorial. This guide is designed for users already familiar with the fundamentals of the Classiq platform and Quantum Machine Learning (QML) concepts. The aim is to showcase how to implement QML using Classiq. It covers three main methods to implement QML with Classiq:\n", + "\n", + "1. **Using the VQE Primitive**\n", + "2. **Using the PyTorch Integration**\n", + "3. **Using the QSVM Built-in App**\n", + "\n", + "Each section briefly explains the method, followed by an illustrative example that demonstrates the integration. These examples are intended to be straightforward to help you get started quickly." + ], + "id": "1" + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## In This Tutorial\n", + "\n", + "1. [Using the VQE Primitive](#Using-the-VQE-Primitive)\n", + " * [Example Using Classiq](#Example-Using-Classiq)\n", + " * [Summary and Exercise](#summary-exercise-vqe)\n", + " * [Read More](#read-more-vqe)\n", + "2. [Using the PyTorch Integration](#Using-the-PyTorch-Integration)\n", + " * [Workflow](#Workflow)\n", + " * [Example - Demonstrate PyTorch Integration with Classiq](#example-code-demonstrating-pytorch-integration-with-classiq)\n", + " * [Step 1.1 - Define the Quantum Model and Synthesize It into a Quantum Program](#step-11---define-the-quantum-model-and-synthesize-it-into-a-quantum-program)\n", + " * [Step 1.2 - Define the Execute and Post-process Callables](#step-12---define-the-execute-and-post-process-callables)\n", + " * [Step 1.3 - Create a torch.nn.Module Network](#step-13---create-a-torchnnmodule-network)\n", + " * [Step 2 - Choose a Dataset, Loss Function, and Optimizer](#step-2---choose-a-dataset-loss-function-and-optimizer)\n", + " * [Step 3 - Train and Evaluate](#step-3-train)\n", + " * [Summary and Exercise](#summary-exercise-pytorch)\n", + " * [Read More](#read-more-pytorch)\n", + "3. [Using QSVM Primitive](#Using-QSVM-Primitive)\n" + ], + "id": "2" + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Using the VQE Primitive" + ], + "id": "3" + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The Variational Quantum Eigensolver (VQE) is an algorithm for finding the ground state energy of a Hamiltonian operator, often described by Pauli operators or in the equivalent matrix form. The VQE was proposed in 2014 [[1](#eigenvaluesolver)]. \n", + "\n", + "The algorithm follows these steps:\n", + "\n", + "1. **Create a Parameterized Quantum Model**: Design a quantum model, also known as an ansatz, that captures the problem.\n", + "2. **Synthesize, Execute, and Estimate Expectation Values**: Synthesize the quantum model into a quantum program. Run the quantum program, then measure and calculate the expected value of the Hamiltonian based on this generated program.\n", + "3. **Optimize Parameters**: Use a classical optimizer to adjust the quantum program's parameters for better results.\n", + "4. **Repeat**: Continue this process until the algorithm converges to a solution or reaches a specified number of iterations.\n", + "\n", + "For more details, refer to this review article [[2](#vqa)] and the corresponding preprint [[3](#preprint)]." + ], + "id": "4" + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Example Using Classiq" + ], + "id": "5" + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Start with this example, creating a VQE algorithm that estimates the minimal eigenvalue of the following 2x2 Hamiltonian:\n", + "\n", + "\\begin{equation}\n", + "H = \\frac{1}{2}I + \\frac{1}{2}Z - X = \\begin{bmatrix} 1 & -1 \\\\ -1 & 0 \\end{bmatrix}\n", + "\\end{equation}" + ], + "id": "6" + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Define the Hamiltonian using `Pauli` terms:" + ], + "id": "7" + }, + { + "cell_type": "code", + "metadata": {}, + "source": [ + "!pip install -qq -U \"classiq[qml]\"" + ], + "execution_count": null, + "outputs": [], + "id": "8" + }, + { + "cell_type": "code", + "metadata": {}, + "source": [ + "from typing import List\n", + "\n", + "from classiq import *\n", + "\n", + "HAMILTONIAN = 0.5 * Pauli.I(0) + 0.5 * Pauli.Z(0) + (-1) * Pauli.X(0)" + ], + "execution_count": 1, + "outputs": [], + "id": "9" + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "For a single qubit problem, to capture any rotation on the Bloch sphere, use the U-gate (also known as the U3-gate). This includes the state with the minimal energy with respect to the Hamiltonian." + ], + "id": "10" + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "
\n", + " NOTE on U-gate\n", + " \n", + "The single-qubit gate applies phase and rotation with three Euler angles.\n", + "\n", + "Matrix representation:\n", + "\n", + "\\begin{equation}\n", + "U(\\gamma,\\phi,\\theta,\\lambda) = e^{i\\gamma}\\begin{pmatrix}\n", + "\\cos(\\frac{\\theta}{2}) & -e^{i\\lambda}\\sin(\\frac{\\theta}{2}) \\\\\n", + "e^{i\\phi}\\sin(\\frac{\\theta}{2}) & e^{i(\\phi+\\lambda)}\\cos(\\frac{\\theta}{2}) \\\\\n", + "\\end{pmatrix}\n", + "\\end{equation}\n", + "\n", + "Parameters:\n", + "\n", + "- `theta`: `CReal`\n", + "- `phi`: `CReal`\n", + "- `lam`: `CReal`\n", + "- `gam`: `CReal`\n", + "- `target`: `QBit`\n", + "\n", + "
" + ], + "id": "11" + }, + { + "cell_type": "code", + "metadata": {}, + "source": [ + "@qfunc\n", + "def main(q: Output[QBit], angles: CArray[CReal, 3]) -> None:\n", + " allocate(q)\n", + " U(angles[0], angles[1], angles[2], 0, q)" + ], + "execution_count": 2, + "outputs": [], + "id": "12" + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "To seamlessly harness the power of VQE, synthesize the ansatz `main`, and use the `minimize` attribute from `ExecutionSession` to optimize it." + ], + "id": "13" + }, + { + "cell_type": "code", + "metadata": {}, + "source": [ + "qprog_1 = synthesize(main)\n", + "\n", + "\n", + "with ExecutionSession(qprog_1) as es:\n", + " result = es.minimize(\n", + " cost_function=HAMILTONIAN,\n", + " initial_params={\"angles\": [0.0] * 3},\n", + " max_iteration=200,\n", + " )" + ], + "execution_count": 3, + "outputs": [], + "id": "14" + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "
\n", + "Description of ExecutionSession Minimize Parameters\n", + "\n", + "Configure the `minimize` function in the `ExecutionSession` workflow with these parameters:\n", + "\n", + "- **cost_function**: The cost function to minimize, it can be either a quantum a quantum cost function specified by a Hamiltonian or a classical function that is represented as a callable and returns a Qmod expression.\n", + "\n", + "- **initial_params**: Initial parameters for the optimization routine. It accepts only a single parameter and should be formatted as a dict in the form {\"parameter\": list}.\n", + "\n", + "- **max_iteration**: The maximum number of iterations for the optimizer.\n", + "\n", + "- **quantile**: The quantile-based cutoff for which outcomes to consider when estimating the cost function.\n", + "\n", + "\n", + "The output will be a list of dicts, containing the `float` values of the cost function and its respective parameters.\n", + "
\n" + ], + "id": "15" + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "At this stage, it is possible to visualize the results of the quantum algorithm. For instance, a graph of Energy versus Iterations can be plotted to illustrate the convergence behavior of the algorithm." + ], + "id": "16" + }, + { + "cell_type": "code", + "metadata": {}, + "source": [ + "import matplotlib.pyplot as plt\n", + "\n", + "cost_list = [term[0] for term in result]\n", + "\n", + "plt.figure(figsize=(10, 6))\n", + "\n", + "plt.plot(range(len(cost_list)), cost_list)\n", + "\n", + "plt.title(\"Cost function convergence\")\n", + "plt.xlabel(\"Iteration\")\n", + "plt.ylabel(\"Cost function value\")\n", + "plt.show()" + ], + "execution_count": 4, + "outputs": [ + { + "output_type": "display_data", + "data": { + "image/png": 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++KFGjx6t6dOna/DgwSotLdWqVav0/vvvq7S0tEOvCQB+EaKuhgDQ6X3//ffG9OnTjfz8fMNutxvJycnGSSedZDzxxBNGbW2t97yGhgZj3rx5Ru/evY3Y2FgjLy/PmD17ts85q1atMi677DKjZ8+ehsPhMLp06WKce+65xsqVK31e8/PPPzcKCgoMu91+2HbubbVwNwzDePfdd40hQ4YYdrvdGDBggPH3v/+9zRbu119/fYvre/Xq5dP+2zAMY9u2bcaUKVOM7Oxsw+FwGH369DGuv/56o66uznvOM888Y/Tp08ew2Ww+7dwPbuFuGIZRXFxsTJs2zcjKyjLsdrsxdOhQ4y9/+Uu73+Phfj6mffv2GTNnzjS6d+9u2O12o0ePHsbUqVN9WooHqpZnnnnGkGQkJycbNTU1rdb31VdfGRdeeKGRmZlpOBwOo1evXsYll1xiLF261HuO+dnt3bu3xfWNjY3G3XffbeTm5hrx8fHGGWecYaxbt87IzMw0rr32Wp9zKyoqjNmzZxv9+vUz7Ha7kZWVZYwdO9Z4+OGHjfr6+iN6n2vXrjUuuOACIy0tzYiLizMGDBhg3H333T7nFBcXG9dff72Rl5dnxMbGGrm5uca4ceOMp59+utWfCQAEmsUwwmjlMQAACHtlZWVKT0/XfffdpzvvvDPU5QBA2GFNFgAAaFNNTU2LY+YawdNOOy24xQBAhGBNFgAAaNPixYv13HPP6ZxzzlFSUpI+/fRT/fOf/9SECRN00kknhbo8AAhLhCwAANCmYcOGKSYmRg899JCcTqe3GcZ9990X6tIAIGyxJgsAAAAA/Ig1WQAAAADgR4QsAAAAAPAj1mQdhtvt1q5du5ScnOyz6SIAAACAzsUwDFVUVKhbt26yWtseryJkHcauXbuUl5cX6jIAAAAAhIkdO3aoR48ebT5OyDqM5ORkSZ4fZEpKSoirAQAAABAqTqdTeXl53ozQFkLWYZhTBFNSUghZAAAAAA67jIjGFwAAAADgR4QsAAAAAPAjQhYAAAAA+BEhCwAAAAD8iJAFAAAAAH5EyAIAAAAAPyJkAQAAAIAfEbIAAAAAwI8IWQAAAADgR4QsAAAAAPAjQhYAAAAA+BEhCwAAAAD8iJAFAAAAAH5EyAIAAAAAP4qokPXJJ59o0qRJ6tatmywWi15//fXDXvPRRx/puOOOk8PhUL9+/fTcc88FvE4AAAAAnVdEhayqqioNHz5cTz31VLvO37Jli37605/q9NNP1+rVq3XTTTfpmmuu0TvvvBPgSgEAAAB0VjGhLqAjzj77bJ199tntPn/hwoXq3bu3HnnkEUnSoEGD9Omnn+r3v/+9Jk6c2Oo1dXV1qqur8953Op1HV7Qf/feHvdpXWa+Jx+Yq3m4LdTkAAAAAWhFRI1kdtWzZMo0fP97n2MSJE7Vs2bI2r5k/f75SU1O9t7y8vECX2W6/+Mcq3bR4tXaV14S6FAAAAABtiOqQVVRUpJycHJ9jOTk5cjqdqqlpPajMnj1b5eXl3tuOHTuCUWq7ZCU5JEn7KutDXAkAAACAtkTUdMFgcDgccjgcoS6jVZmJdm0pqdK+yrrDnwwAAAAgJKJ6JCs3N1fFxcU+x4qLi5WSkqL4+PgQVXXkMhLtkqR9VYxkAQAAAOEqqkPWmDFjtHTpUp9j7733nsaMGROiio5OJtMFAQAAgLAXUSGrsrJSq1ev1urVqyV5WrSvXr1a27dvl+RZTzVlyhTv+ddee602b96s2267TevXr9cf/vAHvfjii7r55ptDUf5Ry0oyR7KYLggAAACEq4gKWStXrtTIkSM1cuRISdKsWbM0cuRI3XPPPZKk3bt3ewOXJPXu3VtvvfWW3nvvPQ0fPlyPPPKI/vSnP7XZvj3cZZrTBRnJAgAAAMJWRDW+OO2002QYRpuPP/fcc61e89VXXwWwquDJMKcLMpIFAAAAhK2IGsnq7LIYyQIAAADCHiErgngbX9BdEAAAAAhbhKwIktnU+GJ/db1c7ranTQIAAAAIHUJWBElPsMtikQzDE7QAAAAAhB9CVgSxWS1KT2BdFgAAABDOCFkR5kAbdzoMAgAAAOGIkBVhzHVZJTS/AAAAAMISISvCZCZ6OgyWMpIFAAAAhCVCVoQxR7Jo4w4AAACEJ0JWhDFHskpofAEAAACEJUJWhPGOZDFdEAAAAAhLhKwIY3YXLGW6IAAAABCWCFkRJjPJM12QNVkAAABAeCJkRRhvC3emCwIAAABhiZAVYbKaGl9U1DaqrtEV4moAAAAAHIyQFWFS4mMUY7VIkvZXNYS4GgAAAAAHI2RFGIvFooxEpgwCAAAA4YqQFYFofgEAAACEL0JWBMpirywAAAAgbBGyIlAGe2UBAAAAYYuQFYEymzoMllQSsgAAAIBwQ8iKQJlMFwQAAADCFiErAnnXZDFdEAAAAAg7hKwIlJFId0EAAAAgXBGyIhDTBQEAAIDwRciKQFnmSBaNLwAAAICwQ8iKQOZIVk2DS9X1jSGuBgAAAEBzhKwIlGC3yRHj+egYzQIAAADCCyErAlksFmUl0fwCAAAACEeErAhF8wsAAAAgPBGyIlRmohmyGMkCAAAAwgkhK0KxVxYAAAAQnghZESqL6YIAAABAWCJkRSjvmixGsgAAAICwQsiKUJlN0wVLGMkCAAAAwgohK0JlNI1klTKSBQAAAIQVQlaEyjIbX9BdEAAAAAgrhKwIdWBNVp0MwwhxNQAAAABMhKwIldG0T1aDy5CztjHE1QAAAAAwEbIiVFysTUmOGEmsywIAAADCCSErgmWyVxYAAAAQdiIuZD311FPKz89XXFycRo8ereXLlx/y/AULFmjAgAGKj49XXl6ebr75ZtXW1gap2sDKbJoyWELzCwAAACBsRFTIWrx4sWbNmqU5c+Zo1apVGj58uCZOnKg9e/a0ev6iRYt0++23a86cOVq3bp3+/Oc/a/HixbrjjjuCXHlgZJgdBqsYyQIAAADCRUSFrEcffVTTp0/XtGnTNHjwYC1cuFAJCQl69tlnWz3/888/10knnaSf/exnys/P14QJE3TZZZcdcvSrrq5OTqfT5xaussy9shjJAgAAAMJGxISs+vp6FRYWavz48d5jVqtV48eP17Jly1q9ZuzYsSosLPSGqs2bN+vtt9/WOeec0+brzJ8/X6mpqd5bXl6ef9+IHx1o407IAgAAAMJFTKgLaK+SkhK5XC7l5OT4HM/JydH69etbveZnP/uZSkpK9JOf/ESGYaixsVHXXnvtIacLzp49W7NmzfLedzqdYRu0MpumC5bQ+AIAAAAIGxEzknUkPvroIz3wwAP6wx/+oFWrVunVV1/VW2+9pXvvvbfNaxwOh1JSUnxu4epAd0FGsgAAAIBwETEjWVlZWbLZbCouLvY5XlxcrNzc3Favufvuu3XFFVfommuukSQNHTpUVVVVmjFjhu68805ZrZGdMc2RLPbJAgAAAMJHxKQMu92ugoICLV261HvM7XZr6dKlGjNmTKvXVFdXtwhSNptNkmQYRuCKDZIDa7KYLggAAACEi4gZyZKkWbNmaerUqRo1apROOOEELViwQFVVVZo2bZokacqUKerevbvmz58vSZo0aZIeffRRjRw5UqNHj9bGjRt19913a9KkSd6wFcnMkFVaVS+X25DNaglxRQAAAAAiKmRNnjxZe/fu1T333KOioiKNGDFCS5Ys8TbD2L59u8/I1V133SWLxaK77rpLO3fuVHZ2tiZNmqT7778/VG/Br9ITPCHLbUhl1fXKTHKEuCIAAAAAFiMa5s0FkNPpVGpqqsrLy8OyCcaI37yrsuoGvXfzKTomJznU5QAAAABRq73ZIGLWZKF1mYme0awSOgwCAAAAYYGQFeHMKYI0vwAAAADCAyErwpkjWeyVBQAAAIQHQlaEO9DGnZAFAAAAhANCVoQzNyTeV8l0QQAAACAcELIiXFYS0wUBAACAcELIinAZiTS+AAAAAMIJISvCsSYLAAAACC+ErAjHdEEAAAAgvBCyIpzZ+KK8pkH1je4QVwMAAACAkBXhUuNjZbNaJEn7qxnNAgAAAEKNkBXhrFaL0hOYMggAAACEC0JWFPCuy6LDIAAAABByhKwokEnzCwAAACBsELKigLlXVkklI1kAAABAqBGyokBmomckq5S9sgAAAICQI2RFAfbKAgAAAMIHISsKZCZ5pgvS+AIAAAAIPUJWFMhomi5YwkgWAAAAEHKErChgThdkTRYAAAAQeoSsKJDZ1F1wH90FAQAAgJAjZEUBc5+sqnqXaupdIa4GAAAA6NwIWVEgyREju83zUdL8AgAAAAgtQlYUsFgs3tEs1mUBAAAAoUXIihKZ7JUFAAAAhAVCVpQwm1+U0PwCAAAACClCVpTITGS6IAAAABAOCFlRwjtdkJAFAAAAhBQhK0pkJjFdEAAAAAgHhKwoYU4XpPEFAAAAEFqErChBC3cAAAAgPBCyooTZXXAf0wUBAACAkCJkRQlzJKukql6GYYS4GgAAAKDzImRFCXMkq77Rrcq6xhBXAwAAAHRehKwoEW+3KcFuk8S6LAAAACCUCFlRxDtlkA6DAAAAQMgQsqIIzS8AAACA0CNkRZGsppGsfUwXBAAAAEKGkBVFMhLZKwsAAAAINUJWFMlM8kwXLGG6IAAAABAyhKwoktk0krWPxhcAAABAyERcyHrqqaeUn5+vuLg4jR49WsuXLz/k+WVlZbr++uvVtWtXORwO9e/fX2+//XaQqg2urKaRrH1VjGQBAAAAoRIT6gI6YvHixZo1a5YWLlyo0aNHa8GCBZo4caI2bNigLl26tDi/vr5eZ555prp06aKXX35Z3bt317Zt25SWlhb84oMgg5EsAAAAIOQiKmQ9+uijmj59uqZNmyZJWrhwod566y09++yzuv3221uc/+yzz6q0tFSff/65YmNjJUn5+fnBLDmoMukuCAAAAIRcxEwXrK+vV2FhocaPH+89ZrVaNX78eC1btqzVa/79739rzJgxuv7665WTk6MhQ4bogQcekMvlavN16urq5HQ6fW6RwpwuWFpVL7fbCHE1AAAAQOcUMSGrpKRELpdLOTk5PsdzcnJUVFTU6jWbN2/Wyy+/LJfLpbffflt33323HnnkEd13331tvs78+fOVmprqveXl5fn1fQRSeoJnJMvlNlRe0xDiagAAAIDOKWJC1pFwu93q0qWLnn76aRUUFGjy5Mm68847tXDhwjavmT17tsrLy723HTt2BLHio2OPsSolzjMDlCmDAAAAQGhEzJqsrKws2Ww2FRcX+xwvLi5Wbm5uq9d07dpVsbGxstls3mODBg1SUVGR6uvrZbfbW1zjcDjkcDj8W3wQZSU55Kxt1L7KOvXrkhTqcgAAAIBOJ2JGsux2uwoKCrR06VLvMbfbraVLl2rMmDGtXnPSSSdp48aNcrvd3mPff/+9unbt2mrAigY0vwAAAABCK2JCliTNmjVLzzzzjJ5//nmtW7dO1113naqqqrzdBqdMmaLZs2d7z7/uuutUWlqqG2+8Ud9//73eeustPfDAA7r++utD9RYC7kAbd/bKAgAAAEIhYqYLStLkyZO1d+9e3XPPPSoqKtKIESO0ZMkSbzOM7du3y2o9kBvz8vL0zjvv6Oabb9awYcPUvXt33Xjjjfr1r38dqrcQcJneDYkZyQIAAABCwWIYBr2+D8HpdCo1NVXl5eVKSUkJdTmH9ei7G/T4Bxt1xYm9dO/5Q0JdDgAAABA12psNImq6IA7vwEgW0wUBAACAUCBkRRlzTVZJJdMFAQAAgFAgZEUZs7tgKWuyAAAAgJAgZEWZLHO6IN0FAQAAgJAgZEWZzKbpgvurG9Toch/mbAAAAAD+RsiKMmkJdlksnu9Lq5kyCAAAAAQbISvK2KwWZSSwLgsAAAAIFUJWFDKbX+yjwyAAAAAQdISsKJSZ6Gl+UULzCwAAACDoCFlRKIORLAAAACBkCFlRKCuRNVkAAABAqBCyolCmuVdWFdMFAQAAgGAjZEUhs/FFCdMFAQAAgKAjZEUhc0PifTS+AAAAAIKOkBWFzOmCrMkCAAAAgo+QFYUOjGQRsgAAAIBgI2RFIXMkq6KuUbUNrhBXAwAAAHQuhKwolBIXo1ibRRJTBgEAAIBgI2RFIYvFogz2ygIAAABCgpAVpTITPVMGS+gwCAAAAAQVIStKmXtl0fwCAAAACC5CVpTydhisYiQLAAAACCZCVpQyOwzuY00WAAAAEFSErCjFdEEAAAAgNAhZUSqrqfHFPhpfAAAAAEFFyIpSGd41WYxkAQAAAMFEyIpSTBcEAAAAQoOQFaWyvI0v6mQYRoirAQAAADoPQlaUMkeyahvcqq53hbgaAAAAoPMgZEWpBHuM4mI9Hy9TBgEAAIDgIWRFsczEA1MGAQAAAAQHISuKZdH8AgAAAAg6QlYUy0xiJAsAAAAINkJWFDP3yiphJAsAAAAImiMKWZs2bdJdd92lyy67THv27JEk/ec//9G3337r1+JwdMwOg6VsSAwAAAAETYdD1scff6yhQ4fqyy+/1KuvvqrKykpJ0po1azRnzhy/F4gjl2U2vqhkuiAAAAAQLB0OWbfffrvuu+8+vffee7Lb7d7jZ5xxhr744gu/FoejY45k7WMkCwAAAAiaDoesb775RhdccEGL4126dFFJSYlfioJ/sCYLAAAACL4Oh6y0tDTt3r27xfGvvvpK3bt390tR8I+spu6CpXQXBAAAAIKmwyHr0ksv1a9//WsVFRXJYrHI7Xbrs88+069+9StNmTIlEDXiCGU22yfLMIwQVwMAAAB0Dh0OWQ888IAGDhyovLw8VVZWavDgwTrllFM0duxY3XXXXYGoEUfInC7Y6DbkrGkMcTUAAABA59DhkGW32/XMM89o06ZNevPNN/X3v/9d69ev19/+9jfZbLZA1OjjqaeeUn5+vuLi4jR69GgtX768Xde98MILslgsOv/88wNbYBhxxNiU7IiRJJUwZRAAAAAIipgjvbBnz57q2bOnP2s5rMWLF2vWrFlauHChRo8erQULFmjixInasGGDunTp0uZ1W7du1a9+9SudfPLJQaw2PGQm2VVR16jSqnr1zQ51NQAAAED063DIuuqqqw75+LPPPnvExRzOo48+qunTp2vatGmSpIULF+qtt97Ss88+q9tvv73Va1wuly6//HLNmzdP//3vf1VWVhaw+sJRZpJDW/dVs1cWAAAAECQdDln79+/3ud/Q0KC1a9eqrKxMZ5xxht8KO1h9fb0KCws1e/Zs7zGr1arx48dr2bJlbV73m9/8Rl26dNHVV1+t//73v4d9nbq6OtXVHQgkTqfz6AoPsUzauAMAAABB1eGQ9dprr7U45na7dd1116lv375+Kao1JSUlcrlcysnJ8Tmek5Oj9evXt3rNp59+qj//+c9avXp1u19n/vz5mjdv3tGUGlaadxgEAAAAEHgdbnzR6pNYrZo1a5Z+//vf++Pp/KKiokJXXHGFnnnmGWVlZbX7utmzZ6u8vNx727FjRwCrDLzMRPbKAgAAAILpiBtfHGzTpk1qbAxcm/CsrCzZbDYVFxf7HC8uLlZubm6r9WzdulWTJk3yHnO73ZKkmJgYbdiwodWRN4fDIYfD4efqQ8ccySqpYiQLAAAACIYOh6xZs2b53DcMQ7t379Zbb72lqVOn+q2wg9ntdhUUFGjp0qXeNuxut1tLly7VzJkzW5w/cOBAffPNNz7H7rrrLlVUVOixxx5TXl5ewGoNJ5lJnsBI4wsAAAAgODocsr766iuf+1arVdnZ2XrkkUcO23nwaM2aNUtTp07VqFGjdMIJJ2jBggWqqqrydhucMmWKunfvrvnz5ysuLk5DhgzxuT4tLU2SWhyPZmbjC9ZkAQAAAMHR4ZD14YcfBqKOdpk8ebL27t2re+65R0VFRRoxYoSWLFnibYaxfft2Wa1+WWYWNczpgqVMFwQAAACCwmIYhhHqIsKZ0+lUamqqysvLlZKSEupyOmxvRZ2Ov/99WSzSxvvPkc1qCXVJAAAAQERqbzZo10jWyJEjZbG07z/OV61a1b4KERTpCbGyWCTDkPZX1ysrKXqaegAAAADhqF0hy2w0gcgTY7MqLT5W+6sbtK+SkAUAAAAEWrtC1pw5cwJdBwIoM8nhCVlVdZKSQ10OAAAAENXoEtEJ0GEQAAAACJ4Odxd0uVz6/e9/rxdffFHbt29Xfb3vf7iXlpb6rTj4h9lhkL2yAAAAgMDr8EjWvHnz9Oijj2ry5MkqLy/XrFmzdOGFF8pqtWru3LkBKBFHKzPRsw6LNu4AAABA4HU4ZP3jH//QM888o1tuuUUxMTG67LLL9Kc//Un33HOPvvjii0DUiKNkjmSVELIAAACAgOtwyCoqKtLQoUMlSUlJSSovL5cknXvuuXrrrbf8Wx38IrOpoyDTBQEAAIDA63DI6tGjh3bv3i1J6tu3r959911J0ooVK+Rw0B48HNH4AgAAAAieDoesCy64QEuXLpUk3XDDDbr77rt1zDHHaMqUKbrqqqv8XiCOnhmyWJMFAAAABF6Huwv+9re/9X4/efJk9erVS59//rmOOeYYTZo0ya/FwT/M6YIlIZwuWNvgksttKNHR4V85AAAAIKJ0+L94a2trFRcX571/4okn6sQTT/RrUfCvrKbGF87aRtU3umWPCe72aIZh6LJnvtCO0mq9P+tUpSXYg/r6AAAAQDB1+L+2u3TpoqlTp+q9996T2+0ORE3ws5S4WNmsFkmhmTK4s6xGX20vU0llvb7YzD5qAAAAiG4dDlnPP/+8qqurdd5556l79+666aabtHLlykDUBj+xWi3KMJtfVAV/ymDhtv3NvidkAQAAILodUeOLl156ScXFxXrggQf03Xff6cQTT1T//v31m9/8JhA1wg9C2WFw5dYDIWtls8AFAAAARKMjXpyTnJysadOm6d1339XXX3+txMREzZs3z5+1wY+yzL2yQjCStWLrgdGrtTvLVdvgCnoNAAAAQLAccciqra3Viy++qPPPP1/HHXecSktLdeutt/qzNvhRRohGspy1DdpQXCFJSo6LUYPL0JodZUGtAQAAAAimDncXfOedd7Ro0SK9/vrriomJ0f/+7//q3Xff1SmnnBKI+uAnmUnmmqzghqyvtpfJMKSeGQka2j1Vb32zWyu37dfoPplBrQMAAAAIliNak1VTU6O//vWvKioq0v/7f/+PgBUBvNMFg7xX1sqmqYKjeqWroFe6zzEAAAAgGnV4JKu4uFjJycmBqAUBFKrGF2bTi1H5GRraPVWSp9ug223I2tRWHgAAAIgmHR7JImBFJnNNVkkQpws2uNxa3bT+alR+ugZ1TVaC3SZnbaM27q0MWh0AAABAMB1x4wtElsym6YKlQewu+N0up2oaXEqJi1G/7CTF2KwakZcmybfjIAAAABBNCFmdRFZS8KcLmntijcrP8E4NHJWfIUkq3Mp+WQAAAIhOhKxOwhzJqq53qbq+MSivWbjNM1plNryQPA0wJDYlBgAAQPQiZHUSiXab7DGejzsYo1mGYWiF2fSiWcga2TNNVou0vbRae5y1Aa8DAAAACLYOh6yqqirdfffdGjt2rPr166c+ffr43BCeLBaLspqaX5QGofnFjtIa7a2oU6zNouFN67AkKTkuVgNzUyQxmgUAAIDo1OEW7tdcc40+/vhjXXHFFeratassFtpwR4rMJId2lddqXxCaX6xsmio4pHuq4mJtPo+Nyk/Xd7udWrl1v84Z2jXgtQAAAADB1OGQ9Z///EdvvfWWTjrppEDUgwDKbGp+URKE6YKtTRU0FfRK11+XbfMGMQAAACCadHi6YHp6ujIyMgJRCwIsI4gbEptNL8xugs0d33Ts213OoDXhAAAAAIKlwyHr3nvv1T333KPq6upA1IMAygrSXlnl1Q36vtiz2XBBKyNZ3dLi1S01Ti634d2sGAAAAIgWHZ4u+Mgjj2jTpk3KyclRfn6+YmNjfR5ftWqV34qDf2UGaSSrcLtnFKt3VqI32B2sID9Du9bs0sqt+zW2b1ZA6wEAAACCqcMh6/zzzw9AGQgGc6+skgB3F1x5iPVYplG90vXGml10GAQAAEDU6XDImjNnTiDqQBAcGMkK7HRBMziNyj9EyGp67Ktt++VyG7JZ6VIJAACA6NDhkGUqLCzUunXrJEnHHnusRo4c6beiEBhmd8FA7pNV3+jWmqZ1VgW92m6QMjA3RUmOGFXUNWpDUYUGd0sJWE0AAABAMHU4ZO3Zs0eXXnqpPvroI6WlpUmSysrKdPrpp+uFF15Qdna2v2uEn5jTBfdV1sswjIDscbZ2V7nqGt1KT4hV3+zENs+zWS0a2TNN//2hRIXbSglZAAAAiBod7i54ww03qKKiQt9++61KS0tVWlqqtWvXyul06pe//GUgaoSfmNMF611uVdQFpnV6YdN6rIJeGYcNcaOaRrpYlwUAAIBo0uGRrCVLluj999/XoEGDvMcGDx6sp556ShMmTPBrcfCvuFibEu02VdW7tK+yXilxsYe/qINWevfHans9lsk8x2yUAQAAAESDDo9kud3uFm3bJSk2NlZut9svRSFwMgO4V5ZhGN7AdHw7QtaIvDTZrBbtLKvR7vIav9cDAAAAhEKHQ9YZZ5yhG2+8Ubt27fIe27lzp26++WaNGzfOr8XB/8zmFyUB2Ctr675q7auqlz3GqiHdUw97fqIjRoO7etZiMZoFAACAaNHhkPXkk0/K6XQqPz9fffv2Vd++fdW7d285nU498cQTgagRfpSZeKD5hb+t3OqZKjise6ocMbZ2XVPQy5wyWOr3egAAAIBQ6PCarLy8PK1atUrvv/++1q9fL0kaNGiQxo8f7/fi4H+B3CvLuwlxftut2w82Kj9dz32+leYXAAAAiBodHsmSJIvFojPPPFM33HCDbrjhhqAGrKeeekr5+fmKi4vT6NGjtXz58jbPfeaZZ3TyyScrPT1d6enpGj9+/CHP7wzM6YL7ArBXlrfpRa/Dr8cymR0G1+12qjJAHQ8BAACAYGrXSNbjjz+uGTNmKC4uTo8//vghzw1kG/fFixdr1qxZWrhwoUaPHq0FCxZo4sSJ2rBhg7p06dLi/I8++kiXXXaZxo4dq7i4OD344IOaMGGCvv32W3Xv3j1gdYYz715Zfg5ZpVX12rS3StKBKYDtkZsapx7p8fpxf42+2r5fJx/DPmsAAACIbBbDMIzDndS7d2+tXLlSmZmZ6t27d9tPZrFo8+bNfi2wudGjR+v444/Xk08+KcnT6TAvL0833HCDbr/99sNe73K5lJ6erieffFJTpkxp12s6nU6lpqaqvLxcKSmRv2Huv1bv1I0vrNbYvplaNP1Evz3ve98Va/pfV6pflyS9P+vUDl170wtf6fXVu3TjuGN085n9/VYTAAAA4E/tzQbtGsnasmVLq98HU319vQoLCzV79mzvMavVqvHjx2vZsmXteo7q6mo1NDQoI6PtNUN1dXWqqzuwXsnpdB550WEow7smy78jWUcyVdA0Kj9Dr6/epULWZQEAACAKdHhN1m9+8xtVV1e3OF5TU6Pf/OY3fimqNSUlJXK5XMrJyfE5npOTo6KionY9x69//Wt169btkGvI5s+fr9TUVO8tLy/vqOoON97ugn6eLljY1PSiI1MFTeamxKu271eji73WAAAAENk6HLLmzZunysrKFserq6s1b948vxQVCL/97W/1wgsv6LXXXlNcXFyb582ePVvl5eXe244dO4JYZeBlNTW+KK2qk9t92Jmi7VLb4NLXP5ZLko7vQGdBU/8uyUqOi1F1vUvriyr8UhMAAAAQKh0OWYZhyGKxtDi+Zs2aQ07DO1pZWVmy2WwqLi72OV5cXKzc3NxDXvvwww/rt7/9rd59910NGzbskOc6HA6lpKT43KJJetN0QbchldU0+OU51+4sV73Lrawku3plJnT4eqvVouN6sl8WAAAAokO7Q1Z6eroyMjJksVjUv39/ZWRkeG+pqak688wzdckllwSsULvdroKCAi1dutR7zO12a+nSpRozZkyb1z300EO69957tWTJEo0aNSpg9UWKWJtVqfGxkvy3V5a5x1VBr/RWA3h7HN80ZXAF67IAAAAQ4dq9GfGCBQtkGIauuuoqzZs3T6mpqd7H7Ha78vPzDxl2/GHWrFmaOnWqRo0apRNOOEELFixQVVWVpk2bJkmaMmWKunfvrvnz50uSHnzwQd1zzz1atGiR8vPzvWu3kpKSlJSUFNBaw1lmkl3lNQ3aV1WvY/zwfObo05FMFTQVNO2XVbh1f5ujpQAAAEAkaHfImjp1qiRPO/eTTjpJMTHtvtRvJk+erL179+qee+5RUVGRRowYoSVLlnibYWzfvl1W64HBuT/+8Y+qr6/X//7v//o8z5w5czR37txglh5WshId2ry3yi8dBg3D8HYFPJKmF6YReWmKsVpU5KzVzrIa9Ujv+LRDAAAAIBx0OClVVVVp6dKlmjhxos/xd955R263W2effbbfimvNzJkzNXPmzFYf++ijj3zub926NaC1RKrMpuYX+6qOfrrgpr1V2l/dIEeMVcd2Sz38BW2It9t0bPdUrdlRpsJt+wlZAAAAiFgdbnxx++23y+VytThuGEa7NgRG6Jl7ZZX4YSTLnCo4Ii9N9pgO/zr5MPfYWkHzCwAAAESwDv9X8Q8//KDBgwe3OD5w4EBt3LjRL0UhsDKTPHtllfphJMtsemHudXU0zJC1civNLwAAABC5OhyyUlNTtXnz5hbHN27cqMTERL8UhcAy98ryx5oscz3WqF5H376/oCmobSiukLPWP+3lAQAAgGDrcMg677zzdNNNN2nTpk3eYxs3btQtt9yi//mf//FrcQiMzETPSNbRhqy9FXXaUlIlSd59ro5Gl+Q49cpMkGFIq2jlDgAAgAjV4ZD10EMPKTExUQMHDlTv3r3Vu3dvDRo0SJmZmXr44YcDUSP8zLsm6yinC5qjWANykpWaEHvUdUkHOhQWErIAAAAQoTrcXTA1NVWff/653nvvPa1Zs0bx8fEaNmyYTjnllEDUhwAwpwuWVh3dSFbhNk+DigI/rMcyHZ+foVdX7WRdFgAAACLWEW12ZbFYNGHCBE2YMMHf9SAIzMYXZdUNanC5FWs7sq6AK7aa67H8F7LM5/pqx/6jqg0AAAAIlSMKWUuXLtXSpUu1Z88eud1un8eeffZZvxSGwEmLj5XVIrkNaX9VvbqkxHX4OWobXPp2V7kkz+iTv/TNTlJqfKzKaxr03S6nhuel+e25AQAAgGDo8DDBvHnzNGHCBC1dulQlJSXav3+/zw3hz2q1HPVeWWt2lKnBZahLskM90uP9Wpu5Lmsl67IAAAAQgTo8krVw4UI999xzuuKKKwJRD4IkM9Ghksr6I16X1Xx/LIvF4s/SNCo/XR+s36OVW0t19U96+/W5AQAAgEDr8EhWfX29xo4dG4haEESZ5l5ZR9hhcOVWT9MLf+yPdTDzOVdu2y/DMPz+/AAAAEAgdThkXXPNNVq0aFEgakEQHc10QbfbOLAJsR87C5qG9UhVrM2ivRV12lFa4/fnBwAAAAKpw9MFa2tr9fTTT+v999/XsGHDFBvruz/So48+6rfiEDhZSeaGxB0fydq4t1LO2kbFx9o0qGuKv0tTXKxNQ7unatX2Mq3YWqqemQl+fw0AAAAgUDocsr7++muNGDFCkrR27Vqfx/y9NgeBk5l45HtlrWiaKjiyZ1rAWqyPys/Qqu1lWrltvy4q6BGQ1wAAAAACocMh68MPPwxEHQgyc6+sI5kuWBiA/bEOZnYYNDc8BgAAACIFO712UuaarCNpfGF2Fizw4/5YBzMD3PfFlSqrPrIOiAAAAEAodHgk6/TTTz/ktMAPPvjgqApCcGSZ3QU7OJK1x1mr7aXVslqk43qmBaAyj8wkh/pkJWpzSZVWbd+vMwbmBOy1AAAAAH/qcMgy12OZGhoatHr1aq1du1ZTp071V10IMHO6YEfXZJmjWANyU5QcF3uYs49OQa90bS6p0sqthCwAAABEjg6HrN///vetHp87d64qKyuPuiAEh7lPVmVdo2obXIqLtbXrupVBWI9lOj4/Qy8V/uh9TQAAACAS+G1N1v/93//p2Wef9dfTIcCSHTGKtXmmfe7rwGjWyqZGFIHYH+tgBU2vsebHMtU3ugP+egAAAIA/+C1kLVu2THFxcf56OgSYxWJRZmLH9sqqrm/Ut7uckjwt1gOtT1aiMhLtqmt0a+2u8oC/HgAAAOAPHZ4ueOGFF/rcNwxDu3fv1sqVK3X33Xf7rTAEXmaSXUXO2naPZK3eUSaX21DX1Dh1T4sPcHWeIFjQK13vfVeslVtLdVzPwI+eAQAAAEerwyNZqampPreMjAyddtppevvttzVnzpxA1IgAMZtftLfDoHc9VhBGsUzm2i/WZQEAACBStGsk6/HHH9eMGTMUFxenefPmqUePHrJa2WIr0mWae2W1c7qg2VkwGE0vTObar8Jt+2UYxiG3DwAAAADCQbuS0qxZs+R0etbi9O7dWyUlJQEtCsHhDVntmC7ochv6ytyEOIgha0j3VNljrNpXVa8tJVVBe10AAADgSLVrJKtbt2565ZVXdM4558gwDP3444+qra1t9dyePXv6tUAETkemC24oqlBFXaOSHDEamJsc6NK8HDE2De+RqhVb92vltv3qk50UtNcGAAAAjkS7QtZdd92lG264QTNnzpTFYtHxxx/f4hxzKpfL5fJ7kQgMc6+sfVWHny5Y2NS6fWTPNMXYgjtVtKBXhlZs3a/Crft1yai8oL42AAAA0FHtClkzZszQZZddpm3btmnYsGF6//33lZmZGejaEGAH1mQdfiRrZQimCprMNWArmoIeAAAAEM7a3cI9OTlZQ4YM0V/+8heddNJJcjgcgawLQXBguuDhR7LM7n7HB7GzoMkMdpv3Vqm0ql4ZTeEQAAAACEcdnvc1depUAlaUaN74wjCMNs/bXV6jnWU1slktGpGXFqTqDkhPtKtfF89arMJttHIHAABAeKMPeydmrsmqa3Srqr7ttXTmKNagrslKdHR4/2q/OLBfFlMGAQAAEN4IWZ1Ygj1G8bE2SYeeMmgGm1G9gj9V0GRugLySkSwAAACEOUJWJ2eOZpUcovmFdxPi/OA3vTCZI1nf/Fiu2gY6WAIAACB8dThk/eY3v1F1dXWL4zU1NfrNb37jl6IQPGbzi9I2NiSurGvUut2ejahDOZLVKzNBWUl21bvc+mZnecjqAAAAAA6nwyFr3rx5qqysbHG8urpa8+bN80tRCJ4sbxv31qcLfrV9v9yG1CM9XrmpccEszYfFYvGGPHONGAAAABCOOhyyzE2HD7ZmzRplZIRupANHJqNZh8HWmIFmVAj2xzqYOV2xkP2yAAAAEMba3SouPT1dFotFFotF/fv39wlaLpdLlZWVuvbaawNSJALHnC5Y0sZIltkyvSAE+2MdzNwva+W2/XK7DVmtLcM+AAAAEGrtDlkLFiyQYRi66qqrNG/ePKWmpnofs9vtys/P15gxYwJSJAInq6nxRWtrshpdbq3abm5CHPqRrGO7pSou1qqy6gZtLqlUvy7JoS4JAAAAaKHdIWvq1KmSpN69e+ukk05STExo9kuCf5ndBfe10l1wfVGFqutdSo6LUf8wCDT2GKuG90jTl1tKtXLrfkIWAAAAwlKH12QlJydr3bp13vv/+te/dP755+uOO+5QfX3bbcARnjIS254uaO6PdVzP9LCZmmeuy1pB8wsAAACEqQ6HrJ///Of6/vvvJUmbN2/W5MmTlZCQoJdeekm33Xab3wtEYGUmtj1d0NwfKxymCprMDoM0vwAAAEC46nDI+v777zVixAhJ0ksvvaRTTz1VixYt0nPPPadXXnnF3/W18NRTTyk/P19xcXEaPXq0li9ffsjzX3rpJQ0cOFBxcXEaOnSo3n777YDXGEmymu2T5XYb3uOGYXg7CxaEcH+sgx3XM10Wi7R1X7X2VrTerAMAAAAIpSNq4e52uyVJ77//vs455xxJUl5enkpKSvxb3UEWL16sWbNmac6cOVq1apWGDx+uiRMnas+ePa2e//nnn+uyyy7T1Vdfra+++krnn3++zj//fK1duzagdUYSs4V7o9uQs7bBe3xnWY2KnLWKsVo0Ii8tRNW1lJoQ610fxmgWAAAAwlGHQ9aoUaN033336W9/+5s+/vhj/fSnP5UkbdmyRTk5OX4vsLlHH31U06dP17Rp0zR48GAtXLhQCQkJevbZZ1s9/7HHHtNZZ52lW2+9VYMGDdK9996r4447Tk8++WRA64wk9hirkuM8TUxKmjW/MFu3H9s9VfF2W0hqa0tB0/RFNiUGAABAOOpwyFqwYIFWrVqlmTNn6s4771S/fv0kSS+//LLGjh3r9wJN9fX1Kiws1Pjx473HrFarxo8fr2XLlrV6zbJly3zOl6SJEye2eb4k1dXVyel0+tyiXfMpg6YVTU0vwmET4oOZa8TMNWMAAABAOOlwH/Zhw4bpm2++aXH8d7/7nWy2wI14lJSUyOVytRgty8nJ0fr161u9pqioqNXzi4qK2nyd+fPna968eUdfcATJTLRrS0mV9jXrMGiOEoVjyDKbX6zdWa6aelfYjbQBAACgc+vwSJapsLBQf//73/X3v/9dq1atUlxcnGJjY/1ZW0jMnj1b5eXl3tuOHTtCXVLAmXtllTSNZDlrG7ShuELSgal54aRHery6JDvU6Da05seyUJcDAAAA+OjwSNaePXs0efJkffzxx0pLS5MklZWV6fTTT9cLL7yg7Oxsf9coScrKypLNZlNxcbHP8eLiYuXm5rZ6TW5ubofOlySHwyGHw3H0BUcQc68scyRr1bb9MgypV2aCuiTHhbK0VlksFh2fn6G3vtmtwm37dWKfzFCXBAAAAHh1eCTrhhtuUGVlpb799luVlpaqtLRUa9euldPp1C9/+ctA1ChJstvtKigo0NKlS73H3G63li5dqjFjxrR6zZgxY3zOl6T33nuvzfM7q6wk372yzKYXBWE4VdBk1mZumAwAAACEiw6PZC1ZskTvv/++Bg0a5D02ePBgPfXUU5owYYJfizvYrFmzNHXqVI0aNUonnHCCFixYoKqqKk2bNk2SNGXKFHXv3l3z58+XJN1444069dRT9cgjj+inP/2pXnjhBa1cuVJPP/10QOuMNOaGxPuaugseWI8VPvtjHWxU0zTGwm375XYbslotIa4IAAAA8OhwyHK73a2uvYqNjfXunxUokydP1t69e3XPPfeoqKhII0aM0JIlS7zNLbZv3y6r9cDg3NixY7Vo0SLddddduuOOO3TMMcfo9ddf15AhQwJaZ6TJbOouWFJZpwaXW1/t8ISs48NwPZZpcNcUJdhtctY26oc9lRqQmxzqkgAAAABJRxCyzjjjDN1444365z//qW7dukmSdu7cqZtvvlnjxo3ze4EHmzlzpmbOnNnqYx999FGLYxdffLEuvvjiAFcV2bwjWVX1+m6XU7UNbqXGx6pvdlKIK2tbjM2qEXlp+nzTPq3cVkrIAgAAQNjo8JqsJ598Uk6nU/n5+erbt6/69u2r3r17y+l06oknnghEjQiwzGb7ZK1sth4r3KfgjerFpsQAAAAIPx0eycrLy9OqVav0/vvve/enGjRoUItNfxE5zBbu+6vr9eXmfZIOrHkKZ6PyPWvGVm6j+QUAAADCR4dDluRpoX3mmWfqzDPP9Hc9CIH0BLssFskwpP/+UCIpvJtemEb2TJPVIu0orVGxs1Y5KeHXbh4AAACdT7unC37wwQcaPHiwnE5ni8fKy8t17LHH6r///a9fi0Nw2KwWpSd4RrNqGlyKtVk0rEdqiKs6vOS4WA3ITZHElEEAAACEj3aHrAULFmj69OlKSUlp8Vhqaqp+/vOf69FHH/VrcQges/mFJA3tnqq4WFsIq2k/77ospgwCAAAgTLQ7ZK1Zs0ZnnXVWm49PmDBBhYWFfikKwWeuy5IOrHWKBM33ywIAAADCQbtDVnFxcav7Y5liYmK0d+9evxSF4DM7DEqezoKRwgyE3+5yqqquMcTVAAAAAB0IWd27d9fatWvbfPzrr79W165d/VIUgq/5dMFRERSyuqfFq2tqnFxuQ2t2lIW6HAAAAKD9Ieucc87R3Xffrdra2haP1dTUaM6cOTr33HP9WhyCJzPRM5LVJyvRZ1QrEpijWStofgEAAIAw0O4W7nfddZdeffVV9e/fXzNnztSAAQMkSevXr9dTTz0ll8ulO++8M2CFIrAGdU2WJJ0xsEuIK+m443qm6Y01u/TNzrJQlwIAAAC0P2Tl5OTo888/13XXXafZs2fLMAxJnj2zJk6cqKeeeko5OTkBKxSBNeHYXC295VT1zEgIdSkdNqirp+Plut0VIa4EAAAA6OBmxL169dLbb7+t/fv3a+PGjTIMQ8ccc4zS0yNnDQ/a1jc7KdQlHJFBTXtl7SyrUXlNg1Lj227QAgAAAARah0KWKT09Xccff7y/awGOSGpCrLqlxmlXea02FFXohN6R04IeAAAA0afdjS+AcGZOGVxf5AxxJQAAAOjsCFmICgObGnes203IAgAAQGgRshAVBubS/AIAAADhgZCFqGBOF9xQVCGX2whxNQAAAOjMCFmICvmZCXLEWFXT4NL20upQlwMAAIBOjJCFqBBjs6p/jmdd1nrWZQEAACCECFmIGoNofgEAAIAwQMhC1PA2vyii+QUAAABCh5CFqGG2cWevLAAAAIQSIQtRY1DTSNaO0hpV1DaEuBoAAAB0VoQsRI30RLtyU+IkeVq5AwAAAKFAyEJU8Ta/IGQBAAAgRAhZiCoDmzYlpsMgAAAAQoWQhagyMJe9sgAAABBahCxElcFNI1nriyrkdhshrgYAAACdESELUaV3VqLsNquq613asb861OUAAACgEyJkIarE2Kw6JidJkrRuN80vAAAAEHyELESdQTS/AAAAQAgRshB1vM0vighZAAAACD5CFqLOoGbNLwAAAIBgI2Qh6pgjWdv2VauyrjHE1QAAAKCzIWQh6mQmOdQl2SFJ2sBoFgAAAIKMkIWodGDKIOuyAAAAEFyELESlgV09UwbpMAgAAIBgI2QhKg3KbRrJYq8sAAAABBkhC1GpeYdBt9sIcTVtc9Y26Pfvfa/d5TWhLgUAAAB+QshCVOqTnahYm0WVdY3aWRa+AWbhR5v02NIf9PA734e6FAAAAPgJIQtRKdZmVb8u4b8u64vN+yRJq7bvD3ElAAAA8JeICVmlpaW6/PLLlZKSorS0NF199dWqrKw85Pk33HCDBgwYoPj4ePXs2VO//OUvVV5eHsSqEUqDvM0vwnNdVm2DS9/s9Pw+bimpUll1fYgrAgAAgD9ETMi6/PLL9e233+q9997Tm2++qU8++UQzZsxo8/xdu3Zp165devjhh7V27Vo999xzWrJkia6++uogVo1Q8ja/CNM27qt3lKnBZfjcBwAAQOSLCXUB7bFu3TotWbJEK1as0KhRoyRJTzzxhM455xw9/PDD6tatW4trhgwZoldeecV7v2/fvrr//vv1f//3f2psbFRMTES8dRwFs437+jDdkHjl1lKf+19tL9NpA7qEqBoAAAD4S0SMZC1btkxpaWnegCVJ48ePl9Vq1Zdfftnu5ykvL1dKSsohA1ZdXZ2cTqfPDZHJ7DC4dV+VqusbQ1xNSyu2etZh9clOlMRIFgAAQLSIiJBVVFSkLl18/4U/JiZGGRkZKioqatdzlJSU6N577z3kFENJmj9/vlJTU723vLy8I64boZWV5FBWkkOGIW0Is9Esl9vQqm2ekDX95D6SpDU/lskwwrfdPAAAANonpCHr9ttvl8ViOeRt/fr1R/06TqdTP/3pTzV48GDNnTv3kOfOnj1b5eXl3tuOHTuO+vUROoPCdMrg+iKnKuoaleSI0QUju8seY1VZdYO27qsOdWkAAAA4SiFdmHTLLbfoyiuvPOQ5ffr0UW5urvbs2eNzvLGxUaWlpcrNzT3k9RUVFTrrrLOUnJys1157TbGxsYc83+FwyOFwtKt+hL9BXVP03x9Kwq6N+4otnvVYx/VKV1ysTUO6pWjV9jKt3rFfvbMSQ1wdAAAAjkZIQ1Z2drays7MPe96YMWNUVlamwsJCFRQUSJI++OADud1ujR49us3rnE6nJk6cKIfDoX//+9+Ki4vzW+2IDANzm0aywqyN+4qmqYIn5KdLkkbkpWvV9jJ9tb1MF4zsEcrSAAAAcJQiYk3WoEGDdNZZZ2n69Olavny5PvvsM82cOVOXXnqpt7Pgzp07NXDgQC1fvlySJ2BNmDBBVVVV+vOf/yyn06mioiIVFRXJ5XKF8u0giMzmF+uKnGGz3skwDO9I1qj8DEnSiJ5pkmh+AQAAEA0ipo/5P/7xD82cOVPjxo2T1WrVRRddpMcff9z7eENDgzZs2KDqas+allWrVnk7D/br18/nubZs2aL8/Pyg1Y7Q6ZudpBirRRW1jdpZVqMe6QmhLkk7Smu0p6JOsTaLRuSlSZJGNn1dt9up2gaX4mJtoSsQAAAARyViQlZGRoYWLVrU5uP5+fk+IxWnnXZa2IxcIHTsMVb165Kk9UUVWr+7IixC1vKm/bGGdk/1hqke6fHKSrKrpLJe3+5yqqBXeihLBAAAwFGIiOmCwNHwThkMk+YX5ibExzdNFZQki+XAqNZX2/eHoiwAAAD4CSELUc/b/CJM2rgvbyVkSfKGLNZlAQAARDZCFqLewGbNL0JtX2WdNu+tkqQWUwJH5HnuE7IAAAAiGyELUc/ckHhrSZVq6kPbWXJlU+v2/jlJSk+0+zw2LC9VFov04/4a7a2oC0V5AAAA8ANCFqJedpJDmYl2uQ3p++LQThk8uHV7cylxseqXnSSJ0SwAAIBIRshC1LNYLN7mF+tDPGXwwCbELUOW1HxdFs0vAAAAIhUhC52C2fxi3e7QjWRV1zfq253lkqRR+a23aGdTYgAAgMhHyEKnMDAM2riv3l6mRrehbqlxbe7XZY5kfb2jXG43+7wBAABEIkIWOgWz+cX6ooqQbVJttm5vbT2WaUBOsuJjbaqoa9SmvZXBKg0AAAB+RMhCp9CvS5JsVovKaxq0u7w2JDWs3OpZZ3V877ZDVozNqqE9UiVJX20vC0ZZAAAA8DNCFjoFR4xNfbMTJYWm+UWjy61V25tCVhvrsUwjm6YMfsW6LAAAgIhEyEKnMci7Liv4zS++2+1Udb1LKXEx6t8l+ZDnHugwWBb4wgAAAOB3hCx0GgNzQ9f8Ynmz/bGsVsshzx3Z0zPStaHIqer6xoDXBgAAAP8iZKHTGNis+UWwmeux2mrd3lxuapxyU+LkNqSvfywPdGkAAADwM0IWOo3BTdMFN++tVG2DK2ivaxiGVm7zjGS1tQnxwZgyCAAAELkIWeg0uiQ7lJ4QK7ch/VAcvPboW0qqVFJZL3vMgc6Bh+PdlJgOgwAAABGHkIVOw2KxHGh+EcQOg+ZUwRE90uSIsbXrmpGMZAEAAEQsQhY6lVA0vziwCfHh12OZhvZIlc1qUZGzVrvLawJVGgAAAAKAkIVOxdv8Ioht3Fc2haxDbUJ8sAR7jPrneGplyiAAAEBkIWShUzGbX6wvcsowjIC/3p6KWm3dVy2LRTquZ/tHsiSaXwAAAEQqQhY6lX5dkmS1SPurG1TsrAv465nrsQbmpig1PrZD15rrsr4iZAEAAEQUQhY6lbhYm/pkJ0kKTvMLcxPi4zuwHss0sqnD4Dc/lqvR5fZnWQAAAAggQhY6HW+HwSA0vzD3xzq+nftjNdc3O0nJjhjVNLi0oTj4GygDAADgyBCy0OkMzA1O84uK2gZ9t8sT5I4kZFmtFg3L8+yrxbosAACAyEHIQqczyOwwGODpgl9tL5PbkPIy4pWbGndEz+FtfkGHQQAAgIhByEKnY04X3LS3SrUNroC9jrd1e6+Oj2KZRuZ51nIxkgUAABA5CFnodHJT4pQaHyuX29DGPZUBe50DmxAfecga0dT8YuPeSjlrG/xRFgAAAAKMkIVOx2KxNJsyGJh1WfWNbu/o0wm9O95Z0JSV5FCP9HgZhvT1jnI/VQcAAIBAImShUxqYG9gOg2t3lau2wa30hFj1bWoZf6QObEq83w+VAQAAINAIWeiUAt38YmWzqYIWi+WonmtkT9ZlAQAARBJCFjqlA3tlVcgwDL8///ItnlGnI9mE+GDmSNZX28sCUisAAAD8i5CFTumYLsmyWqTSqnrtrajz63O73YYKj2IT4oMd2y1FsTaL9lXV68f9NUf9fAAAAAgsQhY6pXi7TflZiZKkdX5ufrFpb6X2VzcoLtaqY7ulHvXzxcXavCNvXzFlEAAAIOwRstBpmcFlvZ+bX6zY6pkqODIvXfYY//yJjWRTYgAAgIhByEKnNSjX0/zC3x0GV5ibEPthPZbJ3C+LDoMAAADhj5CFTss7kuXn6YLekNX76NdjmUbkeQLb2l1O1Te6/fa8AAAA8D9CFjqtgU0ha+OeStU1uvzynLvLa/Tj/hpZLQdar/tDfmaC0hJiVd/oDtjeXgAAAPAPQhY6rW6pcUqJi1Gj29CmPVV+eU5zPdbgbilKcsT45TklyWKxaHiPNEnslwUAABDuCFnotCwWi3c0y1+bEq/c6r/W7Qcb6V2XVeb35wYAAID/ELLQqfm7+cXyLYELWQc2Jab5BQAAQDgjZKFTG+jH5hflNQ3aUOx5nlF+7CxoMkPW1n3V2l9V7/fnBwAAgH9ETMgqLS3V5ZdfrpSUFKWlpenqq69WZWVlu641DENnn322LBaLXn/99cAWiohidhhct/voQ9aqbftlGJ4mFV2S4476+Q6WlmBX76YNlFf/WOb35wcAAIB/REzIuvzyy/Xtt9/qvffe05tvvqlPPvlEM2bMaNe1CxYskMViCXCFiET9c5JksUgllXXaW1F3VM+1IoDrsUxsSgwAABD+IiJkrVu3TkuWLNGf/vQnjR49Wj/5yU/0xBNP6IUXXtCuXbsOee3q1av1yCOP6Nlnnw1StYgkCfYY5Wd6RoeOtvlFMEKWuSnxVzS/AAAACFsREbKWLVumtLQ0jRo1ynts/Pjxslqt+vLLL9u8rrq6Wj/72c/01FNPKTc3t12vVVdXJ6fT6XNDdBvU1dP8Yv1RTBmsbXBpzY5ySf7dhPhg5rqsNTvKZBhGwF4HAAAARy4iQlZRUZG6dOnicywmJkYZGRkqKipq87qbb75ZY8eO1Xnnndfu15o/f75SU1O9t7y8vCOuG5FhYK65LuvIA/U3O8tV73IrK8mu/MwEf5XWwsDcFNljrCqvadCWEv/s7QUAAAD/CmnIuv3222WxWA55W79+/RE997///W998MEHWrBgQYeumz17tsrLy723HTt2HNHrI3J4m18cRYfB5lMFA7n+zx5j1dDuqZLYLwsAACBcxYTyxW+55RZdeeWVhzynT58+ys3N1Z49e3yONzY2qrS0tM1pgB988IE2bdqktLQ0n+MXXXSRTj75ZH300UetXudwOORwONr7FhAFBjbtlbVxT4XqG92yx3T83x5WbvXsXTUqgOuxTCPy0lS4bb9W7yjThcf1CPjrAQAAoGNCGrKys7OVnZ192PPGjBmjsrIyFRYWqqCgQJInRLndbo0ePbrVa26//XZdc801PseGDh2q3//+95o0adLRF4+o0SM9XsmOGFXUNWpzSaV3+mB7ud2GVjaNZJ0QpJAlSV/RYRAAACAsRcSarEGDBumss87S9OnTtXz5cn322WeaOXOmLr30UnXr1k2StHPnTg0cOFDLly+XJOXm5mrIkCE+N0nq2bOnevfuHbL3gvBjsVg08CiaX3y/p0LO2kYl2G3eJhqBZIasdbudqm1wBfz1AAAA0DEREbIk6R//+IcGDhyocePG6ZxzztFPfvITPf30097HGxoatGHDBlVXV4ewSkSqo2l+sWKLZxTruJ7pirEF/k+qR3q8spIcanQb+nZXecBfDwAAAB0T0umCHZGRkaFFixa1+Xh+fv5hW1rT8hptMUeyjqT5xYqm9ViB3B+rOYvFohF5aXp/XbG+2l6mgl7BeV0AAAC0T8SMZAGBZHYYXN/BkSzDMJp1Fkz3e11tGcmmxAAAAGGLkAVIGpDjGcnaU1GnfZV17b5uZ1mNdpfXKsZq0Yim4BMM5rqs1TS/AAAACDuELEBSoiNGvZo2EV7fgSmD5ijWsd1TlWAP3uzbYT1SZbF4Qt7eivaHQgAAAAQeIQtoMugIml+Y67FOCOJUQUlKjovVMV2SJLEpMQAAQLghZAFNvM0vOtDG3ewsGIxNiA/mnTK4Y3/QXxsAAABtI2QBTbzNL4raN5K1v6peP+yplCSN6hXckSxJGpHneU02JQYAAAgvhCygiTld8IfiSjW43Ic9v3CbZwSpb3aiMpMcAa2tNeZI1tc/lsvlZnsCAACAcEHIApr0SI9Xot2mepdbW0qqDnu+2fTihN6h2aeqf06SEuw2VdY1atPeypDUAAAAgJYIWUATq9WigV3b3/zCDFmjQrQZcIzNqqHdUyXRyh0AACCcELKAZgbmtq/5RW2DS9/sLJckHR+CphemEd5NiWl+AQAAEC4IWUAzA9vZ/GL1jjI1uAzlpDiUlxEfjNJaNbJpXRbNLwAAAMIHIQtoZnBTG/f1hxnJat663WKxBLyutozs6ekw+H1xharqGkNWBwAAAA4gZAHN9M/xhKwiZ632V9W3ed6KbeYmxKGbKihJOSlx6poaJ7ch7/RFAAAAhBYhC2gmOS7WO/1vXRtTBl1uQ6uaQtao/ODvj3WwEUwZBAAACCuELOAg5n5ZbU0ZXLfbqcq6RiU7YjSw6dxQMkPWappfAAAAhAVCFnCQw7VxN1u3H9crXTZr6NZjmcx1Wat3lIW2EAAAAEgiZAEteJtfFLU+krVya9N6rBBtQnywod1TZbNaVOys0+7ymlCXAwAA0OkRsoCDmFMAvy+uUKPL7fOYYRjNNiEO/XosSYq32zSgqWEHmxIDAACEHiELOEjPjAQl2G2qa3Rr674qn8e2l1ZrT0Wd7DarhjethQoHBzYlLgtpHQAAACBkAS1YrRYNyPWMDK07qPnFiqapgkN7pCou1hb02tribX7BSBYAAEDIEbKAVphTBg9ufmFuQnx8iPfHOthxTSNZ3+wsbzHFEQAAAMFFyAJaMaiN5hcrtpkhKzzWY5n6ZCUpOS5GNQ0ubShuvWEHAAAAgoOQBbRiUFdzr6wDI1kllXXavNezRqsgTJpemKxWi4b3SJPEpsQAAAChRsgCWmGuydpVXquy6npJB1q3D8hJVlqCPWS1teXApsRlIa0DAACgsyNkAa1IiYtV97R4SQemDHpbt4fZVEHTyKZ1WYQsAACA0CJkAW04eMrgyqaQFS6bEB/MHMnauKdS5TUNoS0GAACgEyNkAW0wm1+s212hqrpGrd3lCVujwqyzoCkzyaG8DM/o29c/loW2GAAAgE6MkAW0wTuSVeTU6h1lcrkNdU+L904jDEcj8jxTGdkvCwAAIHQIWUAbBjY1v9hQXKEvN++TFL7rsUwjaX4BAAAQcoQsoA29MhMVF2tVbYNbr6zaKSn8NiE+2IhmzS8MwwhtMQAAAJ0UIQtog81q0YBcz5TBnWU1ksI/ZA3umqJYm0X7qur14/6aUJcDAADQKRGygEMY1DRlUJJS42N1TJekEFZzeHGxNg1uWku2avv+EFcDAADQORGygEMY2CxkjeqVLqvVEsJq2mdkz6bmF6zLAgAACAlCFnAIZodBKXxbtx9sBM0vAAAAQoqQBRzCwNwDIeuE3uHdWdBkhqxvdzlV1+gKbTEAAACdECELOITUhFhdOTZfZx2bq+E90kJdTrv0ykxQekKs6hvdWre7ItTlAAAAdDoxoS4ACHdz/+fYUJfQIRaLRcPz0vTRhr1avX2/d2QLAAAAwcFIFhCFRubR/AIAACBUCFlAFGq+KTEAAACCi5AFRKERTevHtu6rVmlVfWiLAQAA6GQIWUAUSk2IVZ+sREnSGkazWjAMg86LAAAgYCKm8UVpaaluuOEGvfHGG7Jarbrooov02GOPKSkp6ZDXLVu2THfeeae+/PJL2Ww2jRgxQu+8847i4+ODVDkQGiN6pmlzSZW+2lGm0wd2CXU5QVFV16i9FXUqqazz+bq3sr7pa51Kmr7WN7rVJytRx/VKV0HTrV92UkRsOA0AAMJbxISsyy+/XLt379Z7772nhoYGTZs2TTNmzNCiRYvavGbZsmU666yzNHv2bD3xxBOKiYnRmjVrZLUygIfoNzIvTa+u2hnx67Jq6l2esHRQcPIGqIo6lTSFqJqGjo1ObS6p0uaSKr1c+KMkKTkuRsf19ASuUb3SNTwvTYmOiPmfSQAAECYshmEYoS7icNatW6fBgwdrxYoVGjVqlCRpyZIlOuecc/Tjjz+qW7durV534okn6swzz9S99957xK/tdDqVmpqq8vJypaSkHP4CIEx882O5Jj35qeJjbTprSK6ykuzKTnYoK8nh8zU9wS5bkEdvDMNQeU2D9lTUaY+zTnsqalt8bwaoyrrGDj13fKxN2cnme2z9PWcnORQXa9PaXeVatW2/Crft1+odZaqu9w1pVos0qGuKd6TruJ7p6pEeL4uF0S4AADqj9maDiPgn2mXLliktLc0bsCRp/Pjxslqt+vLLL3XBBRe0uGbPnj368ssvdfnll2vs2LHatGmTBg4cqPvvv18/+clP2nyturo61dXVee87nU7/vhkgSAZ2TVZGol2lVfV67audbZ5ntUiZSZ7gkZVsfrUru1kgMQNKWkLsIQOGy21oX2WdJzBV1DaFJt/vzfBU73K3+704YqytBCV7szB14GtHRp5OH9BFpw/wTKVsdLm1vqhChU2hq3Dbfu0sq9G3u5z6dpdTf122TZLUJdnhDV0FvdJ1bLdU2WMYHT8cwzBUVe9SdV2jUuJjFRdrC3VJAAAETESErKKiInXp4rumJCYmRhkZGSoqKmr1ms2bN0uS5s6dq4cfflgjRozQX//6V40bN05r167VMccc0+p18+fP17x58/z7BoAQiLVZ9fovTtLKbaXNptjVN5tiV6fS6nq5DXmPaffhntOizMQDo0RpCXaVVdc3Bak67ausk7sDY+NpCbHq0hSUuiTHHfg+5cD32ckOJTtiAj56FGOzakj3VA3pnqqpY/MlSUXltQdC1/b9+nZnufZU1Ok/a4v0n7We/+2xx1g1vEeqZ21Xz3Qd1ytdWUmOgNYaSm63oYraRpXV1KusukFlNQ0qq65XeU2D5351g8pq6lXeymONzX45Euw2ZSTalZloV0aiXene7x3KbLrvfTzJHpTfAQAA/CWkIev222/Xgw8+eMhz1q1bd0TP7XZ7/pX85z//uaZNmyZJGjlypJYuXapnn31W8+fPb/W62bNna9asWd77TqdTeXl5R1QDEGo9MxPUMzOhzccbXW6VVnlC0sFB7EDTCM/3ZdUNanAZKnLWqshZ2+ZzmiNjXZLNW5y6pDiaQlPz7x1yxIT3aEZuapx+OqyrfjqsqySptsGlr38s9wavVdv3q7SqXiu27teKrfu91+VnJqhfl2SlxMUoOS5GKfGxSo6LUXKc52tK3IH7KU2PO2KsAQ8RLreh6vpGVdW5VFXfqKq6pu/rGlVV36jqes/3zhpPQPIGp5oGlVfXe48dzSRzi0UyDKm63qXq+hr9uL+mXdfF2ixKT2gKXkmeMJaREOv5muQJY+kJdiU5YmSzWhRjs3i+Ws2vVsXYfO+bjwer2YlhGHK5DbkMQ2635DbM7z3HbVaL7DFW2W1Wxdiie3TUMAw1ug3VNbpV2+BSXaNbdU1fvfebvm90GXLEWOWItSou1ub5Psbz1Xs/1nMs2FOfAaAtIQ1Zt9xyi6688spDntOnTx/l5uZqz549PscbGxtVWlqq3NzcVq/r2tXzH0WDBw/2OT5o0CBt3769zddzOBxyOKL3X6GB5mJsVs+oUUrcYc+tb3RrX5Vv04my6oam0ai4phEohzITHVH7HzpxsTad0DtDJ/TOkOT5D8UtJVXewFW4bb++L67U1n3V2rqvukPPHWuztBLCzCB24H5KXKwSHDbV1LtUXe9SZV3jgeBU1+hzrLLO1fSY5/GONgY5lES7TWkJdqXGxyotwXNLjbd7vo8/6H5CrNKavnfEWFVR16jSynrtq6pXaVW99leZ39dpX9P90qoDj1fXu9TgMrwjpv5msUixzUKXzdYynNmsFtksFm8ochue0OpuCk5uo9kxM0g1hSlX0zkdYbXIG7jsTYHiwP0D38c2fW318eb3bVYZ8tRoGJ6AJ3l+h5sfMzwHPceanW/I8Hw1Wn+OepdnW4S6Brfnq094cqu2lcc6+CNpl1ibRY4Ym+JiDwQxu08Ysymu6asnrFlltVi8789Tk+dza37MkCE1+xkZPt+bPxvfx80l72boj7FaD/xe2VqGfc+xZuc0+xpjO/haz33pwOfjNprV0rz2g+tUU50+jzU7pgO1B0qLGpv9frV6rFnNLT6PVs6X5P1HK6vFIovF8zdlsVhkaXrMe0ye783HzPMtkvcfYHyOWXzP9zzPgcct3u8tTa/p+7reY4d4XQbtW5eV5NCo/IxQl9FuIQ1Z2dnZys7OPux5Y8aMUVlZmQoLC1VQUCBJ+uCDD+R2uzV69OhWr8nPz1e3bt20YcMGn+Pff/+9zj777KMvHuhk7DFWdU2NV9dUtj8wWSwW9clOUp/sJF08yjPiXV7doK927NeuslpV1DaoorZRFbUNcvp89YwWVdQ2qLKuUW5DanAZKm0KFYFms1qUaLcpyRGjBEeMEu02JTpilGCPUZLDpqS4GKV7A5TdG5rM4JQaH3tU69BSmoJjftNebodT2+Dy/mzMMFZa1dD0tV77Kuu1v9rzWG29S41uzyhJo8stV9P35tfWGIY8awTDaOs0tyHVNrhV2+CW1LHmL5HIbjswGuUZoWr6PtaqWKtVda4DI111DS7VNhv5av65NrgMNbgaVen/LA4gxE7pn62/XnVCqMtot4hYkzVo0CCdddZZmj59uhYuXKiGhgbNnDlTl156qbez4M6dOzVu3Dj99a9/1QknnCCLxaJbb71Vc+bM0fDhwzVixAg9//zzWr9+vV5++eUQvyMA0So1IVanDWj/vmRmQwhP6Gr0BjNns2B2IJR57lfXuxRvtynRHqOEpoCU6Gj6ao9p+tr68QS7LShTE/0pLtambmnx6pZ2dAHfnK7XPHR5vrrV6Gp+zN0U0prdd3lGp6wWz2iCtelfpM3vbVbzuHzPaRoBs1rl+Woea3bcajkwSlbf6PbcXJ6vdc3uNzQd8x5vdr++0XXgvqv587hU3+hWg8vw+ddz81/wPTuatPxXfWvT74f3X+nl+Vd9i+d07zHzOe1No0Le0aLYVqb0NR9hirUqrumr3WY9qimbjS63d3phXaNLteaIWUPLqYfmOeboWm2DWzKMtkcfDjp24OfSdMzn52I58HO1HBiN8P6eHfQ71tDK75zLbTQdd/v8nrb4BwOX5/fWrOXgEZVW62x6TAe9n4NHVczzA/2/Eb6jPs1HiFp5T2r987AcVL/585eajWypadTV/N7tO3onNR/FOzBS29aIpu/oWsuRwuaja1KzY83Ob/6aB48ghn/P79Dp3+XQe+OGm4gIWZL0j3/8QzNnztS4ceO8mxE//vjj3scbGhq0YcMGVVcfmKJz0003qba2VjfffLNKS0s1fPhwvffee+rbt28o3gIAtGCxWJTkiFES+3EFnMXSNG0rTJcCWmVRrM2qRGasd0hM0xo2fm4AwklE7JMVSuyTBQAAAEBqfzaI7vZFAAAAABBkhCwAAAAA8CNCFgAAAAD4ESELAAAAAPyIkAUAAAAAfkTIAgAAAAA/ImQBAAAAgB8RsgAAAADAjwhZAAAAAOBHhCwAAAAA8CNCFgAAAAD4ESELAAAAAPyIkAUAAAAAfkTIAgAAAAA/ImQBAAAAgB8RsgAAAADAjwhZAAAAAOBHMaEuINwZhiFJcjqdIa4EAAAAQCiZmcDMCG0hZB1GRUWFJCkvLy/ElQAAAAAIBxUVFUpNTW3zcYtxuBjWybndbu3atUvJycmyWCwhrcXpdCovL087duxQSkpKSGuB//C5Rh8+0+jDZxqd+FyjD59pdAqnz9UwDFVUVKhbt26yWtteecVI1mFYrVb16NEj1GX4SElJCfkvGPyPzzX68JlGHz7T6MTnGn34TKNTuHyuhxrBMtH4AgAAAAD8iJAFAAAAAH5EyIogDodDc+bMkcPhCHUp8CM+1+jDZxp9+EyjE59r9OEzjU6R+LnS+AIAAAAA/IiRLAAAAADwI0IWAAAAAPgRIQsAAAAA/IiQBQAAAAB+RMiKIE899ZTy8/MVFxen0aNHa/ny5aEuCUdo7ty5slgsPreBAweGuix00CeffKJJkyapW7duslgsev31130eNwxD99xzj7p27ar4+HiNHz9eP/zwQ2iKRbsc7jO98sorW/ztnnXWWaEpFu0yf/58HX/88UpOTlaXLl10/vnna8OGDT7n1NbW6vrrr1dmZqaSkpJ00UUXqbi4OEQVoz3a87medtppLf5er7322hBVjMP54x//qGHDhnk3HB4zZoz+85//eB+PtL9TQlaEWLx4sWbNmqU5c+Zo1apVGj58uCZOnKg9e/aEujQcoWOPPVa7d+/23j799NNQl4QOqqqq0vDhw/XUU0+1+vhDDz2kxx9/XAsXLtSXX36pxMRETZw4UbW1tUGuFO11uM9Uks466yyfv91//vOfQawQHfXxxx/r+uuv1xdffKH33ntPDQ0NmjBhgqqqqrzn3HzzzXrjjTf00ksv6eOPP9auXbt04YUXhrBqHE57PldJmj59us/f60MPPRSiinE4PXr00G9/+1sVFhZq5cqVOuOMM3Teeefp22+/lRSBf6cGIsIJJ5xgXH/99d77LpfL6NatmzF//vwQVoUjNWfOHGP48OGhLgN+JMl47bXXvPfdbreRm5tr/O53v/MeKysrMxwOh/HPf/4zBBWiow7+TA3DMKZOnWqcd955IakH/rFnzx5DkvHxxx8bhuH5u4yNjTVeeukl7znr1q0zJBnLli0LVZnooIM/V8MwjFNPPdW48cYbQ1cUjlp6errxpz/9KSL/ThnJigD19fUqLCzU+PHjvcesVqvGjx+vZcuWhbAyHI0ffvhB3bp1U58+fXT55Zdr+/btoS4JfrRlyxYVFRX5/N2mpqZq9OjR/N1GuI8++khdunTRgAEDdN1112nfvn2hLgkdUF5eLknKyMiQJBUWFqqhocHnb3XgwIHq2bMnf6sR5ODP1fSPf/xDWVlZGjJkiGbPnq3q6upQlIcOcrlceuGFF1RVVaUxY8ZE5N9pTKgLwOGVlJTI5XIpJyfH53hOTo7Wr18foqpwNEaPHq3nnntOAwYM0O7duzVv3jydfPLJWrt2rZKTk0NdHvygqKhIklr9uzUfQ+Q566yzdOGFF6p3797atGmT7rjjDp199tlatmyZbDZbqMvDYbjdbt1000066aSTNGTIEEmev1W73a60tDSfc/lbjRytfa6S9LOf/Uy9evVSt27d9PXXX+vXv/61NmzYoFdffTWE1eJQvvnmG40ZM0a1tbVKSkrSa6+9psGDB2v16tUR93dKyAJC4Oyzz/Z+P2zYMI0ePVq9evXSiy++qKuvvjqElQE4lEsvvdT7/dChQzVs2DD17dtXH330kcaNGxfCytAe119/vdauXcsa2CjT1uc6Y8YM7/dDhw5V165dNW7cOG3atEl9+/YNdplohwEDBmj16tUqLy/Xyy+/rKlTp+rjjz8OdVlHhOmCESArK0s2m61FB5Xi4mLl5uaGqCr4U1pamvr376+NGzeGuhT4ifm3yd9tdOvTp4+ysrL4240AM2fO1JtvvqkPP/xQPXr08B7Pzc1VfX29ysrKfM7nbzUytPW5tmb06NGSxN9rGLPb7erXr58KCgo0f/58DR8+XI899lhE/p0SsiKA3W5XQUGBli5d6j3mdru1dOlSjRkzJoSVwV8qKyu1adMmde3aNdSlwE969+6t3Nxcn79bp9OpL7/8kr/bKPLjjz9q3759/O2GMcMwNHPmTL322mv64IMP1Lt3b5/HCwoKFBsb6/O3umHDBm3fvp2/1TB2uM+1NatXr5Yk/l4jiNvtVl1dXUT+nTJdMELMmjVLU6dO1ahRo3TCCSdowYIFqqqq0rRp00JdGo7Ar371K02aNEm9evXSrl27NGfOHNlsNl122WWhLg0dUFlZ6fMvolu2bNHq1auVkZGhnj176qabbtJ9992nY445Rr1799bdd9+tbt266fzzzw9d0TikQ32mGRkZmjdvni666CLl5uZq06ZNuu2229SvXz9NnDgxhFXjUK6//notWrRI//rXv5ScnOxdv5Gamqr4+Hilpqbq6quv1qxZs5SRkaGUlBTdcMMNGjNmjE488cQQV4+2HO5z3bRpkxYtWqRzzjlHmZmZ+vrrr3XzzTfrlFNO0bBhw0JcPVoze/ZsnX322erZs6cqKiq0aNEiffTRR3rnnXci8+801O0N0X5PPPGE0bNnT8NutxsnnHCC8cUXX4S6JByhyZMnG127djXsdrvRvXt3Y/LkycbGjRtDXRY66MMPPzQktbhNnTrVMAxPG/e7777byMnJMRwOhzFu3Dhjw4YNoS0ah3Soz7S6utqYMGGCkZ2dbcTGxhq9evUypk+fbhQVFYW6bBxCa5+nJOMvf/mL95yamhrjF7/4hZGenm4kJCQYF1xwgbF79+7QFY3DOtznun37duOUU04xMjIyDIfDYfTr18+49dZbjfLy8tAWjjZdddVVRq9evQy73W5kZ2cb48aNM959913v45H2d2oxDMMIZqgDAAAAgGjGmiwAAAAA8CNCFgAAAAD4ESELAAAAAPyIkAUAAAAAfkTIAgAAAAA/ImQBAAAAgB8RsgAAAADAjwhZAAAAAOBHhCwAAPwkPz9fCxYsCHUZAIAQI2QBACLSlVdeqfPPP1+SdNppp+mmm24K2ms/99xzSktLa3F8xYoVmjFjRtDqAACEp5hQFwAAQLior6+X3W4/4uuzs7P9WA0AIFIxkgUAiGhXXnmlPv74Yz322GOyWCyyWCzaunWrJGnt2rU6++yzlZSUpJycHF1xxRUqKSnxXnvaaadp5syZuummm5SVlaWJEydKkh599FENHTpUiYmJysvL0y9+8QtVVlZKkj766CNNmzZN5eXl3tebO3eupJbTBbdv367zzjtPSUlJSklJ0SWXXKLi4mLv43PnztWIESP0t7/9Tfn5+UpNTdWll16qioqKwP7QAAABRcgCAES0xx57TGPGjNH06dO1e/du7d69W3l5eSorK9MZZ5yhkSNHauXKlVqyZImKi4t1ySWX+Fz//PPPy26367PPPtPChQslSVarVY8//ri+/fZbPf/88/rggw902223SZLGjh2rBQsWKCUlxft6v/rVr1rU5Xa7dd5556m0tFQff/yx3nvvPW3evFmTJ0/2OW/Tpk16/fXX9eabb+rNN9/Uxx9/rN/+9rcB+mkBAIKB6YIAgIiWmpoqu92uhIQE5ebmeo8/+eSTGjlypB544AHvsWeffVZ5eXn6/vvv1b9/f0nSMccco4ceesjnOZuv78rPz9d9992na6+9Vn/4wx9kt9uVmpoqi8Xi83oHW7p0qb755htt2bJFeXl5kqS//vWvOvbYY7VixQodf/zxkjxh7LnnnlNycrIk6YorrtDSpUt1//33H90PBgAQMoxkAQCi0po1a/Thhx8qKSnJexs4cKAkz+iRqaCgoMW177//vsaNG6fu3bsrOTlZV1xxhfbt26fq6up2v/66deuUl5fnDViSNHjwYKWlpWndunXeY/n5+d6AJUldu3bVnj17OvReAQDhhZEsAEBUqqys1KRJk/Tggw+2eKxr167e7xMTE30e27p1q84991xdd911uv/++5WRkaFPP/1UV199terr65WQkODXOmNjY33uWywWud1uv74GACC4CFkAgIhnt9vlcrl8jh133HF65ZVXlJ+fr5iY9v/fXWFhodxutx555BFZrZ4JHy+++OJhX+9ggwYN0o4dO7Rjxw7vaNZ3332nsrIyDR48uN31AAAiD9MFAQARLz8/X19++aW2bt2qkpISud1uXX/99SotLdVll12mFStWaNOmTXrnnXc0bdq0Qwakfv36qaGhQU888YQ2b96sv/3tb96GGM1fr7KyUkuXLlVJSUmr0wjHjx+voUOH6vLLL9eqVau0fPlyTZkyRaeeeqpGjRrl958BACB8ELIAABHvV7/6lWw2mwYPHqzs7Gxt375d3bp102effSaXy6UJEyZo6NChuummm5SWluYdoWrN8OHD9eijj+rBBx/UkCFD9I9//EPz58/3OWfs2LG69tprNXnyZGVnZ7donCF5pv3961//Unp6uk455RSNHz9effr00eLFi/3+/gEA4cViGIYR6iIAAAAAIFowkgUAAAAAfkTIAgAAAAA/ImQBAAAAgB8RsgAAAADAjwhZAAAAAOBHhCwAAAAA8CNCFgAAAAD4ESELAAAAAPyIkAUAAAAAfkTIAgAAAAA/ImQBAAAAgB/9f5DZL6qSVhHlAAAAAElFTkSuQmCC", + "text/plain": [ + "
" + ] + } + } + ], + "id": "17" + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "When this is not necessary, it is possible to print only the final results:" + ], + "id": "18" + }, + { + "cell_type": "code", + "metadata": {}, + "source": [ + "optimal_energy = result[-1][0]\n", + "optimal_parameters = result[-1][1]\n", + "\n", + "print(f\"Optimal energy: {optimal_energy}\")\n", + "print(f\"Optimal parameters: {optimal_parameters}\")" + ], + "execution_count": 5, + "outputs": [ + { + "output_type": "stream", + "text": [ + "Optimal energy: -0.61572265625\n", + "Optimal parameters: {'angles': [2.1377203480076377, 0.004060541282730399, -0.3165621830160506]}\n" + ] + } + ], + "id": "19" + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The VQE algorithm outputs these key results:\n", + "\n", + "- **Optimal energy**: The lowest energy found for the Hamiltonian, representing the ground state energy (minimal eigenvalue).\n", + "- **Optimal parameters**: The parameters of the quantum program that achieve the optimal energy, corresponding to rotation angles in the U-gate.\n", + "- **Eigenstate**: The quantum state associated with the optimal energy, given as probability amplitudes for the basis states." + ], + "id": "20" + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Summary and Exercise " + ], + "id": "21" + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "You designed a parameterized quantum circuit capable of capturing a simple Hamiltonian. You initialized an `ExecutionSession` and used `minimize` to execute it, visualizing the results.\n" + ], + "id": "22" + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "
\n", + "Exercise - Two Qubits VQE\n", + "\n", + "Now, practice the implementation of a similar case to the previous example, but this time for two qubits, following the Hamiltonian:\n", + "\n", + "$$ H = \\frac{1}{2}I \\otimes I + \\frac{1}{2}Z \\otimes Z - X \\otimes X $$\n", + "\n", + "**Use the last example to implement and execute VQE for this Hamiltonian.**\n", + "\n", + "Code skeleton:\n", + "\n", + "```python\n", + "HAMILTONIAN = QConstant(\"HAMILTONIAN\", List[PauliTerm], [...]) #TODO: Complete Hamiltonian\n", + "\n", + "@qfunc\n", + "def main(...) -> None:\n", + " #TODO: Complete the function according to the instructions, choosing simple ansatz.\n", + "\n", + "qprog = synthesize(synthesize)\n", + "show(qprog)\n", + "\n", + "with ExecutionSession(qprog_1) as es:\n", + " result = es.minimize(\n", + " cost_function=HAMILTONIAN,\n", + " initial_params={\"params\": [0.0] * n_params},\n", + " max_iteration=200,\n", + " )\n", + "\n", + "\n", + "```\n", + "
" + ], + "id": "23" + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Read More " + ], + "id": "24" + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Further reading from the reference manual:\n", + " - [Execution Primitives](https://docs.classiq.io/latest/user-guide/execution/ExecutionSession/)" + ], + "id": "25" + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Using the PyTorch Integration" + ], + "id": "26" + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Classiq integrates with PyTorch, enabling the seamless development of quantum machine learning and hybrid classical quantum machine learning models. This integration leverages PyTorch's powerful machine learning capabilities alongside quantum computing." + ], + "id": "27" + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "
\n", + "Note on PyTorch Installation:\n", + "\n", + "To properly install and run PyTorch locally, check [this page](https://pytorch.org/get-started/locally/).\n", + "\n", + "
\n" + ], + "id": "28" + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Workflow" + ], + "id": "29" + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "1. **Defining the Model**\n", + " - **1.1**: Define the quantum model and synthesize it into a quantum program.\n", + " - **1.2**: Define the execute and post-process callables.\n", + " - **1.3**: Create a `torch.nn.Module` network.\n", + "2. **Choosing the Dataset, Loss Function, and Optimizer**\n", + "3. **Training the Model**\n", + "4. **Testing the Model**\n" + ], + "id": "30" + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "If you are not familiar with PyTorch, read the following documentation:\n", + "\n", + "
\n", + "PyTorch Documentation\n", + "\n", + "- [Creating Models](https://pytorch.org/tutorials/beginner/basics/quickstart_tutorial.html#creating-models)\n", + "- [Building Neural Networks](https://pytorch.org/tutorials/beginner/basics/buildmodel_tutorial.html)\n", + "- [Optimizing Model Parameters](https://pytorch.org/tutorials/beginner/basics/quickstart_tutorial.html#optimizing-the-model-parameters)\n", + "- [Tensors](https://pytorch.org/tutorials/beginner/basics/tensorqs_tutorial.html)\n", + "- [Datasets and DataLoaders](https://pytorch.org/tutorials/beginner/basics/data_tutorial.html)\n", + "\n", + "
\n" + ], + "id": "31" + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Example - Demonstrate PyTorch Integration with Classiq " + ], + "id": "32" + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This example demonstrates PyTorch integration using a simple parameterized quantum model.\n", + "\n", + "It utilizes one input from the user and one weight, while using one qubit in the model. The goal of the learning process is to determine the correct angle for an RX gate to perform a \"NOT\" operation. (Spoiler alert: The correct answer is $\\pi$.)\n" + ], + "id": "33" + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The dataset `DATALOADER_NOT` is used, as defined [here](https://docs.classiq.io/latest/user-guide/applications/qml/qnn/datasets/). \n", + "`DatasetXor` is also available from the link for further practice." + ], + "id": "34" + }, + { + "cell_type": "code", + "metadata": {}, + "source": [ + "from classiq import *\n", + "from classiq.applications.qnn.datasets import DATALOADER_NOT\n", + "\n", + "for data, label in DATALOADER_NOT:\n", + " print(f\"--> Data for training:\\n{data}\")\n", + " print(f\"--> Corresponding labels:\\n{label}\")" + ], + "execution_count": 7, + "outputs": [ + { + "output_type": "stream", + "text": [ + "--> Data for training:\n", + "tensor([[3.1416],\n", + " [0.0000]])\n", + "--> Corresponding labels:\n", + "tensor([1., 0.])\n" + ] + } + ], + "id": "35" + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This dataset contains two items. The first item indicates no rotation (`0.0000`) and is labeled as 0, indicating the state $|0\\rangle$. The second item indicates a rotation of `3.1416` and is labeled as 1, indicating the state $|1\\rangle$." + ], + "id": "36" + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Read an explanation on creating PyTorch datasets here: \n", + "- [Creating a custom dataset for your files](https://pytorch.org/tutorials/beginner/basics/data_tutorial.html#creating-a-custom-dataset-for-your-files)\n", + "- [Writing custom datasets, dataLoaders, and transforms](https://pytorch.org/tutorials/beginner/data_loading_tutorial.html)" + ], + "id": "37" + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### Step 1.1 - Define the Quantum Model and Synthesize It into a Quantum Program\n", + "" + ], + "id": "38" + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The first part of the parameterized quantum model has an encoding section, which loads input data ($|0\\rangle$ or $|1\\rangle$) into the parameterized quantum model:\n" + ], + "id": "39" + }, + { + "cell_type": "code", + "metadata": {}, + "source": [ + "@qfunc\n", + "def encoding(theta: CReal, q: QArray) -> None:\n", + " RX(theta=theta, target=q[0])" + ], + "execution_count": 8, + "outputs": [], + "id": "40" + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The second part is the `mixing` function, which includes an adjustable parameter for training the RX gate to act later as a NOT gate:" + ], + "id": "41" + }, + { + "cell_type": "code", + "metadata": {}, + "source": [ + "@qfunc\n", + "def mixing(theta: CReal, q: QArray) -> None:\n", + " RX(theta=theta, target=q[0])" + ], + "execution_count": 9, + "outputs": [], + "id": "42" + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Combining the two functions into the `main` function:" + ], + "id": "43" + }, + { + "cell_type": "code", + "metadata": {}, + "source": [ + "@qfunc\n", + "def main(input_0: CReal, weight_0: CReal, res: Output[QArray]) -> None:\n", + " allocate(1, res)\n", + " encoding(theta=input_0, q=res) # Loading input\n", + " mixing(theta=weight_0, q=res) # Adjustable parameter" + ], + "execution_count": 10, + "outputs": [], + "id": "44" + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Finally, create a model, synthesize it, and display it in the IDE:" + ], + "id": "45" + }, + { + "cell_type": "code", + "metadata": {}, + "source": [ + "qprog_2 = synthesize(main)\n", + "show(qprog_2)" + ], + "execution_count": 11, + "outputs": [ + { + "output_type": "stream", + "text": [ + "Quantum program link: https://platform.classiq.io/circuit/2zPLS8EIKI59yhuhNxg7NFlKTRn\n" + ] + } + ], + "id": "46" + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### Step 1.2 - Define the Execute and Postprocess Callables" + ], + "id": "47" + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Before using the quantum layer (QLayer), define the `execute` and `post-processing` functions. These functions are essential for integrating the quantum layer in a PyTorch neural network, as classical layers require classical data as input. This means that only after executing the QLayer (the ansatz) and post-processing the results the data can be further used in other layers of the neural network or be output." + ], + "id": "48" + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The `execute` function is straightforward. It takes the quantum program (here, the QLayer) and its parameters, and executes it:" + ], + "id": "49" + }, + { + "cell_type": "code", + "metadata": {}, + "source": [ + "from classiq.applications.qnn.types import (\n", + " MultipleArguments,\n", + " ResultsCollection,\n", + " SavedResult,\n", + ")\n", + "\n", + "\n", + "def execute(\n", + " quantum_program: QuantumProgram, arguments: MultipleArguments\n", + ") -> ResultsCollection:\n", + " return execute_qnn(quantum_program, arguments)" + ], + "execution_count": 12, + "outputs": [ + { + "output_type": "stream", + "text": [ + "gio: https://platform.classiq.io/circuit/2zPLS8EIKI59yhuhNxg7NFlKTRn?login=True&version=0.85.0: Operation not supported\n" + ] + } + ], + "id": "50" + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In general, the `post_process` function is needed to prepare the execution results for output or for loss calculation during the training phase.\n", + "\n", + "In this specific example, it returns the probability of measuring $|0\\rangle$. This function assumes that only the differentiation between the single state $|0\\rangle$ and all other states is relevant. If a different differentiation is needed, modify this function accordingly." + ], + "id": "51" + }, + { + "cell_type": "code", + "metadata": {}, + "source": [ + "import torch\n", + "\n", + "\n", + "def post_process(result: SavedResult) -> torch.Tensor:\n", + " \"\"\"\n", + " Take in a `SavedResult` with `ExecutionDetails` value type, and return the\n", + " probability of measuring |0> which equals the amount of `|0>` measurements\n", + " divided by the total number of measurements.\n", + " \"\"\"\n", + " counts: dict = result.value.counts\n", + " # The probability of measuring |0>\n", + " p_zero: float = counts.get(\"0\", 0.0) / sum(counts.values())\n", + " return torch.tensor(p_zero)" + ], + "execution_count": 13, + "outputs": [], + "id": "52" + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Using these functions allows QLayers and PyTorch layers to be properly integrated into the same neural network." + ], + "id": "53" + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### Step 1.3 - Create a torch.nn.Module Network" + ], + "id": "54" + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Define the `torch.nn.Module` class with a single `QLayer` as follows:" + ], + "id": "55" + }, + { + "cell_type": "code", + "metadata": {}, + "source": [ + "from classiq.applications.qnn import QLayer\n", + "\n", + "\n", + "class Net(torch.nn.Module):\n", + " def __init__(self, *args, **kwargs) -> None:\n", + " super().__init__()\n", + " self.qlayer = QLayer(\n", + " qprog_2, # the quantum program, the result of `synthesize()`\n", + " execute, # a callable that takes\n", + " # - a quantum program\n", + " # - parameters to that program (a tuple of dictionaries)\n", + " # and returns a `ResultsCollection`\n", + " post_process, # a callable that takes\n", + " # - a single `SavedResult`\n", + " # and returns a `torch.Tensor`\n", + " *args,\n", + " **kwargs\n", + " )\n", + "\n", + " def forward(self, x: torch.Tensor) -> torch.Tensor:\n", + " x = self.qlayer(x)\n", + " return x\n", + "\n", + "\n", + "model = Net()" + ], + "execution_count": 14, + "outputs": [], + "id": "56" + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In `self.qlayer = QLayer(...)`, define the only layer in the neural network as a single QLayer. Specify the previously defined `quantum_program`, `execute`, and `post_process` as arguments for the layer. Finally, create the neural network and assign it to the variable `model`." + ], + "id": "57" + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### Step 2 - Choose a Dataset, Loss Function, and Optimizer" + ], + "id": "58" + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "For the loss function and optimizer, use [L1Loss](https://pytorch.org/docs/stable/generated/torch.nn.L1Loss.html) and [SGD](https://pytorch.org/docs/stable/generated/torch.optim.SGD.html), respectively." + ], + "id": "59" + }, + { + "cell_type": "code", + "metadata": {}, + "source": [ + "import torch.nn as nn\n", + "import torch.optim as optim\n", + "\n", + "_LEARNING_RATE = 1\n", + "\n", + "# choosing the data\n", + "data_loader = DATALOADER_NOT\n", + "\n", + "# choosing the loss function\n", + "loss_func = nn.L1Loss() # Mean Absolute Error (MAE)\n", + "\n", + "# choosing the optimizer\n", + "optimizer = optim.SGD(model.parameters(), lr=_LEARNING_RATE)" + ], + "execution_count": 15, + "outputs": [], + "id": "60" + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "
\n", + "Available Optimization Algorithms and Loss Functions\n", + "\n", + "For details of the optimization algorithms and a comprehensive list of loss functions in PyTorch, refer to the official documentation:\n", + "\n", + "- [Optimization Algorithms](https://pytorch.org/docs/stable/optim.html#algorithms)\n", + "- [Loss Functions](https://pytorch.org/docs/stable/nn.html#loss-functions)\n", + "\n", + "
\n" + ], + "id": "61" + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### Step 3 - Train and Evaluate " + ], + "id": "62" + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Import `DataLoader`:" + ], + "id": "63" + }, + { + "cell_type": "code", + "metadata": {}, + "source": [ + "from torch.utils.data import DataLoader" + ], + "execution_count": 16, + "outputs": [], + "id": "64" + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "A `DataLoader` in PyTorch efficiently iterates over datasets, handling batching, shuffling, and parallel data loading. It streamlines the process of training and evaluating models by managing data efficiently." + ], + "id": "65" + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now you are ready to define the training function. \\\n", + "This simple example follows a loop similar to that recommended by PyTorch [here](https://pytorch.org/tutorials/beginner/blitz/neural_networks_tutorial.html#update-the-weights).\n" + ], + "id": "66" + }, + { + "cell_type": "code", + "metadata": {}, + "source": [ + "def train(\n", + " model: nn.Module,\n", + " data_loader: DataLoader,\n", + " loss_func: nn.modules.loss._Loss,\n", + " optimizer: optim.Optimizer,\n", + " epoch: int = 5, # About 40 epochs needed for full training\n", + ") -> None:\n", + " for index in range(epoch):\n", + " print(index, model.qlayer.weight)\n", + " for data, label in data_loader:\n", + " optimizer.zero_grad()\n", + "\n", + " output = model(data)\n", + "\n", + " loss = loss_func(output, label)\n", + " loss.backward()\n", + " optimizer.step()" + ], + "execution_count": 17, + "outputs": [], + "id": "67" + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here, trained parameters are loaded for demonstration, and only one epoch is performed.\\\n", + "You may comment on the following cell, change the number of epochs above, and expect about 40 epochs for full training for non-trained parameters." + ], + "id": "68" + }, + { + "cell_type": "code", + "metadata": {}, + "source": [ + "with torch.no_grad():\n", + " model.qlayer.weight.copy_(\n", + " torch.tensor([3])\n", + " ) # The value from the last step of the training" + ], + "execution_count": 18, + "outputs": [], + "id": "69" + }, + { + "cell_type": "code", + "metadata": {}, + "source": [ + "train(model, data_loader, loss_func, optimizer)" + ], + "execution_count": 19, + "outputs": [ + { + "output_type": "stream", + "text": [ + "0 Parameter containing:\n", + "tensor([3.], requires_grad=True)\n", + "1 Parameter containing:\n", + "tensor([3.0488], requires_grad=True)\n", + "2 Parameter containing:\n", + "tensor([3.1465], requires_grad=True)\n", + "3 Parameter containing:\n", + "tensor([3.1465], requires_grad=True)\n", + "4 Parameter containing:\n", + "tensor([3.1465], requires_grad=True)\n" + ] + } + ], + "id": "70" + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Great!Observe that the parameter is approximately equal to $\\pi$. \\\n", + "Now, test the network accuracy using the suggested method [here](https://stackoverflow.com/questions/52176178/pytorch-model-accuracy-test#answer-64838681)." + ], + "id": "71" + }, + { + "cell_type": "code", + "metadata": {}, + "source": [ + "def check_accuracy(model: nn.Module, data_loader: DataLoader, atol=1e-2) -> float:\n", + " num_correct = 0\n", + " total = 0\n", + " model.eval()\n", + "\n", + " with torch.no_grad(): # Temporarily disable gradient calculation\n", + " for data, labels in data_loader:\n", + " # Let the model predict\n", + " predictions = model(data)\n", + "\n", + " # Get a tensor of Booleans, indicating if each label is close to the real label\n", + " is_prediction_correct = predictions.isclose(labels, atol=atol)\n", + "\n", + " # Count the number of `True` predictions\n", + " num_correct += is_prediction_correct.sum().item()\n", + " # Count the total evaluations\n", + " # the first dimension of `labels` is `batch_size`\n", + " total += labels.size(0)\n", + "\n", + " accuracy = float(num_correct) / float(total)\n", + " print(f\"Test Accuracy of the model: {accuracy*100:.2f}%\")\n", + " return accuracy" + ], + "execution_count": 20, + "outputs": [], + "id": "72" + }, + { + "cell_type": "code", + "metadata": {}, + "source": [ + "check_accuracy(model, data_loader)" + ], + "execution_count": 21, + "outputs": [ + { + "output_type": "stream", + "text": [ + "Test Accuracy of the model: 100.00%\n" + ] + }, + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "1.0" + ] + } + } + ], + "id": "73" + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**The results show an accuracy of 1**, indicating a 100% success rate in performing the required transformation (i.e., the network learned to perform an X-gate). You can further validate this by printing the value of `model.qlayer.weight`, which is a tensor of shape (1,1). After training, this value should be close to $\\pi$." + ], + "id": "74" + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Summary and Exercise " + ], + "id": "75" + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In this tutorial, you integrated a quantum layer in a PyTorch neural network, defined the necessary execution and post-processing functions, and trained the model using a simple dataset. You tested the network's accuracy using a recommended method. To explore further, try experimenting with different quantum circuits, datasets, and optimizers. Integrating more classic layers or more complex layers should be straightforward now for those with experience in PyTorch." + ], + "id": "76" + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "
\n", + "Exercise - Training U Gate\n", + "\n", + "Now, for practice, implement a similar case to the last example, but this time train the U gate to act as a NOT gate instead of the Rx gate. \n", + "How many parameters must you train? \n", + "What must you change to accomplish this?\n", + "\n", + "
\n", + "Hint\n", + " \n", + "You only have to adapt `mixing` and `model`.\n", + "\n", + "
\n", + "
\n" + ], + "id": "77" + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Read More \n", + "" + ], + "id": "78" + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Algorithms and application tutorials using the PyTorch integration:\n", + "- [Quantum Autoencoder](https://docs.classiq.io/latest/explore/algorithms/QML/quantum_autoencoder/quantum_autoencoder/)\n", + "- [QGAN](https://docs.classiq.io/latest/explore/algorithms/QML/qgan/qgan_bars_and_strips/)\n", + "\n", + "Further reading from the reference manual: \n", + "- [QNNs with Classiq](https://docs.classiq.io/latest/user-guide/applications/qml/qnn/)\n", + "- [QLayer](https://docs.classiq.io/latest/user-guide/applications/qml/qnn/qlayer/)" + ], + "id": "79" + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Using QSVM Primitive " + ], + "id": "80" + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Classiq also enables executing classification tasks using the **Quantum Support Vector Machine** (QSVM) module. This module leverages the principles of quantum computing to enhance traditional support vector machine algorithms, offering significant improvements in classification accuracy and efficiency. The QSVM module integrates seamlessly with the Classiq platform, allowing you to implement quantum-enhanced classification models effortlessly. By utilizing quantum kernels, the QSVM can handle complex datasets and capture intricate patterns that may be challenging for classical SVMs, making it a powerful tool for machine learning applications.\n", + "\n" + ], + "id": "81" + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "To understand how to use it and explore it further, examine this example: [QSVM with Classiq](https://docs.classiq.io/latest/explore/algorithms/QML/qsvm/qsvm/)." + ], + "id": "82" + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## References" + ], + "id": "83" + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "[1]: [Peruzzo, A., McClean, J., Shadbolt, P., et al. (2014). A variational eigenvalue solver on a photonic quantum processor, *Nature Communications*](https://doi.org/10.1038/ncomms5213).\n", + "\n", + "[2]: [Cerezo, M., Arrasmith, A., Babbush, R., et al. (2021). Variational quantum algorithms, *Nature Reviews Physics*, 3, 625–644](https://doi.org/10.1038/s42254-021-00348-9).\n", + "\n", + "[3]: [Corresponding preprint arXiv:2104.02281](https://arxiv.org/abs/2104.02281).\n", + "\n", + "[4]: [Barkoutsos, Panagiotis Kl., et al. (2020). Improving variational quantum optimization using CVaR, *Quantum* 4, 256](https://doi.org/10.22331/q-2020-04-20-256)." + ], + "id": "84" } - ], - "source": [ - "train(model, data_loader, loss_func, optimizer)" - ] - }, - { - "cell_type": "markdown", - "id": "71", - "metadata": {}, - "source": [ - "Great!Observe that the parameter is approximately equal to $\\pi$. \\\n", - "Now, test the network accuracy using the suggested method [here](https://stackoverflow.com/questions/52176178/pytorch-model-accuracy-test#answer-64838681)." - ] - }, - { - "cell_type": "code", - "execution_count": 20, - "id": "72", - "metadata": {}, - "outputs": [], - "source": [ - "def check_accuracy(model: nn.Module, data_loader: DataLoader, atol=1e-2) -> float:\n", - " num_correct = 0\n", - " total = 0\n", - " model.eval()\n", - "\n", - " with torch.no_grad(): # Temporarily disable gradient calculation\n", - " for data, labels in data_loader:\n", - " # Let the model predict\n", - " predictions = model(data)\n", - "\n", - " # Get a tensor of Booleans, indicating if each label is close to the real label\n", - " is_prediction_correct = predictions.isclose(labels, atol=atol)\n", - "\n", - " # Count the number of `True` predictions\n", - " num_correct += is_prediction_correct.sum().item()\n", - " # Count the total evaluations\n", - " # the first dimension of `labels` is `batch_size`\n", - " total += labels.size(0)\n", - "\n", - " accuracy = float(num_correct) / float(total)\n", - " print(f\"Test Accuracy of the model: {accuracy*100:.2f}%\")\n", - " return accuracy" - ] - }, - { - "cell_type": "code", - "execution_count": 21, - "id": "73", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Test Accuracy of the model: 100.00%\n" - ] - }, - { - "data": { - "text/plain": [ - "1.0" - ] - }, - "execution_count": 21, - "metadata": {}, - "output_type": "execute_result" + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.11.9" } - ], - "source": [ - "check_accuracy(model, data_loader)" - ] - }, - { - "cell_type": "markdown", - "id": "74", - "metadata": {}, - "source": [ - "**The results show an accuracy of 1**, indicating a 100% success rate in performing the required transformation (i.e., the network learned to perform an X-gate). You can further validate this by printing the value of `model.qlayer.weight`, which is a tensor of shape (1,1). After training, this value should be close to $\\pi$." - ] - }, - { - "cell_type": "markdown", - "id": "75", - "metadata": {}, - "source": [ - "### Summary and Exercise " - ] - }, - { - "cell_type": "markdown", - "id": "76", - "metadata": {}, - "source": [ - "In this tutorial, you integrated a quantum layer in a PyTorch neural network, defined the necessary execution and post-processing functions, and trained the model using a simple dataset. You tested the network's accuracy using a recommended method. To explore further, try experimenting with different quantum circuits, datasets, and optimizers. Integrating more classic layers or more complex layers should be straightforward now for those with experience in PyTorch." - ] - }, - { - "cell_type": "markdown", - "id": "77", - "metadata": {}, - "source": [ - "
\n", - "Exercise - Training U Gate\n", - "\n", - "Now, for practice, implement a similar case to the last example, but this time train the U gate to act as a NOT gate instead of the Rx gate. \n", - "How many parameters must you train? \n", - "What must you change to accomplish this?\n", - "\n", - "
\n", - "Hint\n", - " \n", - "You only have to adapt `mixing` and `model`.\n", - "\n", - "
\n", - "
\n" - ] - }, - { - "cell_type": "markdown", - "id": "78", - "metadata": {}, - "source": [ - "### Read More \n", - "" - ] - }, - { - "cell_type": "markdown", - "id": "79", - "metadata": {}, - "source": [ - "Algorithms and application tutorials using the PyTorch integration:\n", - "- [Quantum Autoencoder](https://docs.classiq.io/latest/explore/algorithms/QML/quantum_autoencoder/quantum_autoencoder/)\n", - "- [QGAN](https://docs.classiq.io/latest/explore/algorithms/QML/qgan/qgan_bars_and_strips/)\n", - "\n", - "Further reading from the reference manual: \n", - "- [QNNs with Classiq](https://docs.classiq.io/latest/user-guide/applications/qml/qnn/)\n", - "- [QLayer](https://docs.classiq.io/latest/user-guide/applications/qml/qnn/qlayer/)" - ] - }, - { - "cell_type": "markdown", - "id": "80", - "metadata": {}, - "source": [ - "## Using QSVM Primitive " - ] - }, - { - "cell_type": "markdown", - "id": "81", - "metadata": {}, - "source": [ - "Classiq also enables executing classification tasks using the **Quantum Support Vector Machine** (QSVM) module. This module leverages the principles of quantum computing to enhance traditional support vector machine algorithms, offering significant improvements in classification accuracy and efficiency. The QSVM module integrates seamlessly with the Classiq platform, allowing you to implement quantum-enhanced classification models effortlessly. By utilizing quantum kernels, the QSVM can handle complex datasets and capture intricate patterns that may be challenging for classical SVMs, making it a powerful tool for machine learning applications.\n", - "\n" - ] - }, - { - "cell_type": "markdown", - "id": "82", - "metadata": {}, - "source": [ - "To understand how to use it and explore it further, examine this example: [QSVM with Classiq](https://docs.classiq.io/latest/explore/algorithms/QML/qsvm/qsvm/)." - ] - }, - { - "cell_type": "markdown", - "id": "83", - "metadata": {}, - "source": [ - "## References" - ] - }, - { - "cell_type": "markdown", - "id": "84", - "metadata": {}, - "source": [ - "[1]: [Peruzzo, A., McClean, J., Shadbolt, P., et al. (2014). A variational eigenvalue solver on a photonic quantum processor, *Nature Communications*](https://doi.org/10.1038/ncomms5213).\n", - "\n", - "[2]: [Cerezo, M., Arrasmith, A., Babbush, R., et al. (2021). Variational quantum algorithms, *Nature Reviews Physics*, 3, 625–644](https://doi.org/10.1038/s42254-021-00348-9).\n", - "\n", - "[3]: [Corresponding preprint arXiv:2104.02281](https://arxiv.org/abs/2104.02281).\n", - "\n", - "[4]: [Barkoutsos, Panagiotis Kl., et al. (2020). Improving variational quantum optimization using CVaR, *Quantum* 4, 256](https://doi.org/10.22331/q-2020-04-20-256)." - ] - } - ], - "metadata": { - "kernelspec": { - "display_name": "Python 3 (ipykernel)", - "language": "python", - "name": "python3" }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.11.9" - } - }, - "nbformat": 4, - "nbformat_minor": 9 -} + "nbformat": 4, + "nbformat_minor": 9 +} \ No newline at end of file