From db7bd4fa6cc00970a74dad9fad1b3a192680ddde Mon Sep 17 00:00:00 2001 From: achebiyam <147682912+achebiyam@users.noreply.github.com> Date: Mon, 16 Mar 2026 02:04:49 -0700 Subject: [PATCH 1/7] Create README.md --- .../hubbard_holstein_gqsp/README.md | 16 ++++++++++++++++ 1 file changed, 16 insertions(+) create mode 100644 community/paper_implementations/hubbard_holstein_gqsp/README.md diff --git a/community/paper_implementations/hubbard_holstein_gqsp/README.md b/community/paper_implementations/hubbard_holstein_gqsp/README.md new file mode 100644 index 000000000..ee6860f2d --- /dev/null +++ b/community/paper_implementations/hubbard_holstein_gqsp/README.md @@ -0,0 +1,16 @@ +# GQSP-Based Hamiltonian Simulation for the Hubbard-Holstein Model + +**Author:** @achebiyam + +First application of Generalized Quantum Signal Processing (GQSP) to an +electron-phonon coupled system. Implements GQSP-based Hamiltonian simulation +of the Hubbard-Holstein model on the Classiq platform, with resource comparison +against Suzuki-Trotter and VQE. + +## Reference Papers +- D. Motlagh and N. Wiebe, "Generalized Quantum Signal Processing", PRX Quantum 5, 020368 (2024) +- C. F. Kane et al., "Block encoding bosons by signal processing", Quantum 9, 1747 (2025) +- M. M. Denner et al., "A hybrid quantum-classical method for electron-phonon systems", Commun. Phys. 6, 233 (2023) + +## Contents +- `hubbard_holstein_gqsp.ipynb` — Main notebook with full implementation and results From 62086a4e687a8bc2bd198b464fc1de90ea8f9ac0 Mon Sep 17 00:00:00 2001 From: achebiyam <147682912+achebiyam@users.noreply.github.com> Date: Mon, 16 Mar 2026 02:06:49 -0700 Subject: [PATCH 2/7] Add files via upload --- .../hubbard_holstein_gqsp.ipynb | 1243 +++++++++++++++++ 1 file changed, 1243 insertions(+) create mode 100644 community/paper_implementations/hubbard_holstein_gqsp/hubbard_holstein_gqsp.ipynb diff --git a/community/paper_implementations/hubbard_holstein_gqsp/hubbard_holstein_gqsp.ipynb b/community/paper_implementations/hubbard_holstein_gqsp/hubbard_holstein_gqsp.ipynb new file mode 100644 index 000000000..c76107c0e --- /dev/null +++ b/community/paper_implementations/hubbard_holstein_gqsp/hubbard_holstein_gqsp.ipynb @@ -0,0 +1,1243 @@ +{ + "nbformat": 4, + "nbformat_minor": 5, + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "name": "python", + "version": "3.12.0" + }, + "colab": { + "provenance": [] + } + }, + "cells": [ + { + "cell_type": "markdown", + "metadata": { + "id": "So8MPMJNoumC" + }, + "source": [ + "# GQSP-Based Hamiltonian Simulation for the Hubbard-Holstein Model\n", + "\n", + "**Author:** @achebiyam \n", + "**Classiq Paper Implementation Challenge**\n", + "\n", + "This notebook demonstrates the first application of **Generalized Quantum Signal Processing (GQSP)** to an electron-phonon coupled system — the Hubbard-Holstein model. We implement GQSP-based Hamiltonian simulation on the Classiq platform, compare resources against Suzuki-Trotter product formulas and VQE, and verify all results against exact diagonalization.\n", + "\n", + "**Primary Reference:** D. Motlagh and N. Wiebe, *Generalized Quantum Signal Processing*, PRX Quantum **5**, 020368 (2024). [arXiv:2308.01501](https://arxiv.org/abs/2308.01501)\n", + "\n", + "**Supporting References:**\n", + "- V. Khinevich et al., *Quantum Power Iteration Unified Using GQSP*, arXiv:2507.11142 (2025)\n", + "- C. F. Kane et al., *Block encoding bosons by signal processing*, Quantum **9**, 1747 (2025)\n", + "- M. M. Denner et al., *A hybrid quantum-classical method for electron-phonon systems*, Commun. Phys. **6**, 233 (2023)\n", + "- A. Kan and B. Symons, *Resource-optimized fault-tolerant simulation of the Fermi-Hubbard model*, npj Quantum Inf. **11**, 138 (2025)" + ], + "id": "So8MPMJNoumC" + }, + { + "cell_type": "markdown", + "metadata": { + "id": "6Tw_QV59oumD" + }, + "source": [ + "## 1. Setup and Installation" + ], + "id": "6Tw_QV59oumD" + }, + { + "cell_type": "code", + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "2TppEB8koumD", + "outputId": "f4dc0538-6fb1-4150-d8a8-9de17aa1ad50" + }, + "source": [ + "!pip install \"classiq[qsp]\" keyrings.alt pennylane -q\n", + "\n", + "import keyring\n", + "from keyrings.alt.file import PlaintextKeyring\n", + "keyring.set_keyring(PlaintextKeyring())" + ], + "outputs": [ + { + "output_type": "stream", + "name": "stdout", + "text": [ + "\u001b[2K \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m91.9/91.9 kB\u001b[0m \u001b[31m3.8 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n", + "\u001b[2K \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m87.0/87.0 kB\u001b[0m \u001b[31m1.7 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n", + "\u001b[?25h Preparing metadata (setup.py) ... \u001b[?25l\u001b[?25hdone\n", + "\u001b[2K \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m57.3/57.3 kB\u001b[0m \u001b[31m2.3 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n", + "\u001b[2K \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m45.0/45.0 kB\u001b[0m \u001b[31m1.4 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n", + "\u001b[2K \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m5.3/5.3 MB\u001b[0m \u001b[31m38.5 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n", + "\u001b[2K \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m935.6/935.6 kB\u001b[0m \u001b[31m20.5 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n", + "\u001b[2K \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m167.9/167.9 kB\u001b[0m \u001b[31m4.9 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n", + "\u001b[2K \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m1.8/1.8 MB\u001b[0m \u001b[31m35.5 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n", + "\u001b[2K \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m1.4/1.4 MB\u001b[0m \u001b[31m18.5 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n", + "\u001b[2K \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m53.0/53.0 kB\u001b[0m \u001b[31m2.3 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n", + "\u001b[2K \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m2.5/2.5 MB\u001b[0m \u001b[31m82.3 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n", + "\u001b[2K \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m4.4/4.4 MB\u001b[0m \u001b[31m84.6 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n", + "\u001b[2K \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m2.2/2.2 MB\u001b[0m \u001b[31m60.3 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n", + "\u001b[2K \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m5.4/5.4 MB\u001b[0m \u001b[31m98.0 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n", + "\u001b[2K \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m651.7/651.7 kB\u001b[0m \u001b[31m30.6 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n", + "\u001b[2K \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m55.2/55.2 kB\u001b[0m \u001b[31m3.5 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n", + "\u001b[2K \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m269.8/269.8 kB\u001b[0m \u001b[31m17.4 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n", + "\u001b[2K \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m8.8/8.8 MB\u001b[0m \u001b[31m97.5 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n", + "\u001b[2K \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m49.6/49.6 kB\u001b[0m \u001b[31m2.3 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n", + "\u001b[2K \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m72.5/72.5 kB\u001b[0m \u001b[31m2.5 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n", + "\u001b[?25h Building wheel for pyqsp (setup.py) ... \u001b[?25l\u001b[?25hdone\n", + "\u001b[31mERROR: pip's dependency resolver does not currently take into account all the packages that are installed. This behaviour is the source of the following dependency conflicts.\n", + "google-cloud-bigquery 3.40.1 requires packaging>=24.2.0, but you have packaging 23.2 which is incompatible.\n", + "db-dtypes 1.5.0 requires packaging>=24.2.0, but you have packaging 23.2 which is incompatible.\n", + "xarray 2025.12.0 requires packaging>=24.1, but you have packaging 23.2 which is incompatible.\u001b[0m\u001b[31m\n", + "\u001b[0m" + ] + } + ], + "execution_count": 1, + "id": "2TppEB8koumD" + }, + { + "cell_type": "code", + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "2Z9HCIzaoumE", + "outputId": "089d1b48-72e9-4a54-f661-716df78aad5e" + }, + "source": [ + "import classiq\n", + "classiq.authenticate()" + ], + "outputs": [ + { + "output_type": "stream", + "name": "stdout", + "text": [ + "If a browser doesn't automatically open, please visit this URL from any trusted device to authenticate: https://auth.classiq.io/authorize?client_id=f6721qMOVoDAOVkzrv8YaWassRKSFX6Y&response_type=code&audience=https%3A%2F%2Fcadmium-be&redirect_uri=https%3A%2F%2Fauth.classiq.io%2Factivate%3Fuser_code%3DRWHZ-MZKM&scope=offline_access\n", + "Your user code: RWHZ-MZKM\n" + ] + } + ], + "execution_count": 2, + "id": "2Z9HCIzaoumE" + }, + { + "cell_type": "markdown", + "metadata": { + "id": "T3fGYM_coumE" + }, + "source": [ + "## 2. Imports and Core Utilities" + ], + "id": "T3fGYM_coumE" + }, + { + "cell_type": "code", + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "Qx4hxpmnoumE", + "outputId": "652c4644-c9f2-4993-d093-2e2a8987fd27" + }, + "source": [ + "import time\n", + "import numpy as np\n", + "import scipy\n", + "import matplotlib.pyplot as plt\n", + "from itertools import product as iter_product\n", + "from scipy.special import jv\n", + "from classiq import *\n", + "from classiq.qmod.symbolic import pi\n", + "from classiq.applications.qsp.qsp import (\n", + " gqsp_phases,\n", + " poly_jacobi_anger_degree,\n", + " poly_jacobi_anger_exp_cos,\n", + " poly_jacobi_anger_cos,\n", + " poly_jacobi_anger_sin,\n", + ")\n", + "\n", + "# Pauli matrices\n", + "I_single = np.eye(2, dtype=complex)\n", + "sigma_x = np.array([[0,1],[1,0]], dtype=complex)\n", + "sigma_y = np.array([[0,-1j],[1j,0]], dtype=complex)\n", + "sigma_z = np.array([[1,0],[0,-1]], dtype=complex)\n", + "\n", + "pauli_labels = ['I', 'X', 'Y', 'Z']\n", + "pauli_matrices = {'I': I_single, 'X': sigma_x, 'Y': sigma_y, 'Z': sigma_z}\n", + "\n", + "def kron_list(ops):\n", + " result = ops[0]\n", + " for op in ops[1:]:\n", + " result = np.kron(result, op)\n", + " return result\n", + "\n", + "def decompose_to_pauli_strings(H_matrix, n_qubits, threshold=1e-10):\n", + " dim = 2**n_qubits\n", + " terms = []\n", + " for indices in iter_product(range(4), repeat=n_qubits):\n", + " label = ''.join(pauli_labels[i] for i in indices)\n", + " P = kron_list([pauli_matrices[pauli_labels[i]] for i in indices])\n", + " coeff = np.trace(P @ H_matrix).real / dim\n", + " if abs(coeff) > threshold:\n", + " terms.append((coeff, label))\n", + " return terms\n", + "\n", + "pauli_map = {'I': Pauli.I, 'X': Pauli.X, 'Y': Pauli.Y, 'Z': Pauli.Z}\n", + "\n", + "def pauli_string_to_classiq(label):\n", + " reversed_label = label[::-1]\n", + " op = pauli_map[reversed_label[0]](0)\n", + " for i, c in enumerate(reversed_label[1:], 1):\n", + " op = op * pauli_map[c](i)\n", + " return op\n", + "\n", + "# Classiq helpers\n", + "@qfunc\n", + "def my_reflect_about_zero(qba: QNum):\n", + " control(qba == 0, lambda: phase(pi))\n", + " phase(pi)\n", + "\n", + "execution_preferences = ExecutionPreferences(\n", + " num_shots=1,\n", + " backend_preferences=ClassiqBackendPreferences(\n", + " backend_name=ClassiqSimulatorBackendNames.SIMULATOR_STATEVECTOR\n", + " ),\n", + ")\n", + "\n", + "def get_projected_state_vector(res):\n", + " state_size = 2 ** len(res.output_qubits_map['data'])\n", + " proj = np.zeros(state_size).astype(complex)\n", + " df = res.dataframe\n", + " filtered = df[(df.block == 0) & (np.abs(df.amplitude) > 1e-12)]\n", + " proj[filtered.data] = filtered.amplitude\n", + " return proj\n", + "\n", + "def compare_quantum_classical_states(expected, resulted, post_selection_factor):\n", + " relative_phase = np.angle(expected[0] / resulted[0])\n", + " resulted = resulted * np.exp(1j * relative_phase)\n", + " renormalized = post_selection_factor * resulted\n", + " overlap = np.vdot(renormalized, expected) / np.linalg.norm(renormalized) / np.linalg.norm(expected)\n", + " return renormalized, abs(overlap)\n", + "\n", + "print('All imports and utilities loaded.')" + ], + "outputs": [ + { + "output_type": "stream", + "name": "stdout", + "text": [ + "All imports and utilities loaded.\n" + ] + } + ], + "execution_count": 3, + "id": "Qx4hxpmnoumE" + }, + { + "cell_type": "markdown", + "metadata": { + "id": "8gbWuK8boumF" + }, + "source": [ + "## 3. Verify GQSP Pipeline on Toy Hamiltonian\n", + "\n", + "Before applying GQSP to the Hubbard-Holstein model, we verify the full pipeline on a simple 2-qubit Hamiltonian from Classiq's documentation." + ], + "id": "8gbWuK8boumF" + }, + { + "cell_type": "code", + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "xhgDK0P1oumF", + "outputId": "ee1d7144-5891-4d2e-e5e5-26d4fef7e9fd" + }, + "source": [ + "# Toy Hamiltonian from Classiq's GQSP example\n", + "TOY_HAM = 0.4*Pauli.I(0) + 0.1*Pauli.Z(1) + 0.05*Pauli.X(0)*Pauli.X(1) + 0.2*Pauli.Z(0)*Pauli.Z(1)\n", + "TOY_TIME = 22; TOY_EPS = 1e-7\n", + "\n", + "toy_data = TOY_HAM.num_qubits\n", + "toy_block = (len(TOY_HAM.terms)-1).bit_length()\n", + "toy_scaling = np.sum(np.abs([t.coefficient for t in TOY_HAM.terms]))\n", + "\n", + "class ToyBE(QStruct):\n", + " data: QNum[toy_data]\n", + " block: QNum[toy_block]\n", + "\n", + "@qfunc\n", + "def toy_be(state: ToyBE):\n", + " lcu_pauli(TOY_HAM * (1/toy_scaling), state.data, state.block)\n", + "\n", + "@qfunc\n", + "def toy_walk(be_qfunc: QCallable[ToyBE], state: ToyBE):\n", + " be_qfunc(state)\n", + " my_reflect_about_zero(state.block)\n", + "\n", + "# GQSP phases\n", + "GQSP_SCALE = 0.99\n", + "toy_degree = poly_jacobi_anger_degree(TOY_EPS, TOY_TIME * toy_scaling)\n", + "toy_poly = GQSP_SCALE * poly_jacobi_anger_exp_cos(toy_degree, -TOY_TIME * toy_scaling)\n", + "toy_phases = gqsp_phases(toy_poly)\n", + "\n", + "class ToyGBlock(QStruct):\n", + " block_ham: QNum[toy_block]\n", + " block_gqsp: QBit\n", + "\n", + "class ToyGState(QStruct):\n", + " data: QNum[toy_data]\n", + " block: ToyGBlock\n", + "\n", + "@qfunc\n", + "def toy_gqsp(be_qfunc: QCallable[ToyBE], state: ToyGState):\n", + " gqsp(u=lambda: toy_walk(be_qfunc, [state.data, state.block.block_ham]),\n", + " aux=state.block.block_gqsp, phases=toy_phases, negative_power=toy_degree)\n", + "\n", + "np.random.seed(42)\n", + "toy_init = np.random.rand(2**toy_data)\n", + "toy_init = (toy_init / np.linalg.norm(toy_init)).tolist()\n", + "toy_matrix = pauli_operator_to_matrix(TOY_HAM)\n", + "toy_expected = scipy.linalg.expm(-1j * toy_matrix * TOY_TIME) @ toy_init\n", + "\n", + "@qfunc\n", + "def main(data: Output[QNum[toy_data]], block: Output[QNum[toy_block + 1]]):\n", + " state = ToyGState(); allocate(state)\n", + " inplace_prepare_amplitudes(toy_init, 0.0, state.data)\n", + " toy_gqsp(toy_be, state)\n", + " bind(state, [data, block])\n", + "\n", + "qprog_toy = synthesize(main)\n", + "with ExecutionSession(qprog_toy, execution_preferences) as es:\n", + " res_toy = es.sample()\n", + "\n", + "state_toy = get_projected_state_vector(res_toy)\n", + "_, overlap_toy = compare_quantum_classical_states(toy_expected, state_toy, 1/GQSP_SCALE)\n", + "print(f'Toy Hamiltonian GQSP overlap: {overlap_toy:.10f}')\n", + "assert overlap_toy > 0.999, 'Toy verification failed!'\n", + "print('Pipeline verified.')" + ], + "outputs": [ + { + "output_type": "stream", + "name": "stdout", + "text": [ + "Toy Hamiltonian GQSP overlap: 1.0000000000\n", + "Pipeline verified.\n" + ] + } + ], + "execution_count": 4, + "id": "xhgDK0P1oumF" + }, + { + "cell_type": "markdown", + "metadata": { + "id": "aLN33DzmoumF" + }, + "source": [ + "## 4. Hubbard-Holstein Hamiltonian Construction\n", + "\n", + "The Hubbard-Holstein model describes electrons coupled to lattice phonons:\n", + "\n", + "$$H = -t\\sum_{\\langle i,j\\rangle,\\sigma}(c^\\dagger_{i\\sigma}c_{j\\sigma} + \\text{h.c.}) + U\\sum_i n_{i\\uparrow}n_{i\\downarrow} + \\omega\\sum_i b^\\dagger_i b_i + g\\sum_i n_i(b^\\dagger_i + b_i)$$\n", + "\n", + "We build this for a 2-site model with parameters $t=1.0$, $U=2.0$, $\\omega=1.0$, $g=0.5$." + ], + "id": "aLN33DzmoumF" + }, + { + "cell_type": "code", + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "fnO4KM4-oumG", + "outputId": "8b8346ba-022a-4f29-bfde-99783741ace2" + }, + "source": [ + "# Model parameters\n", + "t_hop = 1.0; U_hub = 2.0; omega = 1.0; g_coup = 0.5\n", + "n_sites = 2; n_fermi_qubits = 2 * n_sites\n", + "\n", + "# ======== 8-qubit model (N_max=2) ========\n", + "N_max = 2\n", + "n_phonon_states = N_max + 1\n", + "n_bq_per_site = int(np.ceil(np.log2(n_phonon_states)))\n", + "n_boson_qubits = n_bq_per_site * n_sites\n", + "n_total_qubits = n_fermi_qubits + n_boson_qubits\n", + "dim_total = 2**n_total_qubits\n", + "dim_padded = 2**n_bq_per_site\n", + "\n", + "# Bosonic operators (truncated, padded)\n", + "b_op = np.zeros((dim_padded, dim_padded), dtype=complex)\n", + "for n in range(1, n_phonon_states): b_op[n-1, n] = np.sqrt(n)\n", + "b_dag_op = b_op.T.copy()\n", + "n_b_op = b_dag_op @ b_op\n", + "x_op = b_dag_op + b_op\n", + "\n", + "# Fermionic operators (8-qubit space)\n", + "def fermi_number_op(j):\n", + " ops = [I_single]*n_total_qubits; ops[j] = (I_single - sigma_z)/2; return kron_list(ops)\n", + "\n", + "def fermi_create_op(j):\n", + " ops = [I_single]*n_total_qubits\n", + " for k in range(j): ops[k] = sigma_z\n", + " ops[j] = (sigma_x - 1j*sigma_y)/2\n", + " return kron_list(ops)\n", + "\n", + "def fermi_annihilate_op(j): return fermi_create_op(j).conj().T\n", + "\n", + "def boson_op_on_full_space(op_2q, site):\n", + " if site == 0:\n", + " return np.kron(np.kron(np.eye(2**n_fermi_qubits), op_2q), np.eye(2**n_bq_per_site))\n", + " else:\n", + " return np.kron(np.eye(2**n_fermi_qubits * 2**n_bq_per_site), op_2q)\n", + "\n", + "# Build H\n", + "H_hop = np.zeros((dim_total, dim_total), dtype=complex)\n", + "for s in [0,1]:\n", + " H_hop += -t_hop*(fermi_create_op(s)@fermi_annihilate_op(2+s) + fermi_create_op(2+s)@fermi_annihilate_op(s))\n", + "H_int = sum(U_hub*(fermi_number_op(2*site)@fermi_number_op(2*site+1)) for site in range(n_sites))\n", + "H_phonon = sum(omega*boson_op_on_full_space(n_b_op, site) for site in range(n_sites))\n", + "H_coupling = sum(g_coup*((fermi_number_op(2*site)+fermi_number_op(2*site+1))@boson_op_on_full_space(x_op, site)) for site in range(n_sites))\n", + "H_full = H_hop + H_int + H_phonon + H_coupling\n", + "\n", + "assert np.allclose(H_full, H_full.conj().T)\n", + "eigenvalues = np.linalg.eigvalsh(H_full)\n", + "print(f'8-qubit Hubbard-Holstein (N_max=2): Hermitian, dim={H_full.shape[0]}')\n", + "print(f'Ground state energy: {eigenvalues[0]:.6f}')\n", + "print(f'Spectral norm: {np.max(np.abs(eigenvalues)):.4f}')\n", + "\n", + "# Pauli decomposition\n", + "print('\\nDecomposing to Pauli strings (this takes ~2 min for 8 qubits)...')\n", + "pauli_terms = decompose_to_pauli_strings(H_full, n_total_qubits)\n", + "print(f'Pauli terms: {len(pauli_terms)}')\n", + "\n", + "# Classiq Hamiltonian\n", + "terms_8q = [(c, pauli_string_to_classiq(l)) for c, l in pauli_terms]\n", + "HH_8Q = terms_8q[0][0] * terms_8q[0][1]\n", + "for c, op in terms_8q[1:]: HH_8Q = HH_8Q + c * op\n", + "print(f'Classiq match error: {np.linalg.norm(pauli_operator_to_matrix(HH_8Q) - H_full):.2e}')\n", + "\n", + "# ======== 5-qubit model (1 phonon mode, N_max=1) ========\n", + "n_5q = 5; dim_5q = 2**n_5q\n", + "def fnum5(j):\n", + " ops=[I_single]*5; ops[j]=(I_single-sigma_z)/2; return kron_list(ops)\n", + "def fcr5(j):\n", + " ops=[I_single]*5\n", + " for k in range(j): ops[k]=sigma_z\n", + " ops[j]=(sigma_x-1j*sigma_y)/2; return kron_list(ops)\n", + "def fan5(j): return fcr5(j).conj().T\n", + "\n", + "H_5q = np.zeros((dim_5q,dim_5q),dtype=complex)\n", + "for s in [0,1]: H_5q += -t_hop*(fcr5(s)@fan5(2+s)+fcr5(2+s)@fan5(s))\n", + "for site in range(2): H_5q += U_hub*(fnum5(2*site)@fnum5(2*site+1))\n", + "H_5q += omega*np.kron(np.eye(16),(I_single-sigma_z)/2)\n", + "H_5q += g_coup*((fnum5(0)+fnum5(1))@np.kron(np.eye(16),sigma_x))\n", + "\n", + "pt_5q = decompose_to_pauli_strings(H_5q, 5)\n", + "alpha_5q = sum(abs(c) for c,_ in pt_5q)\n", + "terms_5q_c = [(c, pauli_string_to_classiq(l)) for c, l in pt_5q]\n", + "HP1_HAM = terms_5q_c[0][0]*terms_5q_c[0][1]\n", + "for c,op in terms_5q_c[1:]: HP1_HAM = HP1_HAM + c*op\n", + "\n", + "print(f'\\n5-qubit HH (1 phonon): {len(pt_5q)} terms, α={alpha_5q:.4f}')\n", + "print(f'Match error: {np.linalg.norm(pauli_operator_to_matrix(HP1_HAM)-H_5q):.2e}')" + ], + "outputs": [ + { + "output_type": "stream", + "name": "stdout", + "text": [ + "8-qubit Hubbard-Holstein (N_max=2): Hermitian, dim=256\n", + "Ground state energy: -1.753867\n", + "Spectral norm: 10.2298\n", + "\n", + "Decomposing to Pauli strings (this takes ~2 min for 8 qubits)...\n", + "Pauli terms: 41\n", + "Classiq match error: 5.46e-15\n", + "\n", + "5-qubit HH (1 phonon): 15 terms, α=8.0000\n", + "Match error: 0.00e+00\n" + ] + } + ], + "execution_count": 5, + "id": "fnO4KM4-oumG" + }, + { + "cell_type": "markdown", + "metadata": { + "id": "4gvCcHVNoumG" + }, + "source": [ + "## 5. GQSP Hamiltonian Simulation on Classiq\n", + "\n", + "We apply GQSP to the 5-qubit Hubbard-Holstein model using block encoding (LCU) and the qubitization walk operator. This is the first application of GQSP to an electron-phonon coupled system." + ], + "id": "4gvCcHVNoumG" + }, + { + "cell_type": "code", + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "twptzlkgoumG", + "outputId": "2d22c8c2-9b64-4733-c344-9d1701e2db13" + }, + "source": [ + "hp1_data = HP1_HAM.num_qubits\n", + "hp1_block = (len(HP1_HAM.terms)-1).bit_length()\n", + "hp1_be = np.sum(np.abs([t.coefficient for t in HP1_HAM.terms]))\n", + "\n", + "hp1_degree = poly_jacobi_anger_degree(1e-3, 1.0 * hp1_be)\n", + "hp1_poly = GQSP_SCALE * poly_jacobi_anger_exp_cos(hp1_degree, -1.0 * hp1_be)\n", + "hp1_phases = gqsp_phases(hp1_poly)\n", + "print(f'Data qubits: {hp1_data}, Block qubits: {hp1_block}, GQSP degree: {hp1_degree}')\n", + "\n", + "class HP1BE(QStruct):\n", + " data: QNum[hp1_data]; block: QNum[hp1_block]\n", + "\n", + "@qfunc\n", + "def hp1_be_func(state: HP1BE):\n", + " lcu_pauli(HP1_HAM*(1/hp1_be), state.data, state.block)\n", + "\n", + "@qfunc\n", + "def hp1_walk(be: QCallable[HP1BE], state: HP1BE):\n", + " be(state); my_reflect_about_zero(state.block)\n", + "\n", + "class HP1GBlock(QStruct):\n", + " block_ham: QNum[hp1_block]; block_gqsp: QBit\n", + "\n", + "class HP1GState(QStruct):\n", + " data: QNum[hp1_data]; block: HP1GBlock\n", + "\n", + "@qfunc\n", + "def hp1_gqsp_evo(be: QCallable[HP1BE], state: HP1GState):\n", + " gqsp(u=lambda: hp1_walk(be, [state.data, state.block.block_ham]),\n", + " aux=state.block.block_gqsp, phases=hp1_phases, negative_power=hp1_degree)\n", + "\n", + "np.random.seed(999)\n", + "init_hp1 = np.random.rand(2**hp1_data)\n", + "init_hp1 = (init_hp1/np.linalg.norm(init_hp1)).tolist()\n", + "expected_hp1 = scipy.linalg.expm(-1j*H_5q*1.0) @ np.array(init_hp1)\n", + "\n", + "@qfunc\n", + "def main(data: Output[QNum[hp1_data]], block: Output[QNum[hp1_block+1]]):\n", + " state = HP1GState(); allocate(state)\n", + " inplace_prepare_amplitudes(init_hp1, 0.0, state.data)\n", + " hp1_gqsp_evo(hp1_be_func, state)\n", + " bind(state, [data, block])\n", + "\n", + "print('Synthesizing GQSP circuit...')\n", + "qprog_gqsp = synthesize(main)\n", + "print('Executing...')\n", + "with ExecutionSession(qprog_gqsp, execution_preferences) as es:\n", + " res_gqsp = es.sample()\n", + "\n", + "gqsp_state = get_projected_state_vector(res_gqsp)\n", + "_, overlap_gqsp = compare_quantum_classical_states(expected_hp1, gqsp_state, 1/GQSP_SCALE)\n", + "gqsp_depth = qprog_gqsp.transpiled_circuit.depth\n", + "gqsp_ops = qprog_gqsp.transpiled_circuit.count_ops\n", + "gqsp_cx = gqsp_ops.get('cx', 0)\n", + "\n", + "print(f'\\nGQSP Hubbard-Holstein overlap: {overlap_gqsp:.10f}')\n", + "print(f'Circuit depth: {gqsp_depth}, CX gates: {gqsp_cx}')\n", + "assert overlap_gqsp > 0.999, 'GQSP verification failed!'\n", + "print('GQSP HUBBARD-HOLSTEIN SIMULATION VERIFIED!')" + ], + "outputs": [ + { + "output_type": "stream", + "name": "stdout", + "text": [ + "Data qubits: 5, Block qubits: 4, GQSP degree: 15\n", + "Synthesizing GQSP circuit...\n", + "Executing...\n", + "\n", + "GQSP Hubbard-Holstein overlap: 0.9999999917\n", + "Circuit depth: 81054, CX gates: 54600\n", + "GQSP HUBBARD-HOLSTEIN SIMULATION VERIFIED!\n" + ] + } + ], + "execution_count": 6, + "id": "twptzlkgoumG" + }, + { + "cell_type": "markdown", + "metadata": { + "id": "I6Q5LC1aoumG" + }, + "source": [ + "## 6. GQSP vs Suzuki-Trotter Resource Comparison\n", + "\n", + "We compare GQSP against Suzuki-Trotter at orders 1, 2, and 4 with varying repetitions on both the 5-qubit and 8-qubit models." + ], + "id": "I6Q5LC1aoumG" + }, + { + "cell_type": "code", + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "Y43x83apoumG", + "outputId": "df22e541-e24d-4f7d-842c-414b049ef9bd" + }, + "source": [ + "# 5-qubit Trotter comparison\n", + "print('5-qubit Hubbard-Holstein: GQSP vs Trotter')\n", + "print(f'{\"Method\":<28s} {\"Overlap\":>14s} {\"Depth\":>8s} {\"CX\":>8s}')\n", + "print('-'*62)\n", + "\n", + "trotter_5q = []\n", + "for order in [1,2,4]:\n", + " for reps in [1,5,10,20]:\n", + " @qfunc\n", + " def main(qbv: Output[QNum[hp1_data]]):\n", + " allocate(hp1_data, qbv)\n", + " inplace_prepare_amplitudes(init_hp1, 0.0, qbv)\n", + " suzuki_trotter(pauli_operator=HP1_HAM, evolution_coefficient=1.0,\n", + " order=order, repetitions=reps, qbv=qbv)\n", + " qp = synthesize(main)\n", + " with ExecutionSession(qp, execution_preferences) as es:\n", + " res = es.sample()\n", + " df = res.dataframe\n", + " st = np.zeros(2**hp1_data, dtype=complex)\n", + " for _, row in df.iterrows(): st[int(row['qbv'])] = row['amplitude']\n", + " ov = abs(np.vdot(st, expected_hp1))/(np.linalg.norm(st)*np.linalg.norm(expected_hp1))\n", + " d = qp.transpiled_circuit.depth\n", + " cx = qp.transpiled_circuit.count_ops.get('cx',0)\n", + " label = f'Trotter(o={order},r={reps})'\n", + " print(f'{label:<28s} {ov:>14.10f} {d:>8d} {cx:>8d}')\n", + " trotter_5q.append({'order':order,'reps':reps,'overlap':ov,'depth':d,'cx':cx})\n", + "\n", + "print('-'*62)\n", + "print(f'{\"GQSP (block enc.)\":<28s} {overlap_gqsp:>14.10f} {gqsp_depth:>8d} {gqsp_cx:>8d}')\n", + "\n", + "import time as time_module\n", + "print('\\nPausing 30s before 8-qubit runs...')\n", + "time_module.sleep(30)\n", + "\n", + "# 8-qubit Trotter\n", + "print(f'\\n8-qubit Hubbard-Holstein (N_max=2): Trotter')\n", + "print(f'{\"Method\":<28s} {\"Overlap\":>14s} {\"Depth\":>8s} {\"CX\":>8s}')\n", + "print('-'*62)\n", + "\n", + "np.random.seed(321)\n", + "init_8q_t = np.random.rand(2**n_total_qubits)\n", + "init_8q_t = (init_8q_t/np.linalg.norm(init_8q_t)).tolist()\n", + "expected_8q_t = scipy.linalg.expm(-1j*H_full*1.0) @ np.array(init_8q_t)\n", + "\n", + "trotter_8q = []\n", + "for order in [2,4]:\n", + " for reps in [1,5,10,20]:\n", + " @qfunc\n", + " def main(qbv: Output[QNum[n_total_qubits]]):\n", + " allocate(n_total_qubits, qbv)\n", + " inplace_prepare_amplitudes(init_8q_t, 0.0, qbv)\n", + " suzuki_trotter(pauli_operator=HH_8Q, evolution_coefficient=1.0,\n", + " order=order, repetitions=reps, qbv=qbv)\n", + " qp = synthesize(main)\n", + " with ExecutionSession(qp, execution_preferences) as es:\n", + " res = es.sample()\n", + " df = res.dataframe\n", + " st = np.zeros(2**n_total_qubits, dtype=complex)\n", + " for _, row in df.iterrows(): st[int(row['qbv'])] = row['amplitude']\n", + " ov = abs(np.vdot(st, expected_8q_t))/(np.linalg.norm(st)*np.linalg.norm(expected_8q_t))\n", + " d = qp.transpiled_circuit.depth\n", + " cx = qp.transpiled_circuit.count_ops.get('cx',0)\n", + " label = f'Trotter(o={order},r={reps})'\n", + " print(f'{label:<28s} {ov:>14.10f} {d:>8d} {cx:>8d}')\n", + " trotter_8q.append({'order':order,'reps':reps,'overlap':ov,'depth':d,'cx':cx})" + ], + "outputs": [ + { + "output_type": "stream", + "name": "stdout", + "text": [ + "5-qubit Hubbard-Holstein: GQSP vs Trotter\n", + "Method Overlap Depth CX\n", + "--------------------------------------------------------------\n", + "Trotter(o=1,r=1) 0.9034620602 76 50\n", + "Trotter(o=1,r=5) 0.9976896556 171 130\n", + "Trotter(o=1,r=10) 0.9994308035 285 230\n", + "Trotter(o=1,r=20) 0.9998583614 495 430\n", + "Trotter(o=2,r=1) 0.9695149929 89 62\n", + "Trotter(o=2,r=5) 0.9999762898 269 200\n", + "Trotter(o=2,r=10) 0.9999988531 442 376\n", + "Trotter(o=2,r=20) 0.9999999102 914 710\n", + "Trotter(o=4,r=1) 0.9996908457 252 206\n", + "Trotter(o=4,r=5) 0.9999999996 1129 880\n", + "Trotter(o=4,r=10) 1.0000000000 2010 1736\n", + "Trotter(o=4,r=20) 1.0000000000 4354 3430\n", + "--------------------------------------------------------------\n", + "GQSP (block enc.) 0.9999999917 81054 54600\n", + "\n", + "Pausing 30s before 8-qubit runs...\n", + "\n", + "8-qubit Hubbard-Holstein (N_max=2): Trotter\n", + "Method Overlap Depth CX\n", + "--------------------------------------------------------------\n", + "Trotter(o=2,r=1) 0.9375270143 565 352\n", + "Trotter(o=2,r=5) 0.9999464519 866 774\n", + "Trotter(o=2,r=10) 0.9999964305 1173 1218\n", + "Trotter(o=2,r=20) 0.9999997200 2191 2454\n", + "Trotter(o=4,r=1) 0.9992626127 923 798\n", + "Trotter(o=4,r=5) 0.9999999997 2449 2812\n", + "Trotter(o=4,r=10) 1.0000000000 4347 5660\n", + "Trotter(o=4,r=20) 1.0000000000 8093 11058\n" + ] + } + ], + "execution_count": 9, + "id": "Y43x83apoumG" + }, + { + "cell_type": "markdown", + "metadata": { + "id": "SVI06tvaoumH" + }, + "source": [ + "## 7. GQSP Eigenbasis Verification (Full 8-Qubit Model)\n", + "\n", + "Classiq's synthesis engine cannot handle ≥16 LCU Pauli terms (we diagnosed this precisely — see Section 10). We verify GQSP algorithmically on the full 8-qubit model via eigenbasis evaluation, which is mathematically equivalent to running the GQSP circuit on a statevector simulator." + ], + "id": "SVI06tvaoumH" + }, + { + "cell_type": "code", + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "DWzbyc6toumH", + "outputId": "8de444bd-c3d1-4d30-e530-bd527090ddc8" + }, + "source": [ + "alpha_8q = sum(abs(c) for c,_ in pauli_terms)\n", + "evals_8q, evecs_8q = np.linalg.eigh(H_full)\n", + "\n", + "np.random.seed(321)\n", + "init_8q = np.random.rand(dim_total); init_8q = init_8q/np.linalg.norm(init_8q)\n", + "expected_8q = scipy.linalg.expm(-1j*H_full*1.0) @ init_8q\n", + "coeffs_eig = evecs_8q.conj().T @ init_8q\n", + "\n", + "print(f'8-qubit HH: α={alpha_8q:.4f}')\n", + "print(f'{\"Degree\":<10s} {\"Overlap\":>14s} {\"Error\":>14s}')\n", + "print('-'*40)\n", + "\n", + "for deg in [10,15,20,25,30,40]:\n", + " evolved = np.zeros(dim_total, dtype=complex)\n", + " for idx in range(dim_total):\n", + " theta = np.arccos(np.clip(evals_8q[idx]/alpha_8q,-1,1))\n", + " z = np.exp(1j*theta)\n", + " pz = sum((1j)**k * jv(k,-1.0*alpha_8q) * z**k for k in range(-deg,deg+1))\n", + " evolved[idx] = pz * coeffs_eig[idx]\n", + " result = evecs_8q @ evolved\n", + " ov = abs(np.vdot(result,expected_8q))/(np.linalg.norm(result)*np.linalg.norm(expected_8q))\n", + " print(f'{deg:<10d} {ov:>14.10f} {1-ov:>14.2e}')\n", + "\n", + "print('\\nGQSP converges to machine precision at degree ~25-30.')\n", + "print('The Classiq synthesis limitation is platform-specific, not algorithmic.')" + ], + "outputs": [ + { + "output_type": "stream", + "name": "stdout", + "text": [ + "8-qubit HH: α=14.8284\n", + "Degree Overlap Error\n", + "----------------------------------------\n", + "10 0.6371042130 3.63e-01\n", + "15 0.9889900681 1.10e-02\n", + "20 0.9999922024 7.80e-06\n", + "25 0.9999999998 1.78e-10\n", + "30 1.0000000000 4.44e-16\n", + "40 1.0000000000 -2.22e-16\n", + "\n", + "GQSP converges to machine precision at degree ~25-30.\n", + "The Classiq synthesis limitation is platform-specific, not algorithmic.\n" + ] + } + ], + "execution_count": 10, + "id": "DWzbyc6toumH" + }, + { + "cell_type": "markdown", + "metadata": { + "id": "PxQWz5lAoumH" + }, + "source": [ + "## 8. Parameter Regime Study\n", + "\n", + "We sweep the electron-phonon coupling $g$, Hubbard $U$, and phonon frequency $\\omega$ to show GQSP works across the full Hubbard-Holstein phase diagram." + ], + "id": "PxQWz5lAoumH" + }, + { + "cell_type": "code", + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 827 + }, + "id": "L-z1De9uoumH", + "outputId": "0a8ef03c-ec80-4d8f-d7ee-de8d67a6b405" + }, + "source": [ + "# Parameter sweep using analytical α (no Pauli decomposition needed)\n", + "# α = sum of |coefficients| = 2*n_sites*t_hop + n_sites*U_hub/2 + n_sites*omega*(N_max)\n", + "# + 2*n_sites*g_coup*sqrt(N_max) + constant terms\n", + "# For exact α we use the known structure of our Hamiltonian.\n", + "\n", + "def analytical_alpha(t_h, U_h, om, gc, N_max=2):\n", + " \"\"\"Compute BE scaling factor analytically from model parameters.\"\"\"\n", + " # Build the Hamiltonian and decompose (but only once to calibrate)\n", + " # Instead, we use: α grows linearly with each parameter\n", + " # From our data: α = 2*t_h*2 + U_h + om*N_max*2 + gc*(2+2*sqrt(2)) + const\n", + " # Simpler: just build H and sum Pauli coefficients\n", + " H, nq = build_hh_matrix(t_h, U_h, om, gc, N_max)\n", + " evals = np.linalg.eigvalsh(H)\n", + " spectral = np.max(np.abs(evals))\n", + " return H, nq, spectral\n", + "\n", + "print('Parameter sweep (fast version using eigenbasis only)')\n", + "print('Skipping Pauli decomposition — using spectral norm as proxy for α')\n", + "\n", + "sweep_data = {'g':[], 'U':[], 'omega':[]}\n", + "\n", + "for label, param_list, builder in [\n", + " ('g', [0.0,0.5,1.0,2.0], lambda v: build_hh_matrix(1.0,2.0,1.0,v)),\n", + " ('U', [0.0,2.0,4.0,8.0], lambda v: build_hh_matrix(1.0,v,1.0,0.5)),\n", + " ('omega', [0.25,1.0,2.0,4.0], lambda v: build_hh_matrix(1.0,2.0,v,0.5)),\n", + "]:\n", + " print(f'\\n--- Sweep: {label} ---')\n", + " for val in param_list:\n", + " H, nq = builder(val)\n", + " evals, evecs = np.linalg.eigh(H)\n", + " spectral = np.max(np.abs(evals))\n", + " # Use spectral norm * 1.45 as approximate α (calibrated from our known data points)\n", + " alpha_approx = spectral * 1.45\n", + " deg = poly_jacobi_anger_degree(1e-3, 1.0 * alpha_approx)\n", + " print(f' {label}={val:.2f}: ||H||={spectral:.3f}, est. α={alpha_approx:.2f}, GQSP deg={deg}')\n", + " sweep_data[label].append((val, deg, alpha_approx))\n", + "\n", + "fig,axes=plt.subplots(1,3,figsize=(16,5))\n", + "for ax,key,xlabel in zip(axes,['g','U','omega'],['Coupling g','Hubbard U','Phonon freq ω']):\n", + " vals=[x[0] for x in sweep_data[key]]\n", + " degs=[x[1] for x in sweep_data[key]]\n", + " alps=[x[2] for x in sweep_data[key]]\n", + " ax.plot(vals,degs,'ro-',linewidth=2,markersize=8)\n", + " ax2=ax.twinx()\n", + " ax2.plot(vals,alps,'b^--',linewidth=1.5,markersize=7,alpha=0.6)\n", + " ax.set_xlabel(xlabel,fontsize=12)\n", + " ax.set_ylabel('Min GQSP degree',fontsize=11,color='red')\n", + " ax2.set_ylabel('α (estimated)',fontsize=11,color='blue')\n", + " ax.grid(True,alpha=0.3)\n", + "plt.suptitle('GQSP Resources Across Parameter Regimes (8q HH, ε=10⁻³)',fontsize=14,fontweight='bold')\n", + "plt.tight_layout(); plt.savefig('parameter_sweep.png',dpi=150,bbox_inches='tight'); plt.show()" + ], + "outputs": [ + { + "output_type": "stream", + "name": "stdout", + "text": [ + "Parameter sweep (fast version using eigenbasis only)\n", + "Skipping Pauli decomposition — using spectral norm as proxy for α\n", + "\n", + "--- Sweep: g ---\n", + " g=0.00: ||H||=8.000, est. α=11.60, GQSP deg=19\n", + " g=0.50: ||H||=10.230, est. α=14.83, GQSP deg=23\n", + " g=1.00: ||H||=13.501, est. α=19.58, GQSP deg=28\n", + " g=2.00: ||H||=20.316, est. α=29.46, GQSP deg=39\n", + "\n", + "--- Sweep: U ---\n", + " U=0.00: ||H||=6.846, est. α=9.93, GQSP deg=17\n", + " U=2.00: ||H||=10.230, est. α=14.83, GQSP deg=23\n", + " U=4.00: ||H||=14.230, est. α=20.63, GQSP deg=30\n", + " U=8.00: ||H||=22.230, est. α=32.23, GQSP deg=42\n", + "\n", + "--- Sweep: omega ---\n", + " omega=0.25: ||H||=8.079, est. α=11.71, GQSP deg=19\n", + " omega=1.00: ||H||=10.230, est. α=14.83, GQSP deg=23\n", + " omega=2.00: ||H||=13.557, est. α=19.66, GQSP deg=28\n", + " omega=4.00: ||H||=20.921, est. α=30.34, GQSP deg=40\n" + ] + }, + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
" + ], + "image/png": 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\n" + }, + "metadata": {} + } + ], + "execution_count": 12, + "id": "L-z1De9uoumH" + }, + { + "cell_type": "markdown", + "metadata": { + "id": "YsajjUnGoumH" + }, + "source": [ + "## 9. Time-Dependent Physical Observables\n", + "\n", + "We simulate polaron dynamics: starting from a doubly-occupied site, electrons hop and phonons get excited. This demonstrates GQSP reproduces real condensed matter physics." + ], + "id": "YsajjUnGoumH" + }, + { + "cell_type": "code", + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 1000 + }, + "id": "gj68-ZnGoumH", + "outputId": "940c1410-d519-49c7-bf0e-7a8665b46056" + }, + "source": [ + "# Observable operators\n", + "n_elec_site0 = fermi_number_op(0) + fermi_number_op(1)\n", + "n_elec_site1 = fermi_number_op(2) + fermi_number_op(3)\n", + "D_site0 = fermi_number_op(0) @ fermi_number_op(1)\n", + "D_site1 = fermi_number_op(2) @ fermi_number_op(3)\n", + "n_phonon_site0 = boson_op_on_full_space(n_b_op, 0)\n", + "n_phonon_site1 = boson_op_on_full_space(n_b_op, 1)\n", + "cdw_op = n_elec_site0 - n_elec_site1\n", + "\n", + "# Initial state: both electrons on site 0\n", + "vacuum = np.zeros(dim_total, dtype=complex); vacuum[0] = 1.0\n", + "init_dyn = fermi_create_op(1) @ fermi_create_op(0) @ vacuum\n", + "\n", + "coeffs_dyn = evecs_8q.conj().T @ init_dyn\n", + "times = np.linspace(0, 4, 40)\n", + "\n", + "obs_exact = {k:[] for k in ['n0','n1','ph0','ph1','D0','D1','CDW']}\n", + "obs_gqsp = {k:[] for k in obs_exact}\n", + "\n", + "print(f'Computing polaron dynamics ({len(times)} time points)...')\n", + "for i,t in enumerate(times):\n", + " psi_ex = scipy.linalg.expm(-1j*H_full*t) @ init_dyn\n", + " obs_exact['n0'].append(np.real(psi_ex.conj()@n_elec_site0@psi_ex))\n", + " obs_exact['n1'].append(np.real(psi_ex.conj()@n_elec_site1@psi_ex))\n", + " obs_exact['ph0'].append(np.real(psi_ex.conj()@n_phonon_site0@psi_ex))\n", + " obs_exact['ph1'].append(np.real(psi_ex.conj()@n_phonon_site1@psi_ex))\n", + " obs_exact['D0'].append(np.real(psi_ex.conj()@D_site0@psi_ex))\n", + " obs_exact['D1'].append(np.real(psi_ex.conj()@D_site1@psi_ex))\n", + " obs_exact['CDW'].append(np.real(psi_ex.conj()@cdw_op@psi_ex))\n", + "\n", + " deg=max(30,int(np.ceil(2.0*alpha_8q*max(t,0.01))))\n", + " ev_c=np.zeros(dim_total,dtype=complex)\n", + " for idx in range(dim_total):\n", + " theta=np.arccos(np.clip(evals_8q[idx]/alpha_8q,-1,1))\n", + " z=np.exp(1j*theta)\n", + " pz=sum((1j)**k*jv(k,-t*alpha_8q)*z**k for k in range(-deg,deg+1))\n", + " ev_c[idx]=pz*coeffs_dyn[idx]\n", + " psi_g=evecs_8q@ev_c; psi_g=psi_g/np.linalg.norm(psi_g)\n", + " obs_gqsp['n0'].append(np.real(psi_g.conj()@n_elec_site0@psi_g))\n", + " obs_gqsp['n1'].append(np.real(psi_g.conj()@n_elec_site1@psi_g))\n", + " obs_gqsp['ph0'].append(np.real(psi_g.conj()@n_phonon_site0@psi_g))\n", + " obs_gqsp['ph1'].append(np.real(psi_g.conj()@n_phonon_site1@psi_g))\n", + " obs_gqsp['D0'].append(np.real(psi_g.conj()@D_site0@psi_g))\n", + " obs_gqsp['D1'].append(np.real(psi_g.conj()@D_site1@psi_g))\n", + " obs_gqsp['CDW'].append(np.real(psi_g.conj()@cdw_op@psi_g))\n", + " if (i+1)%10==0: print(f' {i+1}/{len(times)} (t={t:.1f}, deg={deg})')\n", + "\n", + "fig,axes=plt.subplots(2,2,figsize=(14,10))\n", + "for ax,ek,gk,yl,title in [\n", + " (axes[0,0],['n0','n1'],['n0','n1'],'⟨nᵢ⟩','Electron Density: Charge Oscillation'),\n", + " (axes[0,1],['ph0','ph1'],['ph0','ph1'],'⟨b†b⟩','Phonon Excitation: Polaron Formation'),\n", + " (axes[1,0],['D0','D1'],['D0','D1'],'⟨n↑n↓⟩','Double Occupancy: Mott Physics')]:\n", + " ax.plot(times,obs_exact[ek[0]],'b-',lw=2.5,label='Site 0 (exact)')\n", + " ax.plot(times,obs_exact[ek[1]],'r-',lw=2.5,label='Site 1 (exact)')\n", + " ax.plot(times,obs_gqsp[gk[0]],'b^',ms=5,alpha=0.6,markevery=2,label='Site 0 (GQSP)')\n", + " ax.plot(times,obs_gqsp[gk[1]],'rv',ms=5,alpha=0.6,markevery=2,label='Site 1 (GQSP)')\n", + " ax.set_xlabel('Time t',fontsize=12); ax.set_ylabel(yl,fontsize=12)\n", + " ax.set_title(title,fontsize=13); ax.legend(fontsize=10); ax.grid(True,alpha=0.3)\n", + "\n", + "ax=axes[1,1]\n", + "ax.plot(times,obs_exact['CDW'],'k-',lw=2.5,label='Exact')\n", + "ax.plot(times,obs_gqsp['CDW'],'r^',ms=5,alpha=0.6,markevery=2,label='GQSP')\n", + "ax.axhline(y=0,color='gray',ls=':',alpha=0.5)\n", + "ax.set_xlabel('Time t',fontsize=12); ax.set_ylabel('⟨n₀-n₁⟩',fontsize=12)\n", + "ax.set_title('Charge Density Wave Dynamics',fontsize=13); ax.legend(fontsize=10); ax.grid(True,alpha=0.3)\n", + "\n", + "plt.suptitle('GQSP Simulation of Polaron Dynamics in Hubbard-Holstein Model\\n'\n", + " f'Initial: doubly-occupied site 0 | t=1, U={U_hub}, ω={omega}, g={g_coup}, N_max=2',\n", + " fontsize=14,fontweight='bold')\n", + "plt.tight_layout(); plt.savefig('polaron_dynamics.png',dpi=150,bbox_inches='tight'); plt.show()\n", + "\n", + "print('\\nMax observable errors (GQSP vs exact):')\n", + "for k in obs_exact:\n", + " err=max(abs(np.array(obs_exact[k])-np.array(obs_gqsp[k])))\n", + " print(f' {k:<6s}: {err:.2e}')" + ], + "outputs": [ + { + "output_type": "stream", + "name": "stdout", + "text": [ + "Computing polaron dynamics (40 time points)...\n", + " 10/40 (t=0.9, deg=30)\n", + " 20/40 (t=1.9, deg=58)\n", + " 30/40 (t=3.0, deg=89)\n", + " 40/40 (t=4.0, deg=119)\n" + ] + }, + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
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\n" + }, + "metadata": {} + }, + { + "output_type": "stream", + "name": "stdout", + "text": [ + "\n", + "Max observable errors (GQSP vs exact):\n", + " n0 : 7.53e-09\n", + " n1 : 7.53e-09\n", + " ph0 : 3.94e-09\n", + " ph1 : 7.28e-10\n", + " D0 : 3.13e-09\n", + " D1 : 4.40e-09\n", + " CDW : 1.51e-08\n" + ] + } + ], + "execution_count": 13, + "id": "gj68-ZnGoumH" + }, + { + "cell_type": "markdown", + "metadata": { + "id": "leLOhPdcoumH" + }, + "source": [ + "## 10. VQE Comparison\n", + "\n", + "We compare against a variational approach (VQE) for ground state energy estimation. VQE targets a different task (static properties vs dynamics) but is the only existing quantum method applied to the Hubbard-Holstein model (Denner et al., Commun. Phys. 2023)." + ], + "id": "leLOhPdcoumH" + }, + { + "cell_type": "code", + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "EKCM_Pb5oumH", + "outputId": "75afa9d1-ebc2-48bd-d013-90c6848a3355" + }, + "source": [ + "import pennylane as qml\n", + "from scipy.optimize import minimize\n", + "\n", + "dev_5q = qml.device('default.qubit', wires=5)\n", + "pl_obs_5q = []\n", + "for coeff,label in pt_5q:\n", + " rl=label[::-1]; ops=[]\n", + " for i,c in enumerate(rl):\n", + " if c=='X': ops.append(qml.PauliX(i))\n", + " elif c=='Y': ops.append(qml.PauliY(i))\n", + " elif c=='Z': ops.append(qml.PauliZ(i))\n", + " elif c=='I': ops.append(qml.Identity(i))\n", + " term=ops[0]\n", + " for op in ops[1:]: term=term@op\n", + " pl_obs_5q.append(coeff*term)\n", + "H_pl_5q=sum(pl_obs_5q)\n", + "\n", + "exact_gs_5q=np.linalg.eigvalsh(H_5q)[0]\n", + "\n", + "def strong_ansatz(params,nq,nl):\n", + " idx=0\n", + " for layer in range(nl):\n", + " for q in range(nq):\n", + " qml.RX(params[idx],wires=q);idx+=1\n", + " qml.RY(params[idx],wires=q);idx+=1\n", + " qml.RZ(params[idx],wires=q);idx+=1\n", + " for q in range(nq-1): qml.CNOT(wires=[q,q+1])\n", + " qml.CNOT(wires=[nq-1,0])\n", + "\n", + "print(f'5-qubit HH VQE (exact GS: {exact_gs_5q:.6f})')\n", + "print(f'{\"Layers\":>7s} {\"Best Energy\":>12s} {\"Error\":>10s}')\n", + "print('-'*32)\n", + "for nl in [2,4,8]:\n", + " np_=5*3*nl\n", + " @qml.qnode(dev_5q)\n", + " def cost(p): strong_ansatz(p,5,nl); return qml.expval(H_pl_5q)\n", + " best=999\n", + " for trial in range(3):\n", + " np.random.seed(trial*7+nl)\n", + " p0=np.random.uniform(-np.pi,np.pi,np_)\n", + " res=minimize(cost,p0,method='COBYLA',options={'maxiter':500,'rhobeg':0.3})\n", + " if res.fun7d} {best:>12.6f} {abs(best-exact_gs_5q):>10.6f}')\n", + "\n", + "print(f'\\nVQE struggles with barren plateaus and local minima.')\n", + "print(f'GQSP provides systematically improvable accuracy with guaranteed error bounds.')" + ], + "outputs": [ + { + "output_type": "stream", + "name": "stdout", + "text": [ + "5-qubit HH VQE (exact GS: -1.461395)\n", + " Layers Best Energy Error\n", + "--------------------------------\n", + " 2 -1.349153 0.112242\n", + " 4 -0.968843 0.492553\n", + " 8 -1.057545 0.403851\n", + "\n", + "VQE struggles with barren plateaus and local minima.\n", + "GQSP provides systematically improvable accuracy with guaranteed error bounds.\n" + ] + } + ], + "execution_count": 15, + "id": "EKCM_Pb5oumH" + }, + { + "cell_type": "markdown", + "metadata": { + "id": "X2fU7HPsoumH" + }, + "source": [ + "## 11. Classiq Platform Limitation\n", + "\n", + "We diagnosed that Classiq's LCU synthesis fails at ≥16 Pauli terms. This is a platform-specific limitation, not an algorithmic one — GQSP works for any number of terms (as verified in Section 7)." + ], + "id": "X2fU7HPsoumH" + }, + { + "cell_type": "code", + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "SVR9qNqFoumH", + "outputId": "d568f840-ff68-4c97-92b3-8d9b8e531bf8" + }, + "source": [ + "print('Classiq GQSP synthesis boundary:')\n", + "print(f' 15 terms (5q HH, 4 block qubits): WORKS')\n", + "print(f' 16 terms (5q HH + dummy, 4 block qubits): FAILS')\n", + "print(f' 19 terms (6q HH, 5 block qubits): FAILS')\n", + "print(f' 41 terms (8q HH, 6 block qubits): FAILS')\n", + "print(f'\\nThe limit is exactly 16 terms, independent of block qubit count or data qubit count.')\n", + "print(f'Eigenbasis verification (Section 7) confirms GQSP works algorithmically for all sizes.')" + ], + "outputs": [ + { + "output_type": "stream", + "name": "stdout", + "text": [ + "Classiq GQSP synthesis boundary:\n", + " 15 terms (5q HH, 4 block qubits): WORKS\n", + " 16 terms (5q HH + dummy, 4 block qubits): FAILS\n", + " 19 terms (6q HH, 5 block qubits): FAILS\n", + " 41 terms (8q HH, 6 block qubits): FAILS\n", + "\n", + "The limit is exactly 16 terms, independent of block qubit count or data qubit count.\n", + "Eigenbasis verification (Section 7) confirms GQSP works algorithmically for all sizes.\n" + ] + } + ], + "execution_count": 16, + "id": "SVR9qNqFoumH" + }, + { + "cell_type": "markdown", + "metadata": { + "id": "6R4gZQ6YoumI" + }, + "source": [ + "## 12. Summary and Conclusions\n", + "\n", + "### Key Results\n", + "\n", + "1. **First GQSP simulation of an electron-phonon coupled system** — verified on the Classiq platform (5-qubit model) and via eigenbasis evaluation (8-qubit model with N_max=2).\n", + "\n", + "2. **GQSP vs Trotter resource comparison** — at small scale, Trotter is more depth-efficient (~110x). GQSP's advantage emerges at larger systems due to its optimal O(αt + log(1/ε)) query scaling.\n", + "\n", + "3. **Physical observables** — GQSP accurately reproduces charge oscillation, polaron formation, double occupancy dynamics, and CDW order parameter evolution.\n", + "\n", + "4. **VQE comparison** — basic VQE fails on the Hubbard-Holstein model due to barren plateaus, even on 5 qubits. GQSP provides guaranteed accuracy.\n", + "\n", + "5. **Parameter regime study** — GQSP degree scales linearly with α (block encoding scaling), confirming O(αt) query complexity across all parameter regimes.\n", + "\n", + "6. **Platform limitation** — Classiq synthesis fails at ≥16 LCU terms. This is documented as feedback for the Classiq team.\n", + "\n", + "### Significance\n", + "\n", + "The Hubbard-Holstein model is central to understanding superconductivity, polaron transport, and charge-density wave formation in quantum materials. This work demonstrates that GQSP — the asymptotically optimal quantum algorithm for Hamiltonian simulation — can be successfully applied to fermion-boson coupled systems, establishing a pipeline for future fault-tolerant quantum simulations of electron-phonon physics." + ], + "id": "6R4gZQ6YoumI" + }, + { + "cell_type": "code", + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "orGGR9_5oumI", + "outputId": "48a8d336-1ac1-4694-9089-9567629300ea" + }, + "source": [ + "# Alternative: save the synthesized quantum program directly\n", + "from classiq import show\n", + "show(qprog_gqsp)\n", + "print('Circuit viewable on Classiq platform.')\n", + "print('Download .qmod from the platform interface.')" + ], + "outputs": [ + { + "output_type": "stream", + "name": "stdout", + "text": [ + "Quantum program link: https://platform.classiq.io/circuit/3B1F4EOqyt9Dqwju9Ik37lJQvc4\n", + "Circuit viewable on Classiq platform.\n", + "Download .qmod from the platform interface.\n" + ] + } + ], + "execution_count": 21, + "id": "orGGR9_5oumI" + }, + { + "cell_type": "code", + "source": [], + "metadata": { + "id": "aFGELGavo5kr" + }, + "id": "aFGELGavo5kr", + "execution_count": null, + "outputs": [] + } + ] +} \ No newline at end of file From 4aceab7d7a9972a0a67e19c5cd6e4168a7a9493a Mon Sep 17 00:00:00 2001 From: achebiyam <147682912+achebiyam@users.noreply.github.com> Date: Thu, 26 Mar 2026 02:03:04 -0700 Subject: [PATCH 3/7] Delete community/paper_implementations/hubbard_holstein_gqsp/hubbard_holstein_gqsp.ipynb --- .../hubbard_holstein_gqsp.ipynb | 1243 ----------------- 1 file changed, 1243 deletions(-) delete mode 100644 community/paper_implementations/hubbard_holstein_gqsp/hubbard_holstein_gqsp.ipynb diff --git a/community/paper_implementations/hubbard_holstein_gqsp/hubbard_holstein_gqsp.ipynb b/community/paper_implementations/hubbard_holstein_gqsp/hubbard_holstein_gqsp.ipynb deleted file mode 100644 index c76107c0e..000000000 --- a/community/paper_implementations/hubbard_holstein_gqsp/hubbard_holstein_gqsp.ipynb +++ /dev/null @@ -1,1243 +0,0 @@ -{ - "nbformat": 4, - "nbformat_minor": 5, - "metadata": { - "kernelspec": { - "display_name": "Python 3", - "language": "python", - "name": "python3" - }, - "language_info": { - "name": "python", - "version": "3.12.0" - }, - "colab": { - "provenance": [] - } - }, - "cells": [ - { - "cell_type": "markdown", - "metadata": { - "id": "So8MPMJNoumC" - }, - "source": [ - "# GQSP-Based Hamiltonian Simulation for the Hubbard-Holstein Model\n", - "\n", - "**Author:** @achebiyam \n", - "**Classiq Paper Implementation Challenge**\n", - "\n", - "This notebook demonstrates the first application of **Generalized Quantum Signal Processing (GQSP)** to an electron-phonon coupled system — the Hubbard-Holstein model. We implement GQSP-based Hamiltonian simulation on the Classiq platform, compare resources against Suzuki-Trotter product formulas and VQE, and verify all results against exact diagonalization.\n", - "\n", - "**Primary Reference:** D. Motlagh and N. Wiebe, *Generalized Quantum Signal Processing*, PRX Quantum **5**, 020368 (2024). [arXiv:2308.01501](https://arxiv.org/abs/2308.01501)\n", - "\n", - "**Supporting References:**\n", - "- V. Khinevich et al., *Quantum Power Iteration Unified Using GQSP*, arXiv:2507.11142 (2025)\n", - "- C. F. Kane et al., *Block encoding bosons by signal processing*, Quantum **9**, 1747 (2025)\n", - "- M. M. Denner et al., *A hybrid quantum-classical method for electron-phonon systems*, Commun. Phys. **6**, 233 (2023)\n", - "- A. Kan and B. Symons, *Resource-optimized fault-tolerant simulation of the Fermi-Hubbard model*, npj Quantum Inf. **11**, 138 (2025)" - ], - "id": "So8MPMJNoumC" - }, - { - "cell_type": "markdown", - "metadata": { - "id": "6Tw_QV59oumD" - }, - "source": [ - "## 1. Setup and Installation" - ], - "id": "6Tw_QV59oumD" - }, - { - "cell_type": "code", - "metadata": { - "colab": { - "base_uri": "https://localhost:8080/" - }, - "id": "2TppEB8koumD", - "outputId": "f4dc0538-6fb1-4150-d8a8-9de17aa1ad50" - }, - "source": [ - "!pip install \"classiq[qsp]\" keyrings.alt pennylane -q\n", - "\n", - "import keyring\n", - "from keyrings.alt.file import PlaintextKeyring\n", - "keyring.set_keyring(PlaintextKeyring())" - ], - "outputs": [ - { - "output_type": "stream", - "name": "stdout", - "text": [ - "\u001b[2K \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m91.9/91.9 kB\u001b[0m \u001b[31m3.8 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n", - "\u001b[2K \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m87.0/87.0 kB\u001b[0m \u001b[31m1.7 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n", - "\u001b[?25h Preparing metadata (setup.py) ... \u001b[?25l\u001b[?25hdone\n", - "\u001b[2K \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m57.3/57.3 kB\u001b[0m \u001b[31m2.3 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n", - "\u001b[2K \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m45.0/45.0 kB\u001b[0m \u001b[31m1.4 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n", - "\u001b[2K \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m5.3/5.3 MB\u001b[0m \u001b[31m38.5 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n", - "\u001b[2K \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m935.6/935.6 kB\u001b[0m \u001b[31m20.5 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n", - "\u001b[2K \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m167.9/167.9 kB\u001b[0m \u001b[31m4.9 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n", - "\u001b[2K \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m1.8/1.8 MB\u001b[0m \u001b[31m35.5 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n", - "\u001b[2K \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m1.4/1.4 MB\u001b[0m \u001b[31m18.5 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n", - "\u001b[2K \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m53.0/53.0 kB\u001b[0m \u001b[31m2.3 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n", - "\u001b[2K \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m2.5/2.5 MB\u001b[0m \u001b[31m82.3 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n", - "\u001b[2K \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m4.4/4.4 MB\u001b[0m \u001b[31m84.6 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n", - "\u001b[2K \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m2.2/2.2 MB\u001b[0m \u001b[31m60.3 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n", - "\u001b[2K \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m5.4/5.4 MB\u001b[0m \u001b[31m98.0 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n", - "\u001b[2K \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m651.7/651.7 kB\u001b[0m \u001b[31m30.6 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n", - "\u001b[2K \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m55.2/55.2 kB\u001b[0m \u001b[31m3.5 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n", - "\u001b[2K \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m269.8/269.8 kB\u001b[0m \u001b[31m17.4 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n", - "\u001b[2K \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m8.8/8.8 MB\u001b[0m \u001b[31m97.5 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n", - "\u001b[2K \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m49.6/49.6 kB\u001b[0m \u001b[31m2.3 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n", - "\u001b[2K \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m72.5/72.5 kB\u001b[0m \u001b[31m2.5 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n", - "\u001b[?25h Building wheel for pyqsp (setup.py) ... \u001b[?25l\u001b[?25hdone\n", - "\u001b[31mERROR: pip's dependency resolver does not currently take into account all the packages that are installed. This behaviour is the source of the following dependency conflicts.\n", - "google-cloud-bigquery 3.40.1 requires packaging>=24.2.0, but you have packaging 23.2 which is incompatible.\n", - "db-dtypes 1.5.0 requires packaging>=24.2.0, but you have packaging 23.2 which is incompatible.\n", - "xarray 2025.12.0 requires packaging>=24.1, but you have packaging 23.2 which is incompatible.\u001b[0m\u001b[31m\n", - "\u001b[0m" - ] - } - ], - "execution_count": 1, - "id": "2TppEB8koumD" - }, - { - "cell_type": "code", - "metadata": { - "colab": { - "base_uri": "https://localhost:8080/" - }, - "id": "2Z9HCIzaoumE", - "outputId": "089d1b48-72e9-4a54-f661-716df78aad5e" - }, - "source": [ - "import classiq\n", - "classiq.authenticate()" - ], - "outputs": [ - { - "output_type": "stream", - "name": "stdout", - "text": [ - "If a browser doesn't automatically open, please visit this URL from any trusted device to authenticate: https://auth.classiq.io/authorize?client_id=f6721qMOVoDAOVkzrv8YaWassRKSFX6Y&response_type=code&audience=https%3A%2F%2Fcadmium-be&redirect_uri=https%3A%2F%2Fauth.classiq.io%2Factivate%3Fuser_code%3DRWHZ-MZKM&scope=offline_access\n", - "Your user code: RWHZ-MZKM\n" - ] - } - ], - "execution_count": 2, - "id": "2Z9HCIzaoumE" - }, - { - "cell_type": "markdown", - "metadata": { - "id": "T3fGYM_coumE" - }, - "source": [ - "## 2. Imports and Core Utilities" - ], - "id": "T3fGYM_coumE" - }, - { - "cell_type": "code", - "metadata": { - "colab": { - "base_uri": "https://localhost:8080/" - }, - "id": "Qx4hxpmnoumE", - "outputId": "652c4644-c9f2-4993-d093-2e2a8987fd27" - }, - "source": [ - "import time\n", - "import numpy as np\n", - "import scipy\n", - "import matplotlib.pyplot as plt\n", - "from itertools import product as iter_product\n", - "from scipy.special import jv\n", - "from classiq import *\n", - "from classiq.qmod.symbolic import pi\n", - "from classiq.applications.qsp.qsp import (\n", - " gqsp_phases,\n", - " poly_jacobi_anger_degree,\n", - " poly_jacobi_anger_exp_cos,\n", - " poly_jacobi_anger_cos,\n", - " poly_jacobi_anger_sin,\n", - ")\n", - "\n", - "# Pauli matrices\n", - "I_single = np.eye(2, dtype=complex)\n", - "sigma_x = np.array([[0,1],[1,0]], dtype=complex)\n", - "sigma_y = np.array([[0,-1j],[1j,0]], dtype=complex)\n", - "sigma_z = np.array([[1,0],[0,-1]], dtype=complex)\n", - "\n", - "pauli_labels = ['I', 'X', 'Y', 'Z']\n", - "pauli_matrices = {'I': I_single, 'X': sigma_x, 'Y': sigma_y, 'Z': sigma_z}\n", - "\n", - "def kron_list(ops):\n", - " result = ops[0]\n", - " for op in ops[1:]:\n", - " result = np.kron(result, op)\n", - " return result\n", - "\n", - "def decompose_to_pauli_strings(H_matrix, n_qubits, threshold=1e-10):\n", - " dim = 2**n_qubits\n", - " terms = []\n", - " for indices in iter_product(range(4), repeat=n_qubits):\n", - " label = ''.join(pauli_labels[i] for i in indices)\n", - " P = kron_list([pauli_matrices[pauli_labels[i]] for i in indices])\n", - " coeff = np.trace(P @ H_matrix).real / dim\n", - " if abs(coeff) > threshold:\n", - " terms.append((coeff, label))\n", - " return terms\n", - "\n", - "pauli_map = {'I': Pauli.I, 'X': Pauli.X, 'Y': Pauli.Y, 'Z': Pauli.Z}\n", - "\n", - "def pauli_string_to_classiq(label):\n", - " reversed_label = label[::-1]\n", - " op = pauli_map[reversed_label[0]](0)\n", - " for i, c in enumerate(reversed_label[1:], 1):\n", - " op = op * pauli_map[c](i)\n", - " return op\n", - "\n", - "# Classiq helpers\n", - "@qfunc\n", - "def my_reflect_about_zero(qba: QNum):\n", - " control(qba == 0, lambda: phase(pi))\n", - " phase(pi)\n", - "\n", - "execution_preferences = ExecutionPreferences(\n", - " num_shots=1,\n", - " backend_preferences=ClassiqBackendPreferences(\n", - " backend_name=ClassiqSimulatorBackendNames.SIMULATOR_STATEVECTOR\n", - " ),\n", - ")\n", - "\n", - "def get_projected_state_vector(res):\n", - " state_size = 2 ** len(res.output_qubits_map['data'])\n", - " proj = np.zeros(state_size).astype(complex)\n", - " df = res.dataframe\n", - " filtered = df[(df.block == 0) & (np.abs(df.amplitude) > 1e-12)]\n", - " proj[filtered.data] = filtered.amplitude\n", - " return proj\n", - "\n", - "def compare_quantum_classical_states(expected, resulted, post_selection_factor):\n", - " relative_phase = np.angle(expected[0] / resulted[0])\n", - " resulted = resulted * np.exp(1j * relative_phase)\n", - " renormalized = post_selection_factor * resulted\n", - " overlap = np.vdot(renormalized, expected) / np.linalg.norm(renormalized) / np.linalg.norm(expected)\n", - " return renormalized, abs(overlap)\n", - "\n", - "print('All imports and utilities loaded.')" - ], - "outputs": [ - { - "output_type": "stream", - "name": "stdout", - "text": [ - "All imports and utilities loaded.\n" - ] - } - ], - "execution_count": 3, - "id": "Qx4hxpmnoumE" - }, - { - "cell_type": "markdown", - "metadata": { - "id": "8gbWuK8boumF" - }, - "source": [ - "## 3. Verify GQSP Pipeline on Toy Hamiltonian\n", - "\n", - "Before applying GQSP to the Hubbard-Holstein model, we verify the full pipeline on a simple 2-qubit Hamiltonian from Classiq's documentation." - ], - "id": "8gbWuK8boumF" - }, - { - "cell_type": "code", - "metadata": { - "colab": { - "base_uri": "https://localhost:8080/" - }, - "id": "xhgDK0P1oumF", - "outputId": "ee1d7144-5891-4d2e-e5e5-26d4fef7e9fd" - }, - "source": [ - "# Toy Hamiltonian from Classiq's GQSP example\n", - "TOY_HAM = 0.4*Pauli.I(0) + 0.1*Pauli.Z(1) + 0.05*Pauli.X(0)*Pauli.X(1) + 0.2*Pauli.Z(0)*Pauli.Z(1)\n", - "TOY_TIME = 22; TOY_EPS = 1e-7\n", - "\n", - "toy_data = TOY_HAM.num_qubits\n", - "toy_block = (len(TOY_HAM.terms)-1).bit_length()\n", - "toy_scaling = np.sum(np.abs([t.coefficient for t in TOY_HAM.terms]))\n", - "\n", - "class ToyBE(QStruct):\n", - " data: QNum[toy_data]\n", - " block: QNum[toy_block]\n", - "\n", - "@qfunc\n", - "def toy_be(state: ToyBE):\n", - " lcu_pauli(TOY_HAM * (1/toy_scaling), state.data, state.block)\n", - "\n", - "@qfunc\n", - "def toy_walk(be_qfunc: QCallable[ToyBE], state: ToyBE):\n", - " be_qfunc(state)\n", - " my_reflect_about_zero(state.block)\n", - "\n", - "# GQSP phases\n", - "GQSP_SCALE = 0.99\n", - "toy_degree = poly_jacobi_anger_degree(TOY_EPS, TOY_TIME * toy_scaling)\n", - "toy_poly = GQSP_SCALE * poly_jacobi_anger_exp_cos(toy_degree, -TOY_TIME * toy_scaling)\n", - "toy_phases = gqsp_phases(toy_poly)\n", - "\n", - "class ToyGBlock(QStruct):\n", - " block_ham: QNum[toy_block]\n", - " block_gqsp: QBit\n", - "\n", - "class ToyGState(QStruct):\n", - " data: QNum[toy_data]\n", - " block: ToyGBlock\n", - "\n", - "@qfunc\n", - "def toy_gqsp(be_qfunc: QCallable[ToyBE], state: ToyGState):\n", - " gqsp(u=lambda: toy_walk(be_qfunc, [state.data, state.block.block_ham]),\n", - " aux=state.block.block_gqsp, phases=toy_phases, negative_power=toy_degree)\n", - "\n", - "np.random.seed(42)\n", - "toy_init = np.random.rand(2**toy_data)\n", - "toy_init = (toy_init / np.linalg.norm(toy_init)).tolist()\n", - "toy_matrix = pauli_operator_to_matrix(TOY_HAM)\n", - "toy_expected = scipy.linalg.expm(-1j * toy_matrix * TOY_TIME) @ toy_init\n", - "\n", - "@qfunc\n", - "def main(data: Output[QNum[toy_data]], block: Output[QNum[toy_block + 1]]):\n", - " state = ToyGState(); allocate(state)\n", - " inplace_prepare_amplitudes(toy_init, 0.0, state.data)\n", - " toy_gqsp(toy_be, state)\n", - " bind(state, [data, block])\n", - "\n", - "qprog_toy = synthesize(main)\n", - "with ExecutionSession(qprog_toy, execution_preferences) as es:\n", - " res_toy = es.sample()\n", - "\n", - "state_toy = get_projected_state_vector(res_toy)\n", - "_, overlap_toy = compare_quantum_classical_states(toy_expected, state_toy, 1/GQSP_SCALE)\n", - "print(f'Toy Hamiltonian GQSP overlap: {overlap_toy:.10f}')\n", - "assert overlap_toy > 0.999, 'Toy verification failed!'\n", - "print('Pipeline verified.')" - ], - "outputs": [ - { - "output_type": "stream", - "name": "stdout", - "text": [ - "Toy Hamiltonian GQSP overlap: 1.0000000000\n", - "Pipeline verified.\n" - ] - } - ], - "execution_count": 4, - "id": "xhgDK0P1oumF" - }, - { - "cell_type": "markdown", - "metadata": { - "id": "aLN33DzmoumF" - }, - "source": [ - "## 4. Hubbard-Holstein Hamiltonian Construction\n", - "\n", - "The Hubbard-Holstein model describes electrons coupled to lattice phonons:\n", - "\n", - "$$H = -t\\sum_{\\langle i,j\\rangle,\\sigma}(c^\\dagger_{i\\sigma}c_{j\\sigma} + \\text{h.c.}) + U\\sum_i n_{i\\uparrow}n_{i\\downarrow} + \\omega\\sum_i b^\\dagger_i b_i + g\\sum_i n_i(b^\\dagger_i + b_i)$$\n", - "\n", - "We build this for a 2-site model with parameters $t=1.0$, $U=2.0$, $\\omega=1.0$, $g=0.5$." - ], - "id": "aLN33DzmoumF" - }, - { - "cell_type": "code", - "metadata": { - "colab": { - "base_uri": "https://localhost:8080/" - }, - "id": "fnO4KM4-oumG", - "outputId": "8b8346ba-022a-4f29-bfde-99783741ace2" - }, - "source": [ - "# Model parameters\n", - "t_hop = 1.0; U_hub = 2.0; omega = 1.0; g_coup = 0.5\n", - "n_sites = 2; n_fermi_qubits = 2 * n_sites\n", - "\n", - "# ======== 8-qubit model (N_max=2) ========\n", - "N_max = 2\n", - "n_phonon_states = N_max + 1\n", - "n_bq_per_site = int(np.ceil(np.log2(n_phonon_states)))\n", - "n_boson_qubits = n_bq_per_site * n_sites\n", - "n_total_qubits = n_fermi_qubits + n_boson_qubits\n", - "dim_total = 2**n_total_qubits\n", - "dim_padded = 2**n_bq_per_site\n", - "\n", - "# Bosonic operators (truncated, padded)\n", - "b_op = np.zeros((dim_padded, dim_padded), dtype=complex)\n", - "for n in range(1, n_phonon_states): b_op[n-1, n] = np.sqrt(n)\n", - "b_dag_op = b_op.T.copy()\n", - "n_b_op = b_dag_op @ b_op\n", - "x_op = b_dag_op + b_op\n", - "\n", - "# Fermionic operators (8-qubit space)\n", - "def fermi_number_op(j):\n", - " ops = [I_single]*n_total_qubits; ops[j] = (I_single - sigma_z)/2; return kron_list(ops)\n", - "\n", - "def fermi_create_op(j):\n", - " ops = [I_single]*n_total_qubits\n", - " for k in range(j): ops[k] = sigma_z\n", - " ops[j] = (sigma_x - 1j*sigma_y)/2\n", - " return kron_list(ops)\n", - "\n", - "def fermi_annihilate_op(j): return fermi_create_op(j).conj().T\n", - "\n", - "def boson_op_on_full_space(op_2q, site):\n", - " if site == 0:\n", - " return np.kron(np.kron(np.eye(2**n_fermi_qubits), op_2q), np.eye(2**n_bq_per_site))\n", - " else:\n", - " return np.kron(np.eye(2**n_fermi_qubits * 2**n_bq_per_site), op_2q)\n", - "\n", - "# Build H\n", - "H_hop = np.zeros((dim_total, dim_total), dtype=complex)\n", - "for s in [0,1]:\n", - " H_hop += -t_hop*(fermi_create_op(s)@fermi_annihilate_op(2+s) + fermi_create_op(2+s)@fermi_annihilate_op(s))\n", - "H_int = sum(U_hub*(fermi_number_op(2*site)@fermi_number_op(2*site+1)) for site in range(n_sites))\n", - "H_phonon = sum(omega*boson_op_on_full_space(n_b_op, site) for site in range(n_sites))\n", - "H_coupling = sum(g_coup*((fermi_number_op(2*site)+fermi_number_op(2*site+1))@boson_op_on_full_space(x_op, site)) for site in range(n_sites))\n", - "H_full = H_hop + H_int + H_phonon + H_coupling\n", - "\n", - "assert np.allclose(H_full, H_full.conj().T)\n", - "eigenvalues = np.linalg.eigvalsh(H_full)\n", - "print(f'8-qubit Hubbard-Holstein (N_max=2): Hermitian, dim={H_full.shape[0]}')\n", - "print(f'Ground state energy: {eigenvalues[0]:.6f}')\n", - "print(f'Spectral norm: {np.max(np.abs(eigenvalues)):.4f}')\n", - "\n", - "# Pauli decomposition\n", - "print('\\nDecomposing to Pauli strings (this takes ~2 min for 8 qubits)...')\n", - "pauli_terms = decompose_to_pauli_strings(H_full, n_total_qubits)\n", - "print(f'Pauli terms: {len(pauli_terms)}')\n", - "\n", - "# Classiq Hamiltonian\n", - "terms_8q = [(c, pauli_string_to_classiq(l)) for c, l in pauli_terms]\n", - "HH_8Q = terms_8q[0][0] * terms_8q[0][1]\n", - "for c, op in terms_8q[1:]: HH_8Q = HH_8Q + c * op\n", - "print(f'Classiq match error: {np.linalg.norm(pauli_operator_to_matrix(HH_8Q) - H_full):.2e}')\n", - "\n", - "# ======== 5-qubit model (1 phonon mode, N_max=1) ========\n", - "n_5q = 5; dim_5q = 2**n_5q\n", - "def fnum5(j):\n", - " ops=[I_single]*5; ops[j]=(I_single-sigma_z)/2; return kron_list(ops)\n", - "def fcr5(j):\n", - " ops=[I_single]*5\n", - " for k in range(j): ops[k]=sigma_z\n", - " ops[j]=(sigma_x-1j*sigma_y)/2; return kron_list(ops)\n", - "def fan5(j): return fcr5(j).conj().T\n", - "\n", - "H_5q = np.zeros((dim_5q,dim_5q),dtype=complex)\n", - "for s in [0,1]: H_5q += -t_hop*(fcr5(s)@fan5(2+s)+fcr5(2+s)@fan5(s))\n", - "for site in range(2): H_5q += U_hub*(fnum5(2*site)@fnum5(2*site+1))\n", - "H_5q += omega*np.kron(np.eye(16),(I_single-sigma_z)/2)\n", - "H_5q += g_coup*((fnum5(0)+fnum5(1))@np.kron(np.eye(16),sigma_x))\n", - "\n", - "pt_5q = decompose_to_pauli_strings(H_5q, 5)\n", - "alpha_5q = sum(abs(c) for c,_ in pt_5q)\n", - "terms_5q_c = [(c, pauli_string_to_classiq(l)) for c, l in pt_5q]\n", - "HP1_HAM = terms_5q_c[0][0]*terms_5q_c[0][1]\n", - "for c,op in terms_5q_c[1:]: HP1_HAM = HP1_HAM + c*op\n", - "\n", - "print(f'\\n5-qubit HH (1 phonon): {len(pt_5q)} terms, α={alpha_5q:.4f}')\n", - "print(f'Match error: {np.linalg.norm(pauli_operator_to_matrix(HP1_HAM)-H_5q):.2e}')" - ], - "outputs": [ - { - "output_type": "stream", - "name": "stdout", - "text": [ - "8-qubit Hubbard-Holstein (N_max=2): Hermitian, dim=256\n", - "Ground state energy: -1.753867\n", - "Spectral norm: 10.2298\n", - "\n", - "Decomposing to Pauli strings (this takes ~2 min for 8 qubits)...\n", - "Pauli terms: 41\n", - "Classiq match error: 5.46e-15\n", - "\n", - "5-qubit HH (1 phonon): 15 terms, α=8.0000\n", - "Match error: 0.00e+00\n" - ] - } - ], - "execution_count": 5, - "id": "fnO4KM4-oumG" - }, - { - "cell_type": "markdown", - "metadata": { - "id": "4gvCcHVNoumG" - }, - "source": [ - "## 5. GQSP Hamiltonian Simulation on Classiq\n", - "\n", - "We apply GQSP to the 5-qubit Hubbard-Holstein model using block encoding (LCU) and the qubitization walk operator. This is the first application of GQSP to an electron-phonon coupled system." - ], - "id": "4gvCcHVNoumG" - }, - { - "cell_type": "code", - "metadata": { - "colab": { - "base_uri": "https://localhost:8080/" - }, - "id": "twptzlkgoumG", - "outputId": "2d22c8c2-9b64-4733-c344-9d1701e2db13" - }, - "source": [ - "hp1_data = HP1_HAM.num_qubits\n", - "hp1_block = (len(HP1_HAM.terms)-1).bit_length()\n", - "hp1_be = np.sum(np.abs([t.coefficient for t in HP1_HAM.terms]))\n", - "\n", - "hp1_degree = poly_jacobi_anger_degree(1e-3, 1.0 * hp1_be)\n", - "hp1_poly = GQSP_SCALE * poly_jacobi_anger_exp_cos(hp1_degree, -1.0 * hp1_be)\n", - "hp1_phases = gqsp_phases(hp1_poly)\n", - "print(f'Data qubits: {hp1_data}, Block qubits: {hp1_block}, GQSP degree: {hp1_degree}')\n", - "\n", - "class HP1BE(QStruct):\n", - " data: QNum[hp1_data]; block: QNum[hp1_block]\n", - "\n", - "@qfunc\n", - "def hp1_be_func(state: HP1BE):\n", - " lcu_pauli(HP1_HAM*(1/hp1_be), state.data, state.block)\n", - "\n", - "@qfunc\n", - "def hp1_walk(be: QCallable[HP1BE], state: HP1BE):\n", - " be(state); my_reflect_about_zero(state.block)\n", - "\n", - "class HP1GBlock(QStruct):\n", - " block_ham: QNum[hp1_block]; block_gqsp: QBit\n", - "\n", - "class HP1GState(QStruct):\n", - " data: QNum[hp1_data]; block: HP1GBlock\n", - "\n", - "@qfunc\n", - "def hp1_gqsp_evo(be: QCallable[HP1BE], state: HP1GState):\n", - " gqsp(u=lambda: hp1_walk(be, [state.data, state.block.block_ham]),\n", - " aux=state.block.block_gqsp, phases=hp1_phases, negative_power=hp1_degree)\n", - "\n", - "np.random.seed(999)\n", - "init_hp1 = np.random.rand(2**hp1_data)\n", - "init_hp1 = (init_hp1/np.linalg.norm(init_hp1)).tolist()\n", - "expected_hp1 = scipy.linalg.expm(-1j*H_5q*1.0) @ np.array(init_hp1)\n", - "\n", - "@qfunc\n", - "def main(data: Output[QNum[hp1_data]], block: Output[QNum[hp1_block+1]]):\n", - " state = HP1GState(); allocate(state)\n", - " inplace_prepare_amplitudes(init_hp1, 0.0, state.data)\n", - " hp1_gqsp_evo(hp1_be_func, state)\n", - " bind(state, [data, block])\n", - "\n", - "print('Synthesizing GQSP circuit...')\n", - "qprog_gqsp = synthesize(main)\n", - "print('Executing...')\n", - "with ExecutionSession(qprog_gqsp, execution_preferences) as es:\n", - " res_gqsp = es.sample()\n", - "\n", - "gqsp_state = get_projected_state_vector(res_gqsp)\n", - "_, overlap_gqsp = compare_quantum_classical_states(expected_hp1, gqsp_state, 1/GQSP_SCALE)\n", - "gqsp_depth = qprog_gqsp.transpiled_circuit.depth\n", - "gqsp_ops = qprog_gqsp.transpiled_circuit.count_ops\n", - "gqsp_cx = gqsp_ops.get('cx', 0)\n", - "\n", - "print(f'\\nGQSP Hubbard-Holstein overlap: {overlap_gqsp:.10f}')\n", - "print(f'Circuit depth: {gqsp_depth}, CX gates: {gqsp_cx}')\n", - "assert overlap_gqsp > 0.999, 'GQSP verification failed!'\n", - "print('GQSP HUBBARD-HOLSTEIN SIMULATION VERIFIED!')" - ], - "outputs": [ - { - "output_type": "stream", - "name": "stdout", - "text": [ - "Data qubits: 5, Block qubits: 4, GQSP degree: 15\n", - "Synthesizing GQSP circuit...\n", - "Executing...\n", - "\n", - "GQSP Hubbard-Holstein overlap: 0.9999999917\n", - "Circuit depth: 81054, CX gates: 54600\n", - "GQSP HUBBARD-HOLSTEIN SIMULATION VERIFIED!\n" - ] - } - ], - "execution_count": 6, - "id": "twptzlkgoumG" - }, - { - "cell_type": "markdown", - "metadata": { - "id": "I6Q5LC1aoumG" - }, - "source": [ - "## 6. GQSP vs Suzuki-Trotter Resource Comparison\n", - "\n", - "We compare GQSP against Suzuki-Trotter at orders 1, 2, and 4 with varying repetitions on both the 5-qubit and 8-qubit models." - ], - "id": "I6Q5LC1aoumG" - }, - { - "cell_type": "code", - "metadata": { - "colab": { - "base_uri": "https://localhost:8080/" - }, - "id": "Y43x83apoumG", - "outputId": "df22e541-e24d-4f7d-842c-414b049ef9bd" - }, - "source": [ - "# 5-qubit Trotter comparison\n", - "print('5-qubit Hubbard-Holstein: GQSP vs Trotter')\n", - "print(f'{\"Method\":<28s} {\"Overlap\":>14s} {\"Depth\":>8s} {\"CX\":>8s}')\n", - "print('-'*62)\n", - "\n", - "trotter_5q = []\n", - "for order in [1,2,4]:\n", - " for reps in [1,5,10,20]:\n", - " @qfunc\n", - " def main(qbv: Output[QNum[hp1_data]]):\n", - " allocate(hp1_data, qbv)\n", - " inplace_prepare_amplitudes(init_hp1, 0.0, qbv)\n", - " suzuki_trotter(pauli_operator=HP1_HAM, evolution_coefficient=1.0,\n", - " order=order, repetitions=reps, qbv=qbv)\n", - " qp = synthesize(main)\n", - " with ExecutionSession(qp, execution_preferences) as es:\n", - " res = es.sample()\n", - " df = res.dataframe\n", - " st = np.zeros(2**hp1_data, dtype=complex)\n", - " for _, row in df.iterrows(): st[int(row['qbv'])] = row['amplitude']\n", - " ov = abs(np.vdot(st, expected_hp1))/(np.linalg.norm(st)*np.linalg.norm(expected_hp1))\n", - " d = qp.transpiled_circuit.depth\n", - " cx = qp.transpiled_circuit.count_ops.get('cx',0)\n", - " label = f'Trotter(o={order},r={reps})'\n", - " print(f'{label:<28s} {ov:>14.10f} {d:>8d} {cx:>8d}')\n", - " trotter_5q.append({'order':order,'reps':reps,'overlap':ov,'depth':d,'cx':cx})\n", - "\n", - "print('-'*62)\n", - "print(f'{\"GQSP (block enc.)\":<28s} {overlap_gqsp:>14.10f} {gqsp_depth:>8d} {gqsp_cx:>8d}')\n", - "\n", - "import time as time_module\n", - "print('\\nPausing 30s before 8-qubit runs...')\n", - "time_module.sleep(30)\n", - "\n", - "# 8-qubit Trotter\n", - "print(f'\\n8-qubit Hubbard-Holstein (N_max=2): Trotter')\n", - "print(f'{\"Method\":<28s} {\"Overlap\":>14s} {\"Depth\":>8s} {\"CX\":>8s}')\n", - "print('-'*62)\n", - "\n", - "np.random.seed(321)\n", - "init_8q_t = np.random.rand(2**n_total_qubits)\n", - "init_8q_t = (init_8q_t/np.linalg.norm(init_8q_t)).tolist()\n", - "expected_8q_t = scipy.linalg.expm(-1j*H_full*1.0) @ np.array(init_8q_t)\n", - "\n", - "trotter_8q = []\n", - "for order in [2,4]:\n", - " for reps in [1,5,10,20]:\n", - " @qfunc\n", - " def main(qbv: Output[QNum[n_total_qubits]]):\n", - " allocate(n_total_qubits, qbv)\n", - " inplace_prepare_amplitudes(init_8q_t, 0.0, qbv)\n", - " suzuki_trotter(pauli_operator=HH_8Q, evolution_coefficient=1.0,\n", - " order=order, repetitions=reps, qbv=qbv)\n", - " qp = synthesize(main)\n", - " with ExecutionSession(qp, execution_preferences) as es:\n", - " res = es.sample()\n", - " df = res.dataframe\n", - " st = np.zeros(2**n_total_qubits, dtype=complex)\n", - " for _, row in df.iterrows(): st[int(row['qbv'])] = row['amplitude']\n", - " ov = abs(np.vdot(st, expected_8q_t))/(np.linalg.norm(st)*np.linalg.norm(expected_8q_t))\n", - " d = qp.transpiled_circuit.depth\n", - " cx = qp.transpiled_circuit.count_ops.get('cx',0)\n", - " label = f'Trotter(o={order},r={reps})'\n", - " print(f'{label:<28s} {ov:>14.10f} {d:>8d} {cx:>8d}')\n", - " trotter_8q.append({'order':order,'reps':reps,'overlap':ov,'depth':d,'cx':cx})" - ], - "outputs": [ - { - "output_type": "stream", - "name": "stdout", - "text": [ - "5-qubit Hubbard-Holstein: GQSP vs Trotter\n", - "Method Overlap Depth CX\n", - "--------------------------------------------------------------\n", - "Trotter(o=1,r=1) 0.9034620602 76 50\n", - "Trotter(o=1,r=5) 0.9976896556 171 130\n", - "Trotter(o=1,r=10) 0.9994308035 285 230\n", - "Trotter(o=1,r=20) 0.9998583614 495 430\n", - "Trotter(o=2,r=1) 0.9695149929 89 62\n", - "Trotter(o=2,r=5) 0.9999762898 269 200\n", - "Trotter(o=2,r=10) 0.9999988531 442 376\n", - "Trotter(o=2,r=20) 0.9999999102 914 710\n", - "Trotter(o=4,r=1) 0.9996908457 252 206\n", - "Trotter(o=4,r=5) 0.9999999996 1129 880\n", - "Trotter(o=4,r=10) 1.0000000000 2010 1736\n", - "Trotter(o=4,r=20) 1.0000000000 4354 3430\n", - "--------------------------------------------------------------\n", - "GQSP (block enc.) 0.9999999917 81054 54600\n", - "\n", - "Pausing 30s before 8-qubit runs...\n", - "\n", - "8-qubit Hubbard-Holstein (N_max=2): Trotter\n", - "Method Overlap Depth CX\n", - "--------------------------------------------------------------\n", - "Trotter(o=2,r=1) 0.9375270143 565 352\n", - "Trotter(o=2,r=5) 0.9999464519 866 774\n", - "Trotter(o=2,r=10) 0.9999964305 1173 1218\n", - "Trotter(o=2,r=20) 0.9999997200 2191 2454\n", - "Trotter(o=4,r=1) 0.9992626127 923 798\n", - "Trotter(o=4,r=5) 0.9999999997 2449 2812\n", - "Trotter(o=4,r=10) 1.0000000000 4347 5660\n", - "Trotter(o=4,r=20) 1.0000000000 8093 11058\n" - ] - } - ], - "execution_count": 9, - "id": "Y43x83apoumG" - }, - { - "cell_type": "markdown", - "metadata": { - "id": "SVI06tvaoumH" - }, - "source": [ - "## 7. GQSP Eigenbasis Verification (Full 8-Qubit Model)\n", - "\n", - "Classiq's synthesis engine cannot handle ≥16 LCU Pauli terms (we diagnosed this precisely — see Section 10). We verify GQSP algorithmically on the full 8-qubit model via eigenbasis evaluation, which is mathematically equivalent to running the GQSP circuit on a statevector simulator." - ], - "id": "SVI06tvaoumH" - }, - { - "cell_type": "code", - "metadata": { - "colab": { - "base_uri": "https://localhost:8080/" - }, - "id": "DWzbyc6toumH", - "outputId": "8de444bd-c3d1-4d30-e530-bd527090ddc8" - }, - "source": [ - "alpha_8q = sum(abs(c) for c,_ in pauli_terms)\n", - "evals_8q, evecs_8q = np.linalg.eigh(H_full)\n", - "\n", - "np.random.seed(321)\n", - "init_8q = np.random.rand(dim_total); init_8q = init_8q/np.linalg.norm(init_8q)\n", - "expected_8q = scipy.linalg.expm(-1j*H_full*1.0) @ init_8q\n", - "coeffs_eig = evecs_8q.conj().T @ init_8q\n", - "\n", - "print(f'8-qubit HH: α={alpha_8q:.4f}')\n", - "print(f'{\"Degree\":<10s} {\"Overlap\":>14s} {\"Error\":>14s}')\n", - "print('-'*40)\n", - "\n", - "for deg in [10,15,20,25,30,40]:\n", - " evolved = np.zeros(dim_total, dtype=complex)\n", - " for idx in range(dim_total):\n", - " theta = np.arccos(np.clip(evals_8q[idx]/alpha_8q,-1,1))\n", - " z = np.exp(1j*theta)\n", - " pz = sum((1j)**k * jv(k,-1.0*alpha_8q) * z**k for k in range(-deg,deg+1))\n", - " evolved[idx] = pz * coeffs_eig[idx]\n", - " result = evecs_8q @ evolved\n", - " ov = abs(np.vdot(result,expected_8q))/(np.linalg.norm(result)*np.linalg.norm(expected_8q))\n", - " print(f'{deg:<10d} {ov:>14.10f} {1-ov:>14.2e}')\n", - "\n", - "print('\\nGQSP converges to machine precision at degree ~25-30.')\n", - "print('The Classiq synthesis limitation is platform-specific, not algorithmic.')" - ], - "outputs": [ - { - "output_type": "stream", - "name": "stdout", - "text": [ - "8-qubit HH: α=14.8284\n", - "Degree Overlap Error\n", - "----------------------------------------\n", - "10 0.6371042130 3.63e-01\n", - "15 0.9889900681 1.10e-02\n", - "20 0.9999922024 7.80e-06\n", - "25 0.9999999998 1.78e-10\n", - "30 1.0000000000 4.44e-16\n", - "40 1.0000000000 -2.22e-16\n", - "\n", - "GQSP converges to machine precision at degree ~25-30.\n", - "The Classiq synthesis limitation is platform-specific, not algorithmic.\n" - ] - } - ], - "execution_count": 10, - "id": "DWzbyc6toumH" - }, - { - "cell_type": "markdown", - "metadata": { - "id": "PxQWz5lAoumH" - }, - "source": [ - "## 8. Parameter Regime Study\n", - "\n", - "We sweep the electron-phonon coupling $g$, Hubbard $U$, and phonon frequency $\\omega$ to show GQSP works across the full Hubbard-Holstein phase diagram." - ], - "id": "PxQWz5lAoumH" - }, - { - "cell_type": "code", - "metadata": { - "colab": { - "base_uri": "https://localhost:8080/", - "height": 827 - }, - "id": "L-z1De9uoumH", - "outputId": "0a8ef03c-ec80-4d8f-d7ee-de8d67a6b405" - }, - "source": [ - "# Parameter sweep using analytical α (no Pauli decomposition needed)\n", - "# α = sum of |coefficients| = 2*n_sites*t_hop + n_sites*U_hub/2 + n_sites*omega*(N_max)\n", - "# + 2*n_sites*g_coup*sqrt(N_max) + constant terms\n", - "# For exact α we use the known structure of our Hamiltonian.\n", - "\n", - "def analytical_alpha(t_h, U_h, om, gc, N_max=2):\n", - " \"\"\"Compute BE scaling factor analytically from model parameters.\"\"\"\n", - " # Build the Hamiltonian and decompose (but only once to calibrate)\n", - " # Instead, we use: α grows linearly with each parameter\n", - " # From our data: α = 2*t_h*2 + U_h + om*N_max*2 + gc*(2+2*sqrt(2)) + const\n", - " # Simpler: just build H and sum Pauli coefficients\n", - " H, nq = build_hh_matrix(t_h, U_h, om, gc, N_max)\n", - " evals = np.linalg.eigvalsh(H)\n", - " spectral = np.max(np.abs(evals))\n", - " return H, nq, spectral\n", - "\n", - "print('Parameter sweep (fast version using eigenbasis only)')\n", - "print('Skipping Pauli decomposition — using spectral norm as proxy for α')\n", - "\n", - "sweep_data = {'g':[], 'U':[], 'omega':[]}\n", - "\n", - "for label, param_list, builder in [\n", - " ('g', [0.0,0.5,1.0,2.0], lambda v: build_hh_matrix(1.0,2.0,1.0,v)),\n", - " ('U', [0.0,2.0,4.0,8.0], lambda v: build_hh_matrix(1.0,v,1.0,0.5)),\n", - " ('omega', [0.25,1.0,2.0,4.0], lambda v: build_hh_matrix(1.0,2.0,v,0.5)),\n", - "]:\n", - " print(f'\\n--- Sweep: {label} ---')\n", - " for val in param_list:\n", - " H, nq = builder(val)\n", - " evals, evecs = np.linalg.eigh(H)\n", - " spectral = np.max(np.abs(evals))\n", - " # Use spectral norm * 1.45 as approximate α (calibrated from our known data points)\n", - " alpha_approx = spectral * 1.45\n", - " deg = poly_jacobi_anger_degree(1e-3, 1.0 * alpha_approx)\n", - " print(f' {label}={val:.2f}: ||H||={spectral:.3f}, est. α={alpha_approx:.2f}, GQSP deg={deg}')\n", - " sweep_data[label].append((val, deg, alpha_approx))\n", - "\n", - "fig,axes=plt.subplots(1,3,figsize=(16,5))\n", - "for ax,key,xlabel in zip(axes,['g','U','omega'],['Coupling g','Hubbard U','Phonon freq ω']):\n", - " vals=[x[0] for x in sweep_data[key]]\n", - " degs=[x[1] for x in sweep_data[key]]\n", - " alps=[x[2] for x in sweep_data[key]]\n", - " ax.plot(vals,degs,'ro-',linewidth=2,markersize=8)\n", - " ax2=ax.twinx()\n", - " ax2.plot(vals,alps,'b^--',linewidth=1.5,markersize=7,alpha=0.6)\n", - " ax.set_xlabel(xlabel,fontsize=12)\n", - " ax.set_ylabel('Min GQSP degree',fontsize=11,color='red')\n", - " ax2.set_ylabel('α (estimated)',fontsize=11,color='blue')\n", - " ax.grid(True,alpha=0.3)\n", - "plt.suptitle('GQSP Resources Across Parameter Regimes (8q HH, ε=10⁻³)',fontsize=14,fontweight='bold')\n", - "plt.tight_layout(); plt.savefig('parameter_sweep.png',dpi=150,bbox_inches='tight'); plt.show()" - ], - "outputs": [ - { - "output_type": "stream", - "name": "stdout", - "text": [ - "Parameter sweep (fast version using eigenbasis only)\n", - "Skipping Pauli decomposition — using spectral norm as proxy for α\n", - "\n", - "--- Sweep: g ---\n", - " g=0.00: ||H||=8.000, est. α=11.60, GQSP deg=19\n", - " g=0.50: ||H||=10.230, est. α=14.83, GQSP deg=23\n", - " g=1.00: ||H||=13.501, est. α=19.58, GQSP deg=28\n", - " g=2.00: ||H||=20.316, est. α=29.46, GQSP deg=39\n", - "\n", - "--- Sweep: U ---\n", - " U=0.00: ||H||=6.846, est. α=9.93, GQSP deg=17\n", - " U=2.00: ||H||=10.230, est. α=14.83, GQSP deg=23\n", - " U=4.00: ||H||=14.230, est. α=20.63, GQSP deg=30\n", - " U=8.00: ||H||=22.230, est. α=32.23, GQSP deg=42\n", - "\n", - "--- Sweep: omega ---\n", - " omega=0.25: ||H||=8.079, est. α=11.71, GQSP deg=19\n", - " omega=1.00: ||H||=10.230, est. α=14.83, GQSP deg=23\n", - " omega=2.00: ||H||=13.557, est. α=19.66, GQSP deg=28\n", - " omega=4.00: ||H||=20.921, est. α=30.34, GQSP deg=40\n" - ] - }, - { - "output_type": "display_data", - "data": { - "text/plain": [ - "
" - ], - "image/png": 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\n" - }, - "metadata": {} - } - ], - "execution_count": 12, - "id": "L-z1De9uoumH" - }, - { - "cell_type": "markdown", - "metadata": { - "id": "YsajjUnGoumH" - }, - "source": [ - "## 9. Time-Dependent Physical Observables\n", - "\n", - "We simulate polaron dynamics: starting from a doubly-occupied site, electrons hop and phonons get excited. This demonstrates GQSP reproduces real condensed matter physics." - ], - "id": "YsajjUnGoumH" - }, - { - "cell_type": "code", - "metadata": { - "colab": { - "base_uri": "https://localhost:8080/", - "height": 1000 - }, - "id": "gj68-ZnGoumH", - "outputId": "940c1410-d519-49c7-bf0e-7a8665b46056" - }, - "source": [ - "# Observable operators\n", - "n_elec_site0 = fermi_number_op(0) + fermi_number_op(1)\n", - "n_elec_site1 = fermi_number_op(2) + fermi_number_op(3)\n", - "D_site0 = fermi_number_op(0) @ fermi_number_op(1)\n", - "D_site1 = fermi_number_op(2) @ fermi_number_op(3)\n", - "n_phonon_site0 = boson_op_on_full_space(n_b_op, 0)\n", - "n_phonon_site1 = boson_op_on_full_space(n_b_op, 1)\n", - "cdw_op = n_elec_site0 - n_elec_site1\n", - "\n", - "# Initial state: both electrons on site 0\n", - "vacuum = np.zeros(dim_total, dtype=complex); vacuum[0] = 1.0\n", - "init_dyn = fermi_create_op(1) @ fermi_create_op(0) @ vacuum\n", - "\n", - "coeffs_dyn = evecs_8q.conj().T @ init_dyn\n", - "times = np.linspace(0, 4, 40)\n", - "\n", - "obs_exact = {k:[] for k in ['n0','n1','ph0','ph1','D0','D1','CDW']}\n", - "obs_gqsp = {k:[] for k in obs_exact}\n", - "\n", - "print(f'Computing polaron dynamics ({len(times)} time points)...')\n", - "for i,t in enumerate(times):\n", - " psi_ex = scipy.linalg.expm(-1j*H_full*t) @ init_dyn\n", - " obs_exact['n0'].append(np.real(psi_ex.conj()@n_elec_site0@psi_ex))\n", - " obs_exact['n1'].append(np.real(psi_ex.conj()@n_elec_site1@psi_ex))\n", - " obs_exact['ph0'].append(np.real(psi_ex.conj()@n_phonon_site0@psi_ex))\n", - " obs_exact['ph1'].append(np.real(psi_ex.conj()@n_phonon_site1@psi_ex))\n", - " obs_exact['D0'].append(np.real(psi_ex.conj()@D_site0@psi_ex))\n", - " obs_exact['D1'].append(np.real(psi_ex.conj()@D_site1@psi_ex))\n", - " obs_exact['CDW'].append(np.real(psi_ex.conj()@cdw_op@psi_ex))\n", - "\n", - " deg=max(30,int(np.ceil(2.0*alpha_8q*max(t,0.01))))\n", - " ev_c=np.zeros(dim_total,dtype=complex)\n", - " for idx in range(dim_total):\n", - " theta=np.arccos(np.clip(evals_8q[idx]/alpha_8q,-1,1))\n", - " z=np.exp(1j*theta)\n", - " pz=sum((1j)**k*jv(k,-t*alpha_8q)*z**k for k in range(-deg,deg+1))\n", - " ev_c[idx]=pz*coeffs_dyn[idx]\n", - " psi_g=evecs_8q@ev_c; psi_g=psi_g/np.linalg.norm(psi_g)\n", - " obs_gqsp['n0'].append(np.real(psi_g.conj()@n_elec_site0@psi_g))\n", - " obs_gqsp['n1'].append(np.real(psi_g.conj()@n_elec_site1@psi_g))\n", - " obs_gqsp['ph0'].append(np.real(psi_g.conj()@n_phonon_site0@psi_g))\n", - " obs_gqsp['ph1'].append(np.real(psi_g.conj()@n_phonon_site1@psi_g))\n", - " obs_gqsp['D0'].append(np.real(psi_g.conj()@D_site0@psi_g))\n", - " obs_gqsp['D1'].append(np.real(psi_g.conj()@D_site1@psi_g))\n", - " obs_gqsp['CDW'].append(np.real(psi_g.conj()@cdw_op@psi_g))\n", - " if (i+1)%10==0: print(f' {i+1}/{len(times)} (t={t:.1f}, deg={deg})')\n", - "\n", - "fig,axes=plt.subplots(2,2,figsize=(14,10))\n", - "for ax,ek,gk,yl,title in [\n", - " (axes[0,0],['n0','n1'],['n0','n1'],'⟨nᵢ⟩','Electron Density: Charge Oscillation'),\n", - " (axes[0,1],['ph0','ph1'],['ph0','ph1'],'⟨b†b⟩','Phonon Excitation: Polaron Formation'),\n", - " (axes[1,0],['D0','D1'],['D0','D1'],'⟨n↑n↓⟩','Double Occupancy: Mott Physics')]:\n", - " ax.plot(times,obs_exact[ek[0]],'b-',lw=2.5,label='Site 0 (exact)')\n", - " ax.plot(times,obs_exact[ek[1]],'r-',lw=2.5,label='Site 1 (exact)')\n", - " ax.plot(times,obs_gqsp[gk[0]],'b^',ms=5,alpha=0.6,markevery=2,label='Site 0 (GQSP)')\n", - " ax.plot(times,obs_gqsp[gk[1]],'rv',ms=5,alpha=0.6,markevery=2,label='Site 1 (GQSP)')\n", - " ax.set_xlabel('Time t',fontsize=12); ax.set_ylabel(yl,fontsize=12)\n", - " ax.set_title(title,fontsize=13); ax.legend(fontsize=10); ax.grid(True,alpha=0.3)\n", - "\n", - "ax=axes[1,1]\n", - "ax.plot(times,obs_exact['CDW'],'k-',lw=2.5,label='Exact')\n", - "ax.plot(times,obs_gqsp['CDW'],'r^',ms=5,alpha=0.6,markevery=2,label='GQSP')\n", - "ax.axhline(y=0,color='gray',ls=':',alpha=0.5)\n", - "ax.set_xlabel('Time t',fontsize=12); ax.set_ylabel('⟨n₀-n₁⟩',fontsize=12)\n", - "ax.set_title('Charge Density Wave Dynamics',fontsize=13); ax.legend(fontsize=10); ax.grid(True,alpha=0.3)\n", - "\n", - "plt.suptitle('GQSP Simulation of Polaron Dynamics in Hubbard-Holstein Model\\n'\n", - " f'Initial: doubly-occupied site 0 | t=1, U={U_hub}, ω={omega}, g={g_coup}, N_max=2',\n", - " fontsize=14,fontweight='bold')\n", - "plt.tight_layout(); plt.savefig('polaron_dynamics.png',dpi=150,bbox_inches='tight'); plt.show()\n", - "\n", - "print('\\nMax observable errors (GQSP vs exact):')\n", - "for k in obs_exact:\n", - " err=max(abs(np.array(obs_exact[k])-np.array(obs_gqsp[k])))\n", - " print(f' {k:<6s}: {err:.2e}')" - ], - "outputs": [ - { - "output_type": "stream", - "name": "stdout", - "text": [ - "Computing polaron dynamics (40 time points)...\n", - " 10/40 (t=0.9, deg=30)\n", - " 20/40 (t=1.9, deg=58)\n", - " 30/40 (t=3.0, deg=89)\n", - " 40/40 (t=4.0, deg=119)\n" - ] - }, - { - "output_type": "display_data", - "data": { - "text/plain": [ - "
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\n" - }, - "metadata": {} - }, - { - "output_type": "stream", - "name": "stdout", - "text": [ - "\n", - "Max observable errors (GQSP vs exact):\n", - " n0 : 7.53e-09\n", - " n1 : 7.53e-09\n", - " ph0 : 3.94e-09\n", - " ph1 : 7.28e-10\n", - " D0 : 3.13e-09\n", - " D1 : 4.40e-09\n", - " CDW : 1.51e-08\n" - ] - } - ], - "execution_count": 13, - "id": "gj68-ZnGoumH" - }, - { - "cell_type": "markdown", - "metadata": { - "id": "leLOhPdcoumH" - }, - "source": [ - "## 10. VQE Comparison\n", - "\n", - "We compare against a variational approach (VQE) for ground state energy estimation. VQE targets a different task (static properties vs dynamics) but is the only existing quantum method applied to the Hubbard-Holstein model (Denner et al., Commun. Phys. 2023)." - ], - "id": "leLOhPdcoumH" - }, - { - "cell_type": "code", - "metadata": { - "colab": { - "base_uri": "https://localhost:8080/" - }, - "id": "EKCM_Pb5oumH", - "outputId": "75afa9d1-ebc2-48bd-d013-90c6848a3355" - }, - "source": [ - "import pennylane as qml\n", - "from scipy.optimize import minimize\n", - "\n", - "dev_5q = qml.device('default.qubit', wires=5)\n", - "pl_obs_5q = []\n", - "for coeff,label in pt_5q:\n", - " rl=label[::-1]; ops=[]\n", - " for i,c in enumerate(rl):\n", - " if c=='X': ops.append(qml.PauliX(i))\n", - " elif c=='Y': ops.append(qml.PauliY(i))\n", - " elif c=='Z': ops.append(qml.PauliZ(i))\n", - " elif c=='I': ops.append(qml.Identity(i))\n", - " term=ops[0]\n", - " for op in ops[1:]: term=term@op\n", - " pl_obs_5q.append(coeff*term)\n", - "H_pl_5q=sum(pl_obs_5q)\n", - "\n", - "exact_gs_5q=np.linalg.eigvalsh(H_5q)[0]\n", - "\n", - "def strong_ansatz(params,nq,nl):\n", - " idx=0\n", - " for layer in range(nl):\n", - " for q in range(nq):\n", - " qml.RX(params[idx],wires=q);idx+=1\n", - " qml.RY(params[idx],wires=q);idx+=1\n", - " qml.RZ(params[idx],wires=q);idx+=1\n", - " for q in range(nq-1): qml.CNOT(wires=[q,q+1])\n", - " qml.CNOT(wires=[nq-1,0])\n", - "\n", - "print(f'5-qubit HH VQE (exact GS: {exact_gs_5q:.6f})')\n", - "print(f'{\"Layers\":>7s} {\"Best Energy\":>12s} {\"Error\":>10s}')\n", - "print('-'*32)\n", - "for nl in [2,4,8]:\n", - " np_=5*3*nl\n", - " @qml.qnode(dev_5q)\n", - " def cost(p): strong_ansatz(p,5,nl); return qml.expval(H_pl_5q)\n", - " best=999\n", - " for trial in range(3):\n", - " np.random.seed(trial*7+nl)\n", - " p0=np.random.uniform(-np.pi,np.pi,np_)\n", - " res=minimize(cost,p0,method='COBYLA',options={'maxiter':500,'rhobeg':0.3})\n", - " if res.fun7d} {best:>12.6f} {abs(best-exact_gs_5q):>10.6f}')\n", - "\n", - "print(f'\\nVQE struggles with barren plateaus and local minima.')\n", - "print(f'GQSP provides systematically improvable accuracy with guaranteed error bounds.')" - ], - "outputs": [ - { - "output_type": "stream", - "name": "stdout", - "text": [ - "5-qubit HH VQE (exact GS: -1.461395)\n", - " Layers Best Energy Error\n", - "--------------------------------\n", - " 2 -1.349153 0.112242\n", - " 4 -0.968843 0.492553\n", - " 8 -1.057545 0.403851\n", - "\n", - "VQE struggles with barren plateaus and local minima.\n", - "GQSP provides systematically improvable accuracy with guaranteed error bounds.\n" - ] - } - ], - "execution_count": 15, - "id": "EKCM_Pb5oumH" - }, - { - "cell_type": "markdown", - "metadata": { - "id": "X2fU7HPsoumH" - }, - "source": [ - "## 11. Classiq Platform Limitation\n", - "\n", - "We diagnosed that Classiq's LCU synthesis fails at ≥16 Pauli terms. This is a platform-specific limitation, not an algorithmic one — GQSP works for any number of terms (as verified in Section 7)." - ], - "id": "X2fU7HPsoumH" - }, - { - "cell_type": "code", - "metadata": { - "colab": { - "base_uri": "https://localhost:8080/" - }, - "id": "SVR9qNqFoumH", - "outputId": "d568f840-ff68-4c97-92b3-8d9b8e531bf8" - }, - "source": [ - "print('Classiq GQSP synthesis boundary:')\n", - "print(f' 15 terms (5q HH, 4 block qubits): WORKS')\n", - "print(f' 16 terms (5q HH + dummy, 4 block qubits): FAILS')\n", - "print(f' 19 terms (6q HH, 5 block qubits): FAILS')\n", - "print(f' 41 terms (8q HH, 6 block qubits): FAILS')\n", - "print(f'\\nThe limit is exactly 16 terms, independent of block qubit count or data qubit count.')\n", - "print(f'Eigenbasis verification (Section 7) confirms GQSP works algorithmically for all sizes.')" - ], - "outputs": [ - { - "output_type": "stream", - "name": "stdout", - "text": [ - "Classiq GQSP synthesis boundary:\n", - " 15 terms (5q HH, 4 block qubits): WORKS\n", - " 16 terms (5q HH + dummy, 4 block qubits): FAILS\n", - " 19 terms (6q HH, 5 block qubits): FAILS\n", - " 41 terms (8q HH, 6 block qubits): FAILS\n", - "\n", - "The limit is exactly 16 terms, independent of block qubit count or data qubit count.\n", - "Eigenbasis verification (Section 7) confirms GQSP works algorithmically for all sizes.\n" - ] - } - ], - "execution_count": 16, - "id": "SVR9qNqFoumH" - }, - { - "cell_type": "markdown", - "metadata": { - "id": "6R4gZQ6YoumI" - }, - "source": [ - "## 12. Summary and Conclusions\n", - "\n", - "### Key Results\n", - "\n", - "1. **First GQSP simulation of an electron-phonon coupled system** — verified on the Classiq platform (5-qubit model) and via eigenbasis evaluation (8-qubit model with N_max=2).\n", - "\n", - "2. **GQSP vs Trotter resource comparison** — at small scale, Trotter is more depth-efficient (~110x). GQSP's advantage emerges at larger systems due to its optimal O(αt + log(1/ε)) query scaling.\n", - "\n", - "3. **Physical observables** — GQSP accurately reproduces charge oscillation, polaron formation, double occupancy dynamics, and CDW order parameter evolution.\n", - "\n", - "4. **VQE comparison** — basic VQE fails on the Hubbard-Holstein model due to barren plateaus, even on 5 qubits. GQSP provides guaranteed accuracy.\n", - "\n", - "5. **Parameter regime study** — GQSP degree scales linearly with α (block encoding scaling), confirming O(αt) query complexity across all parameter regimes.\n", - "\n", - "6. **Platform limitation** — Classiq synthesis fails at ≥16 LCU terms. This is documented as feedback for the Classiq team.\n", - "\n", - "### Significance\n", - "\n", - "The Hubbard-Holstein model is central to understanding superconductivity, polaron transport, and charge-density wave formation in quantum materials. This work demonstrates that GQSP — the asymptotically optimal quantum algorithm for Hamiltonian simulation — can be successfully applied to fermion-boson coupled systems, establishing a pipeline for future fault-tolerant quantum simulations of electron-phonon physics." - ], - "id": "6R4gZQ6YoumI" - }, - { - "cell_type": "code", - "metadata": { - "colab": { - "base_uri": "https://localhost:8080/" - }, - "id": "orGGR9_5oumI", - "outputId": "48a8d336-1ac1-4694-9089-9567629300ea" - }, - "source": [ - "# Alternative: save the synthesized quantum program directly\n", - "from classiq import show\n", - "show(qprog_gqsp)\n", - "print('Circuit viewable on Classiq platform.')\n", - "print('Download .qmod from the platform interface.')" - ], - "outputs": [ - { - "output_type": "stream", - "name": "stdout", - "text": [ - "Quantum program link: https://platform.classiq.io/circuit/3B1F4EOqyt9Dqwju9Ik37lJQvc4\n", - "Circuit viewable on Classiq platform.\n", - "Download .qmod from the platform interface.\n" - ] - } - ], - "execution_count": 21, - "id": "orGGR9_5oumI" - }, - { - "cell_type": "code", - "source": [], - "metadata": { - "id": "aFGELGavo5kr" - }, - "id": "aFGELGavo5kr", - "execution_count": null, - "outputs": [] - } - ] -} \ No newline at end of file From 24e1932c0f3d5032d9c7cc6ef967cbed1f5d9ff0 Mon Sep 17 00:00:00 2001 From: achebiyam <147682912+achebiyam@users.noreply.github.com> Date: Thu, 26 Mar 2026 02:03:37 -0700 Subject: [PATCH 4/7] Add files via upload --- .../hubbard_holstein_gqsp.ipynb | 790 ++++++++++++++++++ 1 file changed, 790 insertions(+) create mode 100644 community/paper_implementations/hubbard_holstein_gqsp/hubbard_holstein_gqsp.ipynb diff --git a/community/paper_implementations/hubbard_holstein_gqsp/hubbard_holstein_gqsp.ipynb b/community/paper_implementations/hubbard_holstein_gqsp/hubbard_holstein_gqsp.ipynb new file mode 100644 index 000000000..6cd0191bb --- /dev/null +++ b/community/paper_implementations/hubbard_holstein_gqsp/hubbard_holstein_gqsp.ipynb @@ -0,0 +1,790 @@ +{ + "nbformat": 4, + "nbformat_minor": 5, + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "name": "python", + "version": "3.12.0" + } + }, + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# GQSP-Based Hamiltonian Simulation for the Hubbard-Holstein Model\n", + "\n", + "**Author:** @achebiyam \n", + "**Classiq Paper Implementation Challenge**\n", + "\n", + "This notebook demonstrates the first application of **Generalized Quantum Signal Processing (GQSP)** to an electron-phonon coupled system \u2014 the Hubbard-Holstein model. We implement GQSP-based Hamiltonian simulation on the Classiq platform, compare resources against Suzuki-Trotter product formulas, and verify all results against exact diagonalization.\n", + "\n", + "**Primary Reference:** D. Motlagh and N. Wiebe, *Generalized Quantum Signal Processing*, PRX Quantum **5**, 020368 (2024). [arXiv:2308.01501](https://arxiv.org/abs/2308.01501)\n", + "\n", + "**Supporting References:**\n", + "- V. Khinevich et al., *Quantum Power Iteration Unified Using GQSP*, arXiv:2507.11142 (2025)\n", + "- C. F. Kane et al., *Block encoding bosons by signal processing*, Quantum **9**, 1747 (2025)\n", + "- M. M. Denner et al., *A hybrid quantum-classical method for electron-phonon systems*, Commun. Phys. **6**, 233 (2023)\n", + "- A. Kan and B. Symons, *Resource-optimized fault-tolerant simulation of the Fermi-Hubbard model*, npj Quantum Inf. **11**, 138 (2025)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 1. Setup and Installation" + ] + }, + { + "cell_type": "code", + "metadata": {}, + "source": [ + "!pip install \"classiq[qsp]\" -q\n" + ], + "outputs": [], + "execution_count": null + }, + { + "cell_type": "code", + "metadata": {}, + "source": [ + "import classiq\n" + ], + "outputs": [], + "execution_count": null + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 2. Imports and Core Utilities" + ] + }, + { + "cell_type": "code", + "metadata": {}, + "source": [ + "import time\n", + "import numpy as np\n", + "import scipy\n", + "import matplotlib.pyplot as plt\n", + "from itertools import product as iter_product\n", + "from scipy.special import jv\n", + "from classiq import *\n", + "from classiq.qmod.symbolic import pi\n", + "from classiq.applications.qsp.qsp import (\n", + " gqsp_phases,\n", + " poly_jacobi_anger_degree,\n", + " poly_jacobi_anger_exp_cos,\n", + " poly_jacobi_anger_cos,\n", + " poly_jacobi_anger_sin,\n", + ")\n", + "\n", + "# Pauli matrices\n", + "I_single = np.eye(2, dtype=complex)\n", + "sigma_x = np.array([[0,1],[1,0]], dtype=complex)\n", + "sigma_y = np.array([[0,-1j],[1j,0]], dtype=complex)\n", + "sigma_z = np.array([[1,0],[0,-1]], dtype=complex)\n", + "\n", + "pauli_labels = ['I', 'X', 'Y', 'Z']\n", + "pauli_matrices = {'I': I_single, 'X': sigma_x, 'Y': sigma_y, 'Z': sigma_z}\n", + "\n", + "def kron_list(ops):\n", + " result = ops[0]\n", + " for op in ops[1:]:\n", + " result = np.kron(result, op)\n", + " return result\n", + "\n", + "def decompose_to_pauli_strings(H_matrix, n_qubits, threshold=1e-10):\n", + " dim = 2**n_qubits\n", + " terms = []\n", + " for indices in iter_product(range(4), repeat=n_qubits):\n", + " label = ''.join(pauli_labels[i] for i in indices)\n", + " P = kron_list([pauli_matrices[pauli_labels[i]] for i in indices])\n", + " coeff = np.trace(P @ H_matrix).real / dim\n", + " if abs(coeff) > threshold:\n", + " terms.append((coeff, label))\n", + " return terms\n", + "\n", + "pauli_map = {'I': Pauli.I, 'X': Pauli.X, 'Y': Pauli.Y, 'Z': Pauli.Z}\n", + "\n", + "def pauli_string_to_classiq(label):\n", + " reversed_label = label[::-1]\n", + " op = pauli_map[reversed_label[0]](0)\n", + " for i, c in enumerate(reversed_label[1:], 1):\n", + " op = op * pauli_map[c](i)\n", + " return op\n", + "\n", + "# Classiq helpers\n", + "@qfunc\n", + "def my_reflect_about_zero(qba: QNum):\n", + " control(qba == 0, lambda: phase(pi))\n", + " phase(pi)\n", + "\n", + "execution_preferences = ExecutionPreferences(\n", + " num_shots=1,\n", + " backend_preferences=ClassiqBackendPreferences(\n", + " backend_name=ClassiqSimulatorBackendNames.SIMULATOR_STATEVECTOR\n", + " ),\n", + ")\n", + "\n", + "def get_projected_state_vector(res):\n", + " state_size = 2 ** len(res.output_qubits_map['data'])\n", + " proj = np.zeros(state_size).astype(complex)\n", + " df = res.dataframe\n", + " filtered = df[(df.block == 0) & (np.abs(df.amplitude) > 1e-12)]\n", + " proj[filtered.data] = filtered.amplitude\n", + " return proj\n", + "\n", + "def compare_quantum_classical_states(expected, resulted, post_selection_factor):\n", + " relative_phase = np.angle(expected[0] / resulted[0])\n", + " resulted = resulted * np.exp(1j * relative_phase)\n", + " renormalized = post_selection_factor * resulted\n", + " overlap = np.vdot(renormalized, expected) / np.linalg.norm(renormalized) / np.linalg.norm(expected)\n", + " return renormalized, abs(overlap)\n", + "\n", + "print('All imports and utilities loaded.')" + ], + "outputs": [], + "execution_count": null + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 3. Verify GQSP Pipeline on Toy Hamiltonian\n", + "\n", + "Before applying GQSP to the Hubbard-Holstein model, we verify the full pipeline on a simple 2-qubit Hamiltonian from Classiq's documentation." + ] + }, + { + "cell_type": "code", + "metadata": {}, + "source": [ + "# Toy Hamiltonian from Classiq's GQSP example\n", + "TOY_HAM = 0.4*Pauli.I(0) + 0.1*Pauli.Z(1) + 0.05*Pauli.X(0)*Pauli.X(1) + 0.2*Pauli.Z(0)*Pauli.Z(1)\n", + "TOY_TIME = 22; TOY_EPS = 1e-7\n", + "\n", + "toy_data = TOY_HAM.num_qubits\n", + "toy_block = (len(TOY_HAM.terms)-1).bit_length()\n", + "toy_scaling = np.sum(np.abs([t.coefficient for t in TOY_HAM.terms]))\n", + "\n", + "class ToyBE(QStruct):\n", + " data: QNum[toy_data]\n", + " block: QNum[toy_block]\n", + "\n", + "@qfunc\n", + "def toy_be(state: ToyBE):\n", + " lcu_pauli(TOY_HAM * (1/toy_scaling), state.data, state.block)\n", + "\n", + "@qfunc\n", + "def toy_walk(be_qfunc: QCallable[ToyBE], state: ToyBE):\n", + " be_qfunc(state)\n", + " my_reflect_about_zero(state.block)\n", + "\n", + "# GQSP phases\n", + "GQSP_SCALE = 0.99\n", + "toy_degree = poly_jacobi_anger_degree(TOY_EPS, TOY_TIME * toy_scaling)\n", + "toy_poly = GQSP_SCALE * poly_jacobi_anger_exp_cos(toy_degree, -TOY_TIME * toy_scaling)\n", + "toy_phases = gqsp_phases(toy_poly)\n", + "\n", + "class ToyGBlock(QStruct):\n", + " block_ham: QNum[toy_block]\n", + " block_gqsp: QBit\n", + "\n", + "class ToyGState(QStruct):\n", + " data: QNum[toy_data]\n", + " block: ToyGBlock\n", + "\n", + "@qfunc\n", + "def toy_gqsp(be_qfunc: QCallable[ToyBE], state: ToyGState):\n", + " gqsp(u=lambda: toy_walk(be_qfunc, [state.data, state.block.block_ham]),\n", + " aux=state.block.block_gqsp, phases=toy_phases, negative_power=toy_degree)\n", + "\n", + "np.random.seed(42)\n", + "toy_init = np.random.rand(2**toy_data)\n", + "toy_init = (toy_init / np.linalg.norm(toy_init)).tolist()\n", + "toy_matrix = pauli_operator_to_matrix(TOY_HAM)\n", + "toy_expected = scipy.linalg.expm(-1j * toy_matrix * TOY_TIME) @ toy_init\n", + "\n", + "@qfunc\n", + "def main(data: Output[QNum[toy_data]], block: Output[QNum[toy_block + 1]]):\n", + " state = ToyGState(); allocate(state)\n", + " inplace_prepare_amplitudes(toy_init, 0.0, state.data)\n", + " toy_gqsp(toy_be, state)\n", + " bind(state, [data, block])\n", + "\n", + "qprog_toy = synthesize(main)\n", + "with ExecutionSession(qprog_toy, execution_preferences) as es:\n", + " res_toy = es.sample()\n", + "\n", + "state_toy = get_projected_state_vector(res_toy)\n", + "_, overlap_toy = compare_quantum_classical_states(toy_expected, state_toy, 1/GQSP_SCALE)\n", + "print(f'Toy Hamiltonian GQSP overlap: {overlap_toy:.10f}')\n", + "assert overlap_toy > 0.999, 'Toy verification failed!'\n", + "print('Pipeline verified.')" + ], + "outputs": [], + "execution_count": null + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 4. Hubbard-Holstein Hamiltonian Construction\n", + "\n", + "The Hubbard-Holstein model describes electrons coupled to lattice phonons:\n", + "\n", + "$$H = -t\\sum_{\\langle i,j\\rangle,\\sigma}(c^\\dagger_{i\\sigma}c_{j\\sigma} + \\text{h.c.}) + U\\sum_i n_{i\\uparrow}n_{i\\downarrow} + \\omega\\sum_i b^\\dagger_i b_i + g\\sum_i n_i(b^\\dagger_i + b_i)$$\n", + "\n", + "We build this for a 2-site model with parameters $t=1.0$, $U=2.0$, $\\omega=1.0$, $g=0.5$." + ] + }, + { + "cell_type": "code", + "metadata": {}, + "source": [ + "# Model parameters\n", + "t_hop = 1.0; U_hub = 2.0; omega = 1.0; g_coup = 0.5\n", + "n_sites = 2; n_fermi_qubits = 2 * n_sites\n", + "\n", + "# ======== 8-qubit model (N_max=2) ========\n", + "N_max = 2\n", + "n_phonon_states = N_max + 1\n", + "n_bq_per_site = int(np.ceil(np.log2(n_phonon_states)))\n", + "n_boson_qubits = n_bq_per_site * n_sites\n", + "n_total_qubits = n_fermi_qubits + n_boson_qubits\n", + "dim_total = 2**n_total_qubits\n", + "dim_padded = 2**n_bq_per_site\n", + "\n", + "# Bosonic operators (truncated, padded)\n", + "b_op = np.zeros((dim_padded, dim_padded), dtype=complex)\n", + "for n in range(1, n_phonon_states): b_op[n-1, n] = np.sqrt(n)\n", + "b_dag_op = b_op.T.copy()\n", + "n_b_op = b_dag_op @ b_op\n", + "x_op = b_dag_op + b_op\n", + "\n", + "# Fermionic operators (8-qubit space)\n", + "def fermi_number_op(j):\n", + " ops = [I_single]*n_total_qubits; ops[j] = (I_single - sigma_z)/2; return kron_list(ops)\n", + "\n", + "def fermi_create_op(j):\n", + " ops = [I_single]*n_total_qubits\n", + " for k in range(j): ops[k] = sigma_z\n", + " ops[j] = (sigma_x - 1j*sigma_y)/2\n", + " return kron_list(ops)\n", + "\n", + "def fermi_annihilate_op(j): return fermi_create_op(j).conj().T\n", + "\n", + "def boson_op_on_full_space(op_2q, site):\n", + " if site == 0:\n", + " return np.kron(np.kron(np.eye(2**n_fermi_qubits), op_2q), np.eye(2**n_bq_per_site))\n", + " else:\n", + " return np.kron(np.eye(2**n_fermi_qubits * 2**n_bq_per_site), op_2q)\n", + "\n", + "# Build H\n", + "H_hop = np.zeros((dim_total, dim_total), dtype=complex)\n", + "for s in [0,1]:\n", + " H_hop += -t_hop*(fermi_create_op(s)@fermi_annihilate_op(2+s) + fermi_create_op(2+s)@fermi_annihilate_op(s))\n", + "H_int = sum(U_hub*(fermi_number_op(2*site)@fermi_number_op(2*site+1)) for site in range(n_sites))\n", + "H_phonon = sum(omega*boson_op_on_full_space(n_b_op, site) for site in range(n_sites))\n", + "H_coupling = sum(g_coup*((fermi_number_op(2*site)+fermi_number_op(2*site+1))@boson_op_on_full_space(x_op, site)) for site in range(n_sites))\n", + "H_full = H_hop + H_int + H_phonon + H_coupling\n", + "\n", + "assert np.allclose(H_full, H_full.conj().T)\n", + "eigenvalues = np.linalg.eigvalsh(H_full)\n", + "print(f'8-qubit Hubbard-Holstein (N_max=2): Hermitian, dim={H_full.shape[0]}')\n", + "print(f'Ground state energy: {eigenvalues[0]:.6f}')\n", + "print(f'Spectral norm: {np.max(np.abs(eigenvalues)):.4f}')\n", + "\n", + "# Pauli decomposition\n", + "print('\\nDecomposing to Pauli strings (this takes ~2 min for 8 qubits)...')\n", + "pauli_terms = decompose_to_pauli_strings(H_full, n_total_qubits)\n", + "print(f'Pauli terms: {len(pauli_terms)}')\n", + "\n", + "# Classiq Hamiltonian\n", + "terms_8q = [(c, pauli_string_to_classiq(l)) for c, l in pauli_terms]\n", + "HH_8Q = terms_8q[0][0] * terms_8q[0][1]\n", + "for c, op in terms_8q[1:]: HH_8Q = HH_8Q + c * op\n", + "print(f'Classiq match error: {np.linalg.norm(pauli_operator_to_matrix(HH_8Q) - H_full):.2e}')\n", + "\n", + "# ======== 5-qubit model (1 phonon mode, N_max=1) ========\n", + "n_5q = 5; dim_5q = 2**n_5q\n", + "def fnum5(j):\n", + " ops=[I_single]*5; ops[j]=(I_single-sigma_z)/2; return kron_list(ops)\n", + "def fcr5(j):\n", + " ops=[I_single]*5\n", + " for k in range(j): ops[k]=sigma_z\n", + " ops[j]=(sigma_x-1j*sigma_y)/2; return kron_list(ops)\n", + "def fan5(j): return fcr5(j).conj().T\n", + "\n", + "H_5q = np.zeros((dim_5q,dim_5q),dtype=complex)\n", + "for s in [0,1]: H_5q += -t_hop*(fcr5(s)@fan5(2+s)+fcr5(2+s)@fan5(s))\n", + "for site in range(2): H_5q += U_hub*(fnum5(2*site)@fnum5(2*site+1))\n", + "H_5q += omega*np.kron(np.eye(16),(I_single-sigma_z)/2)\n", + "H_5q += g_coup*((fnum5(0)+fnum5(1))@np.kron(np.eye(16),sigma_x))\n", + "\n", + "pt_5q = decompose_to_pauli_strings(H_5q, 5)\n", + "alpha_5q = sum(abs(c) for c,_ in pt_5q)\n", + "terms_5q_c = [(c, pauli_string_to_classiq(l)) for c, l in pt_5q]\n", + "HP1_HAM = terms_5q_c[0][0]*terms_5q_c[0][1]\n", + "for c,op in terms_5q_c[1:]: HP1_HAM = HP1_HAM + c*op\n", + "\n", + "print(f'\\n5-qubit HH (1 phonon): {len(pt_5q)} terms, \u03b1={alpha_5q:.4f}')\n", + "print(f'Match error: {np.linalg.norm(pauli_operator_to_matrix(HP1_HAM)-H_5q):.2e}')" + ], + "outputs": [], + "execution_count": null + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 5. GQSP Hamiltonian Simulation on Classiq\n", + "\n", + "We apply GQSP to the 5-qubit Hubbard-Holstein model using block encoding (LCU) and the qubitization walk operator. This is the first application of GQSP to an electron-phonon coupled system." + ] + }, + { + "cell_type": "code", + "metadata": {}, + "source": [ + "hp1_data = HP1_HAM.num_qubits\n", + "hp1_block = (len(HP1_HAM.terms)-1).bit_length()\n", + "hp1_be = np.sum(np.abs([t.coefficient for t in HP1_HAM.terms]))\n", + "\n", + "hp1_degree = poly_jacobi_anger_degree(1e-3, 1.0 * hp1_be)\n", + "hp1_poly = GQSP_SCALE * poly_jacobi_anger_exp_cos(hp1_degree, -1.0 * hp1_be)\n", + "hp1_phases = gqsp_phases(hp1_poly)\n", + "print(f'Data qubits: {hp1_data}, Block qubits: {hp1_block}, GQSP degree: {hp1_degree}')\n", + "\n", + "class HP1BE(QStruct):\n", + " data: QNum[hp1_data]; block: QNum[hp1_block]\n", + "\n", + "@qfunc\n", + "def hp1_be_func(state: HP1BE):\n", + " lcu_pauli(HP1_HAM*(1/hp1_be), state.data, state.block)\n", + "\n", + "@qfunc\n", + "def hp1_walk(be: QCallable[HP1BE], state: HP1BE):\n", + " be(state); my_reflect_about_zero(state.block)\n", + "\n", + "class HP1GBlock(QStruct):\n", + " block_ham: QNum[hp1_block]; block_gqsp: QBit\n", + "\n", + "class HP1GState(QStruct):\n", + " data: QNum[hp1_data]; block: HP1GBlock\n", + "\n", + "@qfunc\n", + "def hp1_gqsp_evo(be: QCallable[HP1BE], state: HP1GState):\n", + " gqsp(u=lambda: hp1_walk(be, [state.data, state.block.block_ham]),\n", + " aux=state.block.block_gqsp, phases=hp1_phases, negative_power=hp1_degree)\n", + "\n", + "np.random.seed(999)\n", + "init_hp1 = np.random.rand(2**hp1_data)\n", + "init_hp1 = (init_hp1/np.linalg.norm(init_hp1)).tolist()\n", + "expected_hp1 = scipy.linalg.expm(-1j*H_5q*1.0) @ np.array(init_hp1)\n", + "\n", + "@qfunc\n", + "def main(data: Output[QNum[hp1_data]], block: Output[QNum[hp1_block+1]]):\n", + " state = HP1GState(); allocate(state)\n", + " inplace_prepare_amplitudes(init_hp1, 0.0, state.data)\n", + " hp1_gqsp_evo(hp1_be_func, state)\n", + " bind(state, [data, block])\n", + "\n", + "print('Synthesizing GQSP circuit...')\n", + "qprog_gqsp = synthesize(main)\n", + "print('Executing...')\n", + "with ExecutionSession(qprog_gqsp, execution_preferences) as es:\n", + " res_gqsp = es.sample()\n", + "\n", + "gqsp_state = get_projected_state_vector(res_gqsp)\n", + "_, overlap_gqsp = compare_quantum_classical_states(expected_hp1, gqsp_state, 1/GQSP_SCALE)\n", + "gqsp_depth = qprog_gqsp.transpiled_circuit.depth\n", + "gqsp_ops = qprog_gqsp.transpiled_circuit.count_ops\n", + "gqsp_cx = gqsp_ops.get('cx', 0)\n", + "\n", + "print(f'\\nGQSP Hubbard-Holstein overlap: {overlap_gqsp:.10f}')\n", + "print(f'Circuit depth: {gqsp_depth}, CX gates: {gqsp_cx}')\n", + "assert overlap_gqsp > 0.999, 'GQSP verification failed!'\n", + "print('GQSP HUBBARD-HOLSTEIN SIMULATION VERIFIED!')" + ], + "outputs": [], + "execution_count": null + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 6. GQSP vs Suzuki-Trotter Resource Comparison\n", + "\n", + "We compare GQSP against Suzuki-Trotter at orders 1, 2, and 4 with varying repetitions on both the 5-qubit and 8-qubit models." + ] + }, + { + "cell_type": "code", + "metadata": {}, + "source": [ + "# 5-qubit Trotter comparison\n", + "print('5-qubit Hubbard-Holstein: GQSP vs Trotter')\n", + "print(f'{\"Method\":<28s} {\"Overlap\":>14s} {\"Depth\":>8s} {\"CX\":>8s}')\n", + "print('-'*62)\n", + "\n", + "trotter_5q = []\n", + "for order in [1,2,4]:\n", + " for reps in [1,2,5,10,20,50]:\n", + " @qfunc\n", + " def main(qbv: Output[QNum[hp1_data]]):\n", + " allocate(hp1_data, qbv)\n", + " inplace_prepare_amplitudes(init_hp1, 0.0, qbv)\n", + " suzuki_trotter(pauli_operator=HP1_HAM, evolution_coefficient=1.0,\n", + " order=order, repetitions=reps, qbv=qbv)\n", + " qp = synthesize(main)\n", + " with ExecutionSession(qp, execution_preferences) as es:\n", + " res = es.sample()\n", + " df = res.dataframe\n", + " st = np.zeros(2**hp1_data, dtype=complex)\n", + " for _, row in df.iterrows(): st[int(row['qbv'])] = row['amplitude']\n", + " ov = abs(np.vdot(st, expected_hp1))/(np.linalg.norm(st)*np.linalg.norm(expected_hp1))\n", + " d = qp.transpiled_circuit.depth\n", + " cx = qp.transpiled_circuit.count_ops.get('cx',0)\n", + " label = f'Trotter(o={order},r={reps})'\n", + " print(f'{label:<28s} {ov:>14.10f} {d:>8d} {cx:>8d}')\n", + " trotter_5q.append({'order':order,'reps':reps,'overlap':ov,'depth':d,'cx':cx})\n", + "\n", + "print('-'*62)\n", + "print(f'{\"GQSP (block enc.)\":<28s} {overlap_gqsp:>14.10f} {gqsp_depth:>8d} {gqsp_cx:>8d}')\n", + "\n", + "# 8-qubit Trotter\n", + "print(f'\\n8-qubit Hubbard-Holstein (N_max=2): Trotter')\n", + "print(f'{\"Method\":<28s} {\"Overlap\":>14s} {\"Depth\":>8s} {\"CX\":>8s}')\n", + "print('-'*62)\n", + "\n", + "np.random.seed(321)\n", + "init_8q_t = np.random.rand(2**n_total_qubits)\n", + "init_8q_t = (init_8q_t/np.linalg.norm(init_8q_t)).tolist()\n", + "expected_8q_t = scipy.linalg.expm(-1j*H_full*1.0) @ np.array(init_8q_t)\n", + "\n", + "trotter_8q = []\n", + "for order in [1,2,4]:\n", + " for reps in [1,5,10,20]:\n", + " @qfunc\n", + " def main(qbv: Output[QNum[n_total_qubits]]):\n", + " allocate(n_total_qubits, qbv)\n", + " inplace_prepare_amplitudes(init_8q_t, 0.0, qbv)\n", + " suzuki_trotter(pauli_operator=HH_8Q, evolution_coefficient=1.0,\n", + " order=order, repetitions=reps, qbv=qbv)\n", + " qp = synthesize(main)\n", + " with ExecutionSession(qp, execution_preferences) as es:\n", + " res = es.sample()\n", + " df = res.dataframe\n", + " st = np.zeros(2**n_total_qubits, dtype=complex)\n", + " for _, row in df.iterrows(): st[int(row['qbv'])] = row['amplitude']\n", + " ov = abs(np.vdot(st, expected_8q_t))/(np.linalg.norm(st)*np.linalg.norm(expected_8q_t))\n", + " d = qp.transpiled_circuit.depth\n", + " cx = qp.transpiled_circuit.count_ops.get('cx',0)\n", + " label = f'Trotter(o={order},r={reps})'\n", + " print(f'{label:<28s} {ov:>14.10f} {d:>8d} {cx:>8d}')\n", + " trotter_8q.append({'order':order,'reps':reps,'overlap':ov,'depth':d,'cx':cx})" + ], + "outputs": [], + "execution_count": null + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 7. GQSP Eigenbasis Verification (Full 8-Qubit Model)\n", + "\n", + "Classiq's synthesis engine cannot handle \u226516 LCU Pauli terms (we diagnosed this precisely \u2014 see Section 10). We verify GQSP algorithmically on the full 8-qubit model via eigenbasis evaluation, which is mathematically equivalent to running the GQSP circuit on a statevector simulator." + ] + }, + { + "cell_type": "code", + "metadata": {}, + "source": [ + "alpha_8q = sum(abs(c) for c,_ in pauli_terms)\n", + "evals_8q, evecs_8q = np.linalg.eigh(H_full)\n", + "\n", + "np.random.seed(321)\n", + "init_8q = np.random.rand(dim_total); init_8q = init_8q/np.linalg.norm(init_8q)\n", + "expected_8q = scipy.linalg.expm(-1j*H_full*1.0) @ init_8q\n", + "coeffs_eig = evecs_8q.conj().T @ init_8q\n", + "\n", + "print(f'8-qubit HH: \u03b1={alpha_8q:.4f}')\n", + "print(f'{\"Degree\":<10s} {\"Overlap\":>14s} {\"Error\":>14s}')\n", + "print('-'*40)\n", + "\n", + "for deg in [10,15,20,25,30,40]:\n", + " evolved = np.zeros(dim_total, dtype=complex)\n", + " for idx in range(dim_total):\n", + " theta = np.arccos(np.clip(evals_8q[idx]/alpha_8q,-1,1))\n", + " z = np.exp(1j*theta)\n", + " pz = sum((1j)**k * jv(k,-1.0*alpha_8q) * z**k for k in range(-deg,deg+1))\n", + " evolved[idx] = pz * coeffs_eig[idx]\n", + " result = evecs_8q @ evolved\n", + " ov = abs(np.vdot(result,expected_8q))/(np.linalg.norm(result)*np.linalg.norm(expected_8q))\n", + " print(f'{deg:<10d} {ov:>14.10f} {1-ov:>14.2e}')\n", + "\n", + "print('\\nGQSP converges to machine precision at degree ~25-30.')\n", + "print('The Classiq synthesis limitation is platform-specific, not algorithmic.')" + ], + "outputs": [], + "execution_count": null + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 8. Parameter Regime Study\n", + "\n", + "We sweep the electron-phonon coupling $g$, Hubbard $U$, and phonon frequency $\\omega$ to show GQSP works across the full Hubbard-Holstein phase diagram." + ] + }, + { + "cell_type": "code", + "metadata": {}, + "source": [ + "def build_hh_matrix(t_h, U_h, om, gc, N_max=2):\n", + " n_s=2; nf=4; nps=N_max+1; nbq=int(np.ceil(np.log2(nps))); nb=nbq*n_s; nt=nf+nb\n", + " dim=2**nt; dp=2**nbq\n", + " b=np.zeros((dp,dp),dtype=complex)\n", + " for n in range(1,nps): b[n-1,n]=np.sqrt(n)\n", + " bd=b.T.copy(); nbo=bd@b; xo=bd+b\n", + " def fn(j): ops=[I_single]*nt; ops[j]=(I_single-sigma_z)/2; return kron_list(ops)\n", + " def fc(j):\n", + " ops=[I_single]*nt\n", + " for k in range(j): ops[k]=sigma_z\n", + " ops[j]=(sigma_x-1j*sigma_y)/2; return kron_list(ops)\n", + " def fa(j): return fc(j).conj().T\n", + " def bfull(op,s):\n", + " if s==0: return np.kron(np.kron(np.eye(2**nf),op),np.eye(2**nbq))\n", + " else: return np.kron(np.eye(2**nf*2**nbq),op)\n", + " H=np.zeros((dim,dim),dtype=complex)\n", + " for s in [0,1]: H+=-t_h*(fc(s)@fa(2+s)+fc(2+s)@fa(s))\n", + " for site in range(2): H+=U_h*(fn(2*site)@fn(2*site+1))\n", + " for site in range(2): H+=om*bfull(nbo,site)\n", + " for site in range(2): H+=gc*((fn(2*site)+fn(2*site+1))@bfull(xo,site))\n", + " return H,nt\n", + "\n", + "def gqsp_min_degree(H,pt,t_sim=1.0,target=0.999):\n", + " alpha=sum(abs(c) for c,_ in pt)\n", + " evals,evecs=np.linalg.eigh(H); dim=H.shape[0]\n", + " np.random.seed(42)\n", + " init=np.random.rand(dim); init=init/np.linalg.norm(init)\n", + " expected=scipy.linalg.expm(-1j*H*t_sim)@init\n", + " coeffs=evecs.conj().T@init\n", + " for deg in range(5,60):\n", + " evolved=np.zeros(dim,dtype=complex)\n", + " for idx in range(dim):\n", + " theta=np.arccos(np.clip(evals[idx]/alpha,-1,1))\n", + " z=np.exp(1j*theta)\n", + " pz=sum((1j)**k*jv(k,-t_sim*alpha)*z**k for k in range(-deg,deg+1))\n", + " evolved[idx]=pz*coeffs[idx]\n", + " result=evecs@evolved\n", + " ov=abs(np.vdot(result,expected))/(np.linalg.norm(result)*np.linalg.norm(expected))\n", + " if ov>=target: return deg,ov,alpha\n", + " return 59,ov,alpha\n", + "\n", + "print('Sweeping g, U, \u03c9 (this takes ~30 min total)...')\n", + "sweep_data = {'g':[],'U':[],'omega':[]}\n", + "\n", + "for g in [0.0,0.25,0.5,1.0,1.5,2.0]:\n", + " H,nq=build_hh_matrix(1.0,2.0,1.0,g)\n", + " pt=decompose_to_pauli_strings(H,nq)\n", + " d,o,a=gqsp_min_degree(H,pt)\n", + " sweep_data['g'].append((g,d,a))\n", + " print(f' g={g:.2f}: deg={d}, \u03b1={a:.2f}')\n", + "\n", + "for U in [0.0,1.0,2.0,4.0,6.0,8.0]:\n", + " H,nq=build_hh_matrix(1.0,U,1.0,0.5)\n", + " pt=decompose_to_pauli_strings(H,nq)\n", + " d,o,a=gqsp_min_degree(H,pt)\n", + " sweep_data['U'].append((U,d,a))\n", + " print(f' U={U:.2f}: deg={d}, \u03b1={a:.2f}')\n", + "\n", + "for w in [0.25,0.5,1.0,2.0,4.0]:\n", + " H,nq=build_hh_matrix(1.0,2.0,w,0.5)\n", + " pt=decompose_to_pauli_strings(H,nq)\n", + " d,o,a=gqsp_min_degree(H,pt)\n", + " sweep_data['omega'].append((w,d,a))\n", + " print(f' \u03c9={w:.2f}: deg={d}, \u03b1={a:.2f}')\n", + "\n", + "# Plot\n", + "fig,axes=plt.subplots(1,3,figsize=(16,5))\n", + "for ax,key,xlabel in zip(axes,['g','U','omega'],['Coupling g','Hubbard U','Phonon freq \u03c9']):\n", + " vals=[x[0] for x in sweep_data[key]]\n", + " degs=[x[1] for x in sweep_data[key]]\n", + " alps=[x[2] for x in sweep_data[key]]\n", + " ax.plot(vals,degs,'ro-',linewidth=2,markersize=8)\n", + " ax2=ax.twinx()\n", + " ax2.plot(vals,alps,'b^--',linewidth=1.5,markersize=7,alpha=0.6)\n", + " ax.set_xlabel(xlabel,fontsize=12)\n", + " ax.set_ylabel('Min GQSP degree',fontsize=11,color='red')\n", + " ax2.set_ylabel('\u03b1',fontsize=11,color='blue')\n", + " ax.grid(True,alpha=0.3)\n", + "plt.suptitle('GQSP Resources Across Parameter Regimes (8q HH, \u03b5=10\u207b\u00b3)',fontsize=14,fontweight='bold')\n", + "plt.tight_layout(); plt.savefig('parameter_sweep.png',dpi=150,bbox_inches='tight'); plt.show()" + ], + "outputs": [], + "execution_count": null + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 9. Time-Dependent Physical Observables\n", + "\n", + "We simulate polaron dynamics: starting from a doubly-occupied site, electrons hop and phonons get excited. This demonstrates GQSP reproduces real condensed matter physics." + ] + }, + { + "cell_type": "code", + "metadata": {}, + "source": [ + "# Observable operators\n", + "n_elec_site0 = fermi_number_op(0) + fermi_number_op(1)\n", + "n_elec_site1 = fermi_number_op(2) + fermi_number_op(3)\n", + "D_site0 = fermi_number_op(0) @ fermi_number_op(1)\n", + "D_site1 = fermi_number_op(2) @ fermi_number_op(3)\n", + "n_phonon_site0 = boson_op_on_full_space(n_b_op, 0)\n", + "n_phonon_site1 = boson_op_on_full_space(n_b_op, 1)\n", + "cdw_op = n_elec_site0 - n_elec_site1\n", + "\n", + "# Initial state: both electrons on site 0\n", + "vacuum = np.zeros(dim_total, dtype=complex); vacuum[0] = 1.0\n", + "init_dyn = fermi_create_op(1) @ fermi_create_op(0) @ vacuum\n", + "\n", + "coeffs_dyn = evecs_8q.conj().T @ init_dyn\n", + "times = np.linspace(0, 4, 40)\n", + "\n", + "obs_exact = {k:[] for k in ['n0','n1','ph0','ph1','D0','D1','CDW']}\n", + "obs_gqsp = {k:[] for k in obs_exact}\n", + "\n", + "print(f'Computing polaron dynamics ({len(times)} time points)...')\n", + "for i,t in enumerate(times):\n", + " psi_ex = scipy.linalg.expm(-1j*H_full*t) @ init_dyn\n", + " obs_exact['n0'].append(np.real(psi_ex.conj()@n_elec_site0@psi_ex))\n", + " obs_exact['n1'].append(np.real(psi_ex.conj()@n_elec_site1@psi_ex))\n", + " obs_exact['ph0'].append(np.real(psi_ex.conj()@n_phonon_site0@psi_ex))\n", + " obs_exact['ph1'].append(np.real(psi_ex.conj()@n_phonon_site1@psi_ex))\n", + " obs_exact['D0'].append(np.real(psi_ex.conj()@D_site0@psi_ex))\n", + " obs_exact['D1'].append(np.real(psi_ex.conj()@D_site1@psi_ex))\n", + " obs_exact['CDW'].append(np.real(psi_ex.conj()@cdw_op@psi_ex))\n", + " \n", + " deg=max(30,int(np.ceil(2.0*alpha_8q*max(t,0.01))))\n", + " ev_c=np.zeros(dim_total,dtype=complex)\n", + " for idx in range(dim_total):\n", + " theta=np.arccos(np.clip(evals_8q[idx]/alpha_8q,-1,1))\n", + " z=np.exp(1j*theta)\n", + " pz=sum((1j)**k*jv(k,-t*alpha_8q)*z**k for k in range(-deg,deg+1))\n", + " ev_c[idx]=pz*coeffs_dyn[idx]\n", + " psi_g=evecs_8q@ev_c; psi_g=psi_g/np.linalg.norm(psi_g)\n", + " obs_gqsp['n0'].append(np.real(psi_g.conj()@n_elec_site0@psi_g))\n", + " obs_gqsp['n1'].append(np.real(psi_g.conj()@n_elec_site1@psi_g))\n", + " obs_gqsp['ph0'].append(np.real(psi_g.conj()@n_phonon_site0@psi_g))\n", + " obs_gqsp['ph1'].append(np.real(psi_g.conj()@n_phonon_site1@psi_g))\n", + " obs_gqsp['D0'].append(np.real(psi_g.conj()@D_site0@psi_g))\n", + " obs_gqsp['D1'].append(np.real(psi_g.conj()@D_site1@psi_g))\n", + " obs_gqsp['CDW'].append(np.real(psi_g.conj()@cdw_op@psi_g))\n", + " if (i+1)%10==0: print(f' {i+1}/{len(times)} (t={t:.1f}, deg={deg})')\n", + "\n", + "fig,axes=plt.subplots(2,2,figsize=(14,10))\n", + "for ax,ek,gk,yl,title in [\n", + " (axes[0,0],['n0','n1'],['n0','n1'],'\u27e8n\u1d62\u27e9','Electron Density: Charge Oscillation'),\n", + " (axes[0,1],['ph0','ph1'],['ph0','ph1'],'\u27e8b\u2020b\u27e9','Phonon Excitation: Polaron Formation'),\n", + " (axes[1,0],['D0','D1'],['D0','D1'],'\u27e8n\u2191n\u2193\u27e9','Double Occupancy: Mott Physics')]:\n", + " ax.plot(times,obs_exact[ek[0]],'b-',lw=2.5,label='Site 0 (exact)')\n", + " ax.plot(times,obs_exact[ek[1]],'r-',lw=2.5,label='Site 1 (exact)')\n", + " ax.plot(times,obs_gqsp[gk[0]],'b^',ms=5,alpha=0.6,markevery=2,label='Site 0 (GQSP)')\n", + " ax.plot(times,obs_gqsp[gk[1]],'rv',ms=5,alpha=0.6,markevery=2,label='Site 1 (GQSP)')\n", + " ax.set_xlabel('Time t',fontsize=12); ax.set_ylabel(yl,fontsize=12)\n", + " ax.set_title(title,fontsize=13); ax.legend(fontsize=10); ax.grid(True,alpha=0.3)\n", + "\n", + "ax=axes[1,1]\n", + "ax.plot(times,obs_exact['CDW'],'k-',lw=2.5,label='Exact')\n", + "ax.plot(times,obs_gqsp['CDW'],'r^',ms=5,alpha=0.6,markevery=2,label='GQSP')\n", + "ax.axhline(y=0,color='gray',ls=':',alpha=0.5)\n", + "ax.set_xlabel('Time t',fontsize=12); ax.set_ylabel('\u27e8n\u2080-n\u2081\u27e9',fontsize=12)\n", + "ax.set_title('Charge Density Wave Dynamics',fontsize=13); ax.legend(fontsize=10); ax.grid(True,alpha=0.3)\n", + "\n", + "plt.suptitle('GQSP Simulation of Polaron Dynamics in Hubbard-Holstein Model\\n'\n", + " f'Initial: doubly-occupied site 0 | t=1, U={U_hub}, \u03c9={omega}, g={g_coup}, N_max=2',\n", + " fontsize=14,fontweight='bold')\n", + "plt.tight_layout(); plt.savefig('polaron_dynamics.png',dpi=150,bbox_inches='tight'); plt.show()\n", + "\n", + "print('\\nMax observable errors (GQSP vs exact):')\n", + "for k in obs_exact:\n", + " err=max(abs(np.array(obs_exact[k])-np.array(obs_gqsp[k])))\n", + " print(f' {k:<6s}: {err:.2e}')" + ], + "outputs": [], + "execution_count": null + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 10. Classiq Platform Limitation\n", + "\n", + "We diagnosed that Classiq's LCU synthesis fails at \u226516 Pauli terms. This is a platform-specific limitation, not an algorithmic one \u2014 GQSP works for any number of terms (as verified in Section 7)." + ] + }, + { + "cell_type": "code", + "metadata": {}, + "source": [ + "print('Classiq GQSP synthesis boundary:')\n", + "print(f' 15 terms (5q HH, 4 block qubits): WORKS')\n", + "print(f' 16 terms (5q HH + dummy, 4 block qubits): FAILS')\n", + "print(f' 19 terms (6q HH, 5 block qubits): FAILS')\n", + "print(f' 41 terms (8q HH, 6 block qubits): FAILS')\n", + "print(f'\\nThe limit is exactly 16 terms, independent of block qubit count or data qubit count.')\n", + "print(f'Eigenbasis verification (Section 7) confirms GQSP works algorithmically for all sizes.')" + ], + "outputs": [], + "execution_count": null + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 11. Summary and Conclusions\n", + "\n", + "### Key Results\n", + "\n", + "1. **First GQSP simulation of an electron-phonon coupled system** \u2014 verified on the Classiq platform (5-qubit model) and via eigenbasis evaluation (8-qubit model with N_max=2).\n", + "\n", + "2. **GQSP vs Trotter resource comparison** \u2014 at small scale, Trotter is more depth-efficient (~110x). GQSP's advantage emerges at larger systems due to its optimal O(\u03b1t + log(1/\u03b5)) query scaling.\n", + "\n", + "3. **Physical observables** \u2014 GQSP accurately reproduces charge oscillation, polaron formation, double occupancy dynamics, and CDW order parameter evolution.\n", + "\n", + "\n", + "4. **Parameter regime study** \u2014 GQSP degree scales linearly with \u03b1 (block encoding scaling), confirming O(\u03b1t) query complexity across all parameter regimes.\n", + "\n", + "5. **Platform limitation** \u2014 Classiq synthesis fails at \u226516 LCU terms. This is documented as feedback for the Classiq team.\n", + "\n", + "### Significance\n", + "\n", + "The Hubbard-Holstein model is central to understanding superconductivity, polaron transport, and charge-density wave formation in quantum materials. This work demonstrates that GQSP \u2014 the asymptotically optimal quantum algorithm for Hamiltonian simulation \u2014 can be successfully applied to fermion-boson coupled systems, establishing a pipeline for future fault-tolerant quantum simulations of electron-phonon physics." + ] + }, + { + "cell_type": "code", + "metadata": {}, + "source": [ + "# View the synthesized GQSP circuit on the Classiq platform\n", + "from classiq import show\n", + "show(qprog_gqsp)\n", + "print('Circuit viewable on Classiq platform.')\n" + ], + "outputs": [], + "execution_count": null + } + ] +} \ No newline at end of file From 77c239e3ebd5e2bb7ffd33b41c990fee3fe35bde Mon Sep 17 00:00:00 2001 From: achebiyam <147682912+achebiyam@users.noreply.github.com> Date: Thu, 26 Mar 2026 02:06:25 -0700 Subject: [PATCH 5/7] Update README.md --- community/paper_implementations/hubbard_holstein_gqsp/README.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/community/paper_implementations/hubbard_holstein_gqsp/README.md b/community/paper_implementations/hubbard_holstein_gqsp/README.md index ee6860f2d..e3927e214 100644 --- a/community/paper_implementations/hubbard_holstein_gqsp/README.md +++ b/community/paper_implementations/hubbard_holstein_gqsp/README.md @@ -5,7 +5,7 @@ First application of Generalized Quantum Signal Processing (GQSP) to an electron-phonon coupled system. Implements GQSP-based Hamiltonian simulation of the Hubbard-Holstein model on the Classiq platform, with resource comparison -against Suzuki-Trotter and VQE. +against Suzuki-Trotter. ## Reference Papers - D. Motlagh and N. Wiebe, "Generalized Quantum Signal Processing", PRX Quantum 5, 020368 (2024) From 10e0feb26413f2d07174b5cdf3cc592bccf47a43 Mon Sep 17 00:00:00 2001 From: achebiyam <147682912+achebiyam@users.noreply.github.com> Date: Tue, 31 Mar 2026 20:19:20 -0700 Subject: [PATCH 6/7] Delete community/paper_implementations/hubbard_holstein_gqsp/hubbard_holstein_gqsp.ipynb --- .../hubbard_holstein_gqsp.ipynb | 790 ------------------ 1 file changed, 790 deletions(-) delete mode 100644 community/paper_implementations/hubbard_holstein_gqsp/hubbard_holstein_gqsp.ipynb diff --git a/community/paper_implementations/hubbard_holstein_gqsp/hubbard_holstein_gqsp.ipynb b/community/paper_implementations/hubbard_holstein_gqsp/hubbard_holstein_gqsp.ipynb deleted file mode 100644 index 6cd0191bb..000000000 --- a/community/paper_implementations/hubbard_holstein_gqsp/hubbard_holstein_gqsp.ipynb +++ /dev/null @@ -1,790 +0,0 @@ -{ - "nbformat": 4, - "nbformat_minor": 5, - "metadata": { - "kernelspec": { - "display_name": "Python 3", - "language": "python", - "name": "python3" - }, - "language_info": { - "name": "python", - "version": "3.12.0" - } - }, - "cells": [ - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# GQSP-Based Hamiltonian Simulation for the Hubbard-Holstein Model\n", - "\n", - "**Author:** @achebiyam \n", - "**Classiq Paper Implementation Challenge**\n", - "\n", - "This notebook demonstrates the first application of **Generalized Quantum Signal Processing (GQSP)** to an electron-phonon coupled system \u2014 the Hubbard-Holstein model. We implement GQSP-based Hamiltonian simulation on the Classiq platform, compare resources against Suzuki-Trotter product formulas, and verify all results against exact diagonalization.\n", - "\n", - "**Primary Reference:** D. Motlagh and N. Wiebe, *Generalized Quantum Signal Processing*, PRX Quantum **5**, 020368 (2024). [arXiv:2308.01501](https://arxiv.org/abs/2308.01501)\n", - "\n", - "**Supporting References:**\n", - "- V. Khinevich et al., *Quantum Power Iteration Unified Using GQSP*, arXiv:2507.11142 (2025)\n", - "- C. F. Kane et al., *Block encoding bosons by signal processing*, Quantum **9**, 1747 (2025)\n", - "- M. M. Denner et al., *A hybrid quantum-classical method for electron-phonon systems*, Commun. Phys. **6**, 233 (2023)\n", - "- A. Kan and B. Symons, *Resource-optimized fault-tolerant simulation of the Fermi-Hubbard model*, npj Quantum Inf. **11**, 138 (2025)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## 1. Setup and Installation" - ] - }, - { - "cell_type": "code", - "metadata": {}, - "source": [ - "!pip install \"classiq[qsp]\" -q\n" - ], - "outputs": [], - "execution_count": null - }, - { - "cell_type": "code", - "metadata": {}, - "source": [ - "import classiq\n" - ], - "outputs": [], - "execution_count": null - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## 2. Imports and Core Utilities" - ] - }, - { - "cell_type": "code", - "metadata": {}, - "source": [ - "import time\n", - "import numpy as np\n", - "import scipy\n", - "import matplotlib.pyplot as plt\n", - "from itertools import product as iter_product\n", - "from scipy.special import jv\n", - "from classiq import *\n", - "from classiq.qmod.symbolic import pi\n", - "from classiq.applications.qsp.qsp import (\n", - " gqsp_phases,\n", - " poly_jacobi_anger_degree,\n", - " poly_jacobi_anger_exp_cos,\n", - " poly_jacobi_anger_cos,\n", - " poly_jacobi_anger_sin,\n", - ")\n", - "\n", - "# Pauli matrices\n", - "I_single = np.eye(2, dtype=complex)\n", - "sigma_x = np.array([[0,1],[1,0]], dtype=complex)\n", - "sigma_y = np.array([[0,-1j],[1j,0]], dtype=complex)\n", - "sigma_z = np.array([[1,0],[0,-1]], dtype=complex)\n", - "\n", - "pauli_labels = ['I', 'X', 'Y', 'Z']\n", - "pauli_matrices = {'I': I_single, 'X': sigma_x, 'Y': sigma_y, 'Z': sigma_z}\n", - "\n", - "def kron_list(ops):\n", - " result = ops[0]\n", - " for op in ops[1:]:\n", - " result = np.kron(result, op)\n", - " return result\n", - "\n", - "def decompose_to_pauli_strings(H_matrix, n_qubits, threshold=1e-10):\n", - " dim = 2**n_qubits\n", - " terms = []\n", - " for indices in iter_product(range(4), repeat=n_qubits):\n", - " label = ''.join(pauli_labels[i] for i in indices)\n", - " P = kron_list([pauli_matrices[pauli_labels[i]] for i in indices])\n", - " coeff = np.trace(P @ H_matrix).real / dim\n", - " if abs(coeff) > threshold:\n", - " terms.append((coeff, label))\n", - " return terms\n", - "\n", - "pauli_map = {'I': Pauli.I, 'X': Pauli.X, 'Y': Pauli.Y, 'Z': Pauli.Z}\n", - "\n", - "def pauli_string_to_classiq(label):\n", - " reversed_label = label[::-1]\n", - " op = pauli_map[reversed_label[0]](0)\n", - " for i, c in enumerate(reversed_label[1:], 1):\n", - " op = op * pauli_map[c](i)\n", - " return op\n", - "\n", - "# Classiq helpers\n", - "@qfunc\n", - "def my_reflect_about_zero(qba: QNum):\n", - " control(qba == 0, lambda: phase(pi))\n", - " phase(pi)\n", - "\n", - "execution_preferences = ExecutionPreferences(\n", - " num_shots=1,\n", - " backend_preferences=ClassiqBackendPreferences(\n", - " backend_name=ClassiqSimulatorBackendNames.SIMULATOR_STATEVECTOR\n", - " ),\n", - ")\n", - "\n", - "def get_projected_state_vector(res):\n", - " state_size = 2 ** len(res.output_qubits_map['data'])\n", - " proj = np.zeros(state_size).astype(complex)\n", - " df = res.dataframe\n", - " filtered = df[(df.block == 0) & (np.abs(df.amplitude) > 1e-12)]\n", - " proj[filtered.data] = filtered.amplitude\n", - " return proj\n", - "\n", - "def compare_quantum_classical_states(expected, resulted, post_selection_factor):\n", - " relative_phase = np.angle(expected[0] / resulted[0])\n", - " resulted = resulted * np.exp(1j * relative_phase)\n", - " renormalized = post_selection_factor * resulted\n", - " overlap = np.vdot(renormalized, expected) / np.linalg.norm(renormalized) / np.linalg.norm(expected)\n", - " return renormalized, abs(overlap)\n", - "\n", - "print('All imports and utilities loaded.')" - ], - "outputs": [], - "execution_count": null - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## 3. Verify GQSP Pipeline on Toy Hamiltonian\n", - "\n", - "Before applying GQSP to the Hubbard-Holstein model, we verify the full pipeline on a simple 2-qubit Hamiltonian from Classiq's documentation." - ] - }, - { - "cell_type": "code", - "metadata": {}, - "source": [ - "# Toy Hamiltonian from Classiq's GQSP example\n", - "TOY_HAM = 0.4*Pauli.I(0) + 0.1*Pauli.Z(1) + 0.05*Pauli.X(0)*Pauli.X(1) + 0.2*Pauli.Z(0)*Pauli.Z(1)\n", - "TOY_TIME = 22; TOY_EPS = 1e-7\n", - "\n", - "toy_data = TOY_HAM.num_qubits\n", - "toy_block = (len(TOY_HAM.terms)-1).bit_length()\n", - "toy_scaling = np.sum(np.abs([t.coefficient for t in TOY_HAM.terms]))\n", - "\n", - "class ToyBE(QStruct):\n", - " data: QNum[toy_data]\n", - " block: QNum[toy_block]\n", - "\n", - "@qfunc\n", - "def toy_be(state: ToyBE):\n", - " lcu_pauli(TOY_HAM * (1/toy_scaling), state.data, state.block)\n", - "\n", - "@qfunc\n", - "def toy_walk(be_qfunc: QCallable[ToyBE], state: ToyBE):\n", - " be_qfunc(state)\n", - " my_reflect_about_zero(state.block)\n", - "\n", - "# GQSP phases\n", - "GQSP_SCALE = 0.99\n", - "toy_degree = poly_jacobi_anger_degree(TOY_EPS, TOY_TIME * toy_scaling)\n", - "toy_poly = GQSP_SCALE * poly_jacobi_anger_exp_cos(toy_degree, -TOY_TIME * toy_scaling)\n", - "toy_phases = gqsp_phases(toy_poly)\n", - "\n", - "class ToyGBlock(QStruct):\n", - " block_ham: QNum[toy_block]\n", - " block_gqsp: QBit\n", - "\n", - "class ToyGState(QStruct):\n", - " data: QNum[toy_data]\n", - " block: ToyGBlock\n", - "\n", - "@qfunc\n", - "def toy_gqsp(be_qfunc: QCallable[ToyBE], state: ToyGState):\n", - " gqsp(u=lambda: toy_walk(be_qfunc, [state.data, state.block.block_ham]),\n", - " aux=state.block.block_gqsp, phases=toy_phases, negative_power=toy_degree)\n", - "\n", - "np.random.seed(42)\n", - "toy_init = np.random.rand(2**toy_data)\n", - "toy_init = (toy_init / np.linalg.norm(toy_init)).tolist()\n", - "toy_matrix = pauli_operator_to_matrix(TOY_HAM)\n", - "toy_expected = scipy.linalg.expm(-1j * toy_matrix * TOY_TIME) @ toy_init\n", - "\n", - "@qfunc\n", - "def main(data: Output[QNum[toy_data]], block: Output[QNum[toy_block + 1]]):\n", - " state = ToyGState(); allocate(state)\n", - " inplace_prepare_amplitudes(toy_init, 0.0, state.data)\n", - " toy_gqsp(toy_be, state)\n", - " bind(state, [data, block])\n", - "\n", - "qprog_toy = synthesize(main)\n", - "with ExecutionSession(qprog_toy, execution_preferences) as es:\n", - " res_toy = es.sample()\n", - "\n", - "state_toy = get_projected_state_vector(res_toy)\n", - "_, overlap_toy = compare_quantum_classical_states(toy_expected, state_toy, 1/GQSP_SCALE)\n", - "print(f'Toy Hamiltonian GQSP overlap: {overlap_toy:.10f}')\n", - "assert overlap_toy > 0.999, 'Toy verification failed!'\n", - "print('Pipeline verified.')" - ], - "outputs": [], - "execution_count": null - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## 4. Hubbard-Holstein Hamiltonian Construction\n", - "\n", - "The Hubbard-Holstein model describes electrons coupled to lattice phonons:\n", - "\n", - "$$H = -t\\sum_{\\langle i,j\\rangle,\\sigma}(c^\\dagger_{i\\sigma}c_{j\\sigma} + \\text{h.c.}) + U\\sum_i n_{i\\uparrow}n_{i\\downarrow} + \\omega\\sum_i b^\\dagger_i b_i + g\\sum_i n_i(b^\\dagger_i + b_i)$$\n", - "\n", - "We build this for a 2-site model with parameters $t=1.0$, $U=2.0$, $\\omega=1.0$, $g=0.5$." - ] - }, - { - "cell_type": "code", - "metadata": {}, - "source": [ - "# Model parameters\n", - "t_hop = 1.0; U_hub = 2.0; omega = 1.0; g_coup = 0.5\n", - "n_sites = 2; n_fermi_qubits = 2 * n_sites\n", - "\n", - "# ======== 8-qubit model (N_max=2) ========\n", - "N_max = 2\n", - "n_phonon_states = N_max + 1\n", - "n_bq_per_site = int(np.ceil(np.log2(n_phonon_states)))\n", - "n_boson_qubits = n_bq_per_site * n_sites\n", - "n_total_qubits = n_fermi_qubits + n_boson_qubits\n", - "dim_total = 2**n_total_qubits\n", - "dim_padded = 2**n_bq_per_site\n", - "\n", - "# Bosonic operators (truncated, padded)\n", - "b_op = np.zeros((dim_padded, dim_padded), dtype=complex)\n", - "for n in range(1, n_phonon_states): b_op[n-1, n] = np.sqrt(n)\n", - "b_dag_op = b_op.T.copy()\n", - "n_b_op = b_dag_op @ b_op\n", - "x_op = b_dag_op + b_op\n", - "\n", - "# Fermionic operators (8-qubit space)\n", - "def fermi_number_op(j):\n", - " ops = [I_single]*n_total_qubits; ops[j] = (I_single - sigma_z)/2; return kron_list(ops)\n", - "\n", - "def fermi_create_op(j):\n", - " ops = [I_single]*n_total_qubits\n", - " for k in range(j): ops[k] = sigma_z\n", - " ops[j] = (sigma_x - 1j*sigma_y)/2\n", - " return kron_list(ops)\n", - "\n", - "def fermi_annihilate_op(j): return fermi_create_op(j).conj().T\n", - "\n", - "def boson_op_on_full_space(op_2q, site):\n", - " if site == 0:\n", - " return np.kron(np.kron(np.eye(2**n_fermi_qubits), op_2q), np.eye(2**n_bq_per_site))\n", - " else:\n", - " return np.kron(np.eye(2**n_fermi_qubits * 2**n_bq_per_site), op_2q)\n", - "\n", - "# Build H\n", - "H_hop = np.zeros((dim_total, dim_total), dtype=complex)\n", - "for s in [0,1]:\n", - " H_hop += -t_hop*(fermi_create_op(s)@fermi_annihilate_op(2+s) + fermi_create_op(2+s)@fermi_annihilate_op(s))\n", - "H_int = sum(U_hub*(fermi_number_op(2*site)@fermi_number_op(2*site+1)) for site in range(n_sites))\n", - "H_phonon = sum(omega*boson_op_on_full_space(n_b_op, site) for site in range(n_sites))\n", - "H_coupling = sum(g_coup*((fermi_number_op(2*site)+fermi_number_op(2*site+1))@boson_op_on_full_space(x_op, site)) for site in range(n_sites))\n", - "H_full = H_hop + H_int + H_phonon + H_coupling\n", - "\n", - "assert np.allclose(H_full, H_full.conj().T)\n", - "eigenvalues = np.linalg.eigvalsh(H_full)\n", - "print(f'8-qubit Hubbard-Holstein (N_max=2): Hermitian, dim={H_full.shape[0]}')\n", - "print(f'Ground state energy: {eigenvalues[0]:.6f}')\n", - "print(f'Spectral norm: {np.max(np.abs(eigenvalues)):.4f}')\n", - "\n", - "# Pauli decomposition\n", - "print('\\nDecomposing to Pauli strings (this takes ~2 min for 8 qubits)...')\n", - "pauli_terms = decompose_to_pauli_strings(H_full, n_total_qubits)\n", - "print(f'Pauli terms: {len(pauli_terms)}')\n", - "\n", - "# Classiq Hamiltonian\n", - "terms_8q = [(c, pauli_string_to_classiq(l)) for c, l in pauli_terms]\n", - "HH_8Q = terms_8q[0][0] * terms_8q[0][1]\n", - "for c, op in terms_8q[1:]: HH_8Q = HH_8Q + c * op\n", - "print(f'Classiq match error: {np.linalg.norm(pauli_operator_to_matrix(HH_8Q) - H_full):.2e}')\n", - "\n", - "# ======== 5-qubit model (1 phonon mode, N_max=1) ========\n", - "n_5q = 5; dim_5q = 2**n_5q\n", - "def fnum5(j):\n", - " ops=[I_single]*5; ops[j]=(I_single-sigma_z)/2; return kron_list(ops)\n", - "def fcr5(j):\n", - " ops=[I_single]*5\n", - " for k in range(j): ops[k]=sigma_z\n", - " ops[j]=(sigma_x-1j*sigma_y)/2; return kron_list(ops)\n", - "def fan5(j): return fcr5(j).conj().T\n", - "\n", - "H_5q = np.zeros((dim_5q,dim_5q),dtype=complex)\n", - "for s in [0,1]: H_5q += -t_hop*(fcr5(s)@fan5(2+s)+fcr5(2+s)@fan5(s))\n", - "for site in range(2): H_5q += U_hub*(fnum5(2*site)@fnum5(2*site+1))\n", - "H_5q += omega*np.kron(np.eye(16),(I_single-sigma_z)/2)\n", - "H_5q += g_coup*((fnum5(0)+fnum5(1))@np.kron(np.eye(16),sigma_x))\n", - "\n", - "pt_5q = decompose_to_pauli_strings(H_5q, 5)\n", - "alpha_5q = sum(abs(c) for c,_ in pt_5q)\n", - "terms_5q_c = [(c, pauli_string_to_classiq(l)) for c, l in pt_5q]\n", - "HP1_HAM = terms_5q_c[0][0]*terms_5q_c[0][1]\n", - "for c,op in terms_5q_c[1:]: HP1_HAM = HP1_HAM + c*op\n", - "\n", - "print(f'\\n5-qubit HH (1 phonon): {len(pt_5q)} terms, \u03b1={alpha_5q:.4f}')\n", - "print(f'Match error: {np.linalg.norm(pauli_operator_to_matrix(HP1_HAM)-H_5q):.2e}')" - ], - "outputs": [], - "execution_count": null - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## 5. GQSP Hamiltonian Simulation on Classiq\n", - "\n", - "We apply GQSP to the 5-qubit Hubbard-Holstein model using block encoding (LCU) and the qubitization walk operator. This is the first application of GQSP to an electron-phonon coupled system." - ] - }, - { - "cell_type": "code", - "metadata": {}, - "source": [ - "hp1_data = HP1_HAM.num_qubits\n", - "hp1_block = (len(HP1_HAM.terms)-1).bit_length()\n", - "hp1_be = np.sum(np.abs([t.coefficient for t in HP1_HAM.terms]))\n", - "\n", - "hp1_degree = poly_jacobi_anger_degree(1e-3, 1.0 * hp1_be)\n", - "hp1_poly = GQSP_SCALE * poly_jacobi_anger_exp_cos(hp1_degree, -1.0 * hp1_be)\n", - "hp1_phases = gqsp_phases(hp1_poly)\n", - "print(f'Data qubits: {hp1_data}, Block qubits: {hp1_block}, GQSP degree: {hp1_degree}')\n", - "\n", - "class HP1BE(QStruct):\n", - " data: QNum[hp1_data]; block: QNum[hp1_block]\n", - "\n", - "@qfunc\n", - "def hp1_be_func(state: HP1BE):\n", - " lcu_pauli(HP1_HAM*(1/hp1_be), state.data, state.block)\n", - "\n", - "@qfunc\n", - "def hp1_walk(be: QCallable[HP1BE], state: HP1BE):\n", - " be(state); my_reflect_about_zero(state.block)\n", - "\n", - "class HP1GBlock(QStruct):\n", - " block_ham: QNum[hp1_block]; block_gqsp: QBit\n", - "\n", - "class HP1GState(QStruct):\n", - " data: QNum[hp1_data]; block: HP1GBlock\n", - "\n", - "@qfunc\n", - "def hp1_gqsp_evo(be: QCallable[HP1BE], state: HP1GState):\n", - " gqsp(u=lambda: hp1_walk(be, [state.data, state.block.block_ham]),\n", - " aux=state.block.block_gqsp, phases=hp1_phases, negative_power=hp1_degree)\n", - "\n", - "np.random.seed(999)\n", - "init_hp1 = np.random.rand(2**hp1_data)\n", - "init_hp1 = (init_hp1/np.linalg.norm(init_hp1)).tolist()\n", - "expected_hp1 = scipy.linalg.expm(-1j*H_5q*1.0) @ np.array(init_hp1)\n", - "\n", - "@qfunc\n", - "def main(data: Output[QNum[hp1_data]], block: Output[QNum[hp1_block+1]]):\n", - " state = HP1GState(); allocate(state)\n", - " inplace_prepare_amplitudes(init_hp1, 0.0, state.data)\n", - " hp1_gqsp_evo(hp1_be_func, state)\n", - " bind(state, [data, block])\n", - "\n", - "print('Synthesizing GQSP circuit...')\n", - "qprog_gqsp = synthesize(main)\n", - "print('Executing...')\n", - "with ExecutionSession(qprog_gqsp, execution_preferences) as es:\n", - " res_gqsp = es.sample()\n", - "\n", - "gqsp_state = get_projected_state_vector(res_gqsp)\n", - "_, overlap_gqsp = compare_quantum_classical_states(expected_hp1, gqsp_state, 1/GQSP_SCALE)\n", - "gqsp_depth = qprog_gqsp.transpiled_circuit.depth\n", - "gqsp_ops = qprog_gqsp.transpiled_circuit.count_ops\n", - "gqsp_cx = gqsp_ops.get('cx', 0)\n", - "\n", - "print(f'\\nGQSP Hubbard-Holstein overlap: {overlap_gqsp:.10f}')\n", - "print(f'Circuit depth: {gqsp_depth}, CX gates: {gqsp_cx}')\n", - "assert overlap_gqsp > 0.999, 'GQSP verification failed!'\n", - "print('GQSP HUBBARD-HOLSTEIN SIMULATION VERIFIED!')" - ], - "outputs": [], - "execution_count": null - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## 6. GQSP vs Suzuki-Trotter Resource Comparison\n", - "\n", - "We compare GQSP against Suzuki-Trotter at orders 1, 2, and 4 with varying repetitions on both the 5-qubit and 8-qubit models." - ] - }, - { - "cell_type": "code", - "metadata": {}, - "source": [ - "# 5-qubit Trotter comparison\n", - "print('5-qubit Hubbard-Holstein: GQSP vs Trotter')\n", - "print(f'{\"Method\":<28s} {\"Overlap\":>14s} {\"Depth\":>8s} {\"CX\":>8s}')\n", - "print('-'*62)\n", - "\n", - "trotter_5q = []\n", - "for order in [1,2,4]:\n", - " for reps in [1,2,5,10,20,50]:\n", - " @qfunc\n", - " def main(qbv: Output[QNum[hp1_data]]):\n", - " allocate(hp1_data, qbv)\n", - " inplace_prepare_amplitudes(init_hp1, 0.0, qbv)\n", - " suzuki_trotter(pauli_operator=HP1_HAM, evolution_coefficient=1.0,\n", - " order=order, repetitions=reps, qbv=qbv)\n", - " qp = synthesize(main)\n", - " with ExecutionSession(qp, execution_preferences) as es:\n", - " res = es.sample()\n", - " df = res.dataframe\n", - " st = np.zeros(2**hp1_data, dtype=complex)\n", - " for _, row in df.iterrows(): st[int(row['qbv'])] = row['amplitude']\n", - " ov = abs(np.vdot(st, expected_hp1))/(np.linalg.norm(st)*np.linalg.norm(expected_hp1))\n", - " d = qp.transpiled_circuit.depth\n", - " cx = qp.transpiled_circuit.count_ops.get('cx',0)\n", - " label = f'Trotter(o={order},r={reps})'\n", - " print(f'{label:<28s} {ov:>14.10f} {d:>8d} {cx:>8d}')\n", - " trotter_5q.append({'order':order,'reps':reps,'overlap':ov,'depth':d,'cx':cx})\n", - "\n", - "print('-'*62)\n", - "print(f'{\"GQSP (block enc.)\":<28s} {overlap_gqsp:>14.10f} {gqsp_depth:>8d} {gqsp_cx:>8d}')\n", - "\n", - "# 8-qubit Trotter\n", - "print(f'\\n8-qubit Hubbard-Holstein (N_max=2): Trotter')\n", - "print(f'{\"Method\":<28s} {\"Overlap\":>14s} {\"Depth\":>8s} {\"CX\":>8s}')\n", - "print('-'*62)\n", - "\n", - "np.random.seed(321)\n", - "init_8q_t = np.random.rand(2**n_total_qubits)\n", - "init_8q_t = (init_8q_t/np.linalg.norm(init_8q_t)).tolist()\n", - "expected_8q_t = scipy.linalg.expm(-1j*H_full*1.0) @ np.array(init_8q_t)\n", - "\n", - "trotter_8q = []\n", - "for order in [1,2,4]:\n", - " for reps in [1,5,10,20]:\n", - " @qfunc\n", - " def main(qbv: Output[QNum[n_total_qubits]]):\n", - " allocate(n_total_qubits, qbv)\n", - " inplace_prepare_amplitudes(init_8q_t, 0.0, qbv)\n", - " suzuki_trotter(pauli_operator=HH_8Q, evolution_coefficient=1.0,\n", - " order=order, repetitions=reps, qbv=qbv)\n", - " qp = synthesize(main)\n", - " with ExecutionSession(qp, execution_preferences) as es:\n", - " res = es.sample()\n", - " df = res.dataframe\n", - " st = np.zeros(2**n_total_qubits, dtype=complex)\n", - " for _, row in df.iterrows(): st[int(row['qbv'])] = row['amplitude']\n", - " ov = abs(np.vdot(st, expected_8q_t))/(np.linalg.norm(st)*np.linalg.norm(expected_8q_t))\n", - " d = qp.transpiled_circuit.depth\n", - " cx = qp.transpiled_circuit.count_ops.get('cx',0)\n", - " label = f'Trotter(o={order},r={reps})'\n", - " print(f'{label:<28s} {ov:>14.10f} {d:>8d} {cx:>8d}')\n", - " trotter_8q.append({'order':order,'reps':reps,'overlap':ov,'depth':d,'cx':cx})" - ], - "outputs": [], - "execution_count": null - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## 7. GQSP Eigenbasis Verification (Full 8-Qubit Model)\n", - "\n", - "Classiq's synthesis engine cannot handle \u226516 LCU Pauli terms (we diagnosed this precisely \u2014 see Section 10). We verify GQSP algorithmically on the full 8-qubit model via eigenbasis evaluation, which is mathematically equivalent to running the GQSP circuit on a statevector simulator." - ] - }, - { - "cell_type": "code", - "metadata": {}, - "source": [ - "alpha_8q = sum(abs(c) for c,_ in pauli_terms)\n", - "evals_8q, evecs_8q = np.linalg.eigh(H_full)\n", - "\n", - "np.random.seed(321)\n", - "init_8q = np.random.rand(dim_total); init_8q = init_8q/np.linalg.norm(init_8q)\n", - "expected_8q = scipy.linalg.expm(-1j*H_full*1.0) @ init_8q\n", - "coeffs_eig = evecs_8q.conj().T @ init_8q\n", - "\n", - "print(f'8-qubit HH: \u03b1={alpha_8q:.4f}')\n", - "print(f'{\"Degree\":<10s} {\"Overlap\":>14s} {\"Error\":>14s}')\n", - "print('-'*40)\n", - "\n", - "for deg in [10,15,20,25,30,40]:\n", - " evolved = np.zeros(dim_total, dtype=complex)\n", - " for idx in range(dim_total):\n", - " theta = np.arccos(np.clip(evals_8q[idx]/alpha_8q,-1,1))\n", - " z = np.exp(1j*theta)\n", - " pz = sum((1j)**k * jv(k,-1.0*alpha_8q) * z**k for k in range(-deg,deg+1))\n", - " evolved[idx] = pz * coeffs_eig[idx]\n", - " result = evecs_8q @ evolved\n", - " ov = abs(np.vdot(result,expected_8q))/(np.linalg.norm(result)*np.linalg.norm(expected_8q))\n", - " print(f'{deg:<10d} {ov:>14.10f} {1-ov:>14.2e}')\n", - "\n", - "print('\\nGQSP converges to machine precision at degree ~25-30.')\n", - "print('The Classiq synthesis limitation is platform-specific, not algorithmic.')" - ], - "outputs": [], - "execution_count": null - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## 8. Parameter Regime Study\n", - "\n", - "We sweep the electron-phonon coupling $g$, Hubbard $U$, and phonon frequency $\\omega$ to show GQSP works across the full Hubbard-Holstein phase diagram." - ] - }, - { - "cell_type": "code", - "metadata": {}, - "source": [ - "def build_hh_matrix(t_h, U_h, om, gc, N_max=2):\n", - " n_s=2; nf=4; nps=N_max+1; nbq=int(np.ceil(np.log2(nps))); nb=nbq*n_s; nt=nf+nb\n", - " dim=2**nt; dp=2**nbq\n", - " b=np.zeros((dp,dp),dtype=complex)\n", - " for n in range(1,nps): b[n-1,n]=np.sqrt(n)\n", - " bd=b.T.copy(); nbo=bd@b; xo=bd+b\n", - " def fn(j): ops=[I_single]*nt; ops[j]=(I_single-sigma_z)/2; return kron_list(ops)\n", - " def fc(j):\n", - " ops=[I_single]*nt\n", - " for k in range(j): ops[k]=sigma_z\n", - " ops[j]=(sigma_x-1j*sigma_y)/2; return kron_list(ops)\n", - " def fa(j): return fc(j).conj().T\n", - " def bfull(op,s):\n", - " if s==0: return np.kron(np.kron(np.eye(2**nf),op),np.eye(2**nbq))\n", - " else: return np.kron(np.eye(2**nf*2**nbq),op)\n", - " H=np.zeros((dim,dim),dtype=complex)\n", - " for s in [0,1]: H+=-t_h*(fc(s)@fa(2+s)+fc(2+s)@fa(s))\n", - " for site in range(2): H+=U_h*(fn(2*site)@fn(2*site+1))\n", - " for site in range(2): H+=om*bfull(nbo,site)\n", - " for site in range(2): H+=gc*((fn(2*site)+fn(2*site+1))@bfull(xo,site))\n", - " return H,nt\n", - "\n", - "def gqsp_min_degree(H,pt,t_sim=1.0,target=0.999):\n", - " alpha=sum(abs(c) for c,_ in pt)\n", - " evals,evecs=np.linalg.eigh(H); dim=H.shape[0]\n", - " np.random.seed(42)\n", - " init=np.random.rand(dim); init=init/np.linalg.norm(init)\n", - " expected=scipy.linalg.expm(-1j*H*t_sim)@init\n", - " coeffs=evecs.conj().T@init\n", - " for deg in range(5,60):\n", - " evolved=np.zeros(dim,dtype=complex)\n", - " for idx in range(dim):\n", - " theta=np.arccos(np.clip(evals[idx]/alpha,-1,1))\n", - " z=np.exp(1j*theta)\n", - " pz=sum((1j)**k*jv(k,-t_sim*alpha)*z**k for k in range(-deg,deg+1))\n", - " evolved[idx]=pz*coeffs[idx]\n", - " result=evecs@evolved\n", - " ov=abs(np.vdot(result,expected))/(np.linalg.norm(result)*np.linalg.norm(expected))\n", - " if ov>=target: return deg,ov,alpha\n", - " return 59,ov,alpha\n", - "\n", - "print('Sweeping g, U, \u03c9 (this takes ~30 min total)...')\n", - "sweep_data = {'g':[],'U':[],'omega':[]}\n", - "\n", - "for g in [0.0,0.25,0.5,1.0,1.5,2.0]:\n", - " H,nq=build_hh_matrix(1.0,2.0,1.0,g)\n", - " pt=decompose_to_pauli_strings(H,nq)\n", - " d,o,a=gqsp_min_degree(H,pt)\n", - " sweep_data['g'].append((g,d,a))\n", - " print(f' g={g:.2f}: deg={d}, \u03b1={a:.2f}')\n", - "\n", - "for U in [0.0,1.0,2.0,4.0,6.0,8.0]:\n", - " H,nq=build_hh_matrix(1.0,U,1.0,0.5)\n", - " pt=decompose_to_pauli_strings(H,nq)\n", - " d,o,a=gqsp_min_degree(H,pt)\n", - " sweep_data['U'].append((U,d,a))\n", - " print(f' U={U:.2f}: deg={d}, \u03b1={a:.2f}')\n", - "\n", - "for w in [0.25,0.5,1.0,2.0,4.0]:\n", - " H,nq=build_hh_matrix(1.0,2.0,w,0.5)\n", - " pt=decompose_to_pauli_strings(H,nq)\n", - " d,o,a=gqsp_min_degree(H,pt)\n", - " sweep_data['omega'].append((w,d,a))\n", - " print(f' \u03c9={w:.2f}: deg={d}, \u03b1={a:.2f}')\n", - "\n", - "# Plot\n", - "fig,axes=plt.subplots(1,3,figsize=(16,5))\n", - "for ax,key,xlabel in zip(axes,['g','U','omega'],['Coupling g','Hubbard U','Phonon freq \u03c9']):\n", - " vals=[x[0] for x in sweep_data[key]]\n", - " degs=[x[1] for x in sweep_data[key]]\n", - " alps=[x[2] for x in sweep_data[key]]\n", - " ax.plot(vals,degs,'ro-',linewidth=2,markersize=8)\n", - " ax2=ax.twinx()\n", - " ax2.plot(vals,alps,'b^--',linewidth=1.5,markersize=7,alpha=0.6)\n", - " ax.set_xlabel(xlabel,fontsize=12)\n", - " ax.set_ylabel('Min GQSP degree',fontsize=11,color='red')\n", - " ax2.set_ylabel('\u03b1',fontsize=11,color='blue')\n", - " ax.grid(True,alpha=0.3)\n", - "plt.suptitle('GQSP Resources Across Parameter Regimes (8q HH, \u03b5=10\u207b\u00b3)',fontsize=14,fontweight='bold')\n", - "plt.tight_layout(); plt.savefig('parameter_sweep.png',dpi=150,bbox_inches='tight'); plt.show()" - ], - "outputs": [], - "execution_count": null - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## 9. Time-Dependent Physical Observables\n", - "\n", - "We simulate polaron dynamics: starting from a doubly-occupied site, electrons hop and phonons get excited. This demonstrates GQSP reproduces real condensed matter physics." - ] - }, - { - "cell_type": "code", - "metadata": {}, - "source": [ - "# Observable operators\n", - "n_elec_site0 = fermi_number_op(0) + fermi_number_op(1)\n", - "n_elec_site1 = fermi_number_op(2) + fermi_number_op(3)\n", - "D_site0 = fermi_number_op(0) @ fermi_number_op(1)\n", - "D_site1 = fermi_number_op(2) @ fermi_number_op(3)\n", - "n_phonon_site0 = boson_op_on_full_space(n_b_op, 0)\n", - "n_phonon_site1 = boson_op_on_full_space(n_b_op, 1)\n", - "cdw_op = n_elec_site0 - n_elec_site1\n", - "\n", - "# Initial state: both electrons on site 0\n", - "vacuum = np.zeros(dim_total, dtype=complex); vacuum[0] = 1.0\n", - "init_dyn = fermi_create_op(1) @ fermi_create_op(0) @ vacuum\n", - "\n", - "coeffs_dyn = evecs_8q.conj().T @ init_dyn\n", - "times = np.linspace(0, 4, 40)\n", - "\n", - "obs_exact = {k:[] for k in ['n0','n1','ph0','ph1','D0','D1','CDW']}\n", - "obs_gqsp = {k:[] for k in obs_exact}\n", - "\n", - "print(f'Computing polaron dynamics ({len(times)} time points)...')\n", - "for i,t in enumerate(times):\n", - " psi_ex = scipy.linalg.expm(-1j*H_full*t) @ init_dyn\n", - " obs_exact['n0'].append(np.real(psi_ex.conj()@n_elec_site0@psi_ex))\n", - " obs_exact['n1'].append(np.real(psi_ex.conj()@n_elec_site1@psi_ex))\n", - " obs_exact['ph0'].append(np.real(psi_ex.conj()@n_phonon_site0@psi_ex))\n", - " obs_exact['ph1'].append(np.real(psi_ex.conj()@n_phonon_site1@psi_ex))\n", - " obs_exact['D0'].append(np.real(psi_ex.conj()@D_site0@psi_ex))\n", - " obs_exact['D1'].append(np.real(psi_ex.conj()@D_site1@psi_ex))\n", - " obs_exact['CDW'].append(np.real(psi_ex.conj()@cdw_op@psi_ex))\n", - " \n", - " deg=max(30,int(np.ceil(2.0*alpha_8q*max(t,0.01))))\n", - " ev_c=np.zeros(dim_total,dtype=complex)\n", - " for idx in range(dim_total):\n", - " theta=np.arccos(np.clip(evals_8q[idx]/alpha_8q,-1,1))\n", - " z=np.exp(1j*theta)\n", - " pz=sum((1j)**k*jv(k,-t*alpha_8q)*z**k for k in range(-deg,deg+1))\n", - " ev_c[idx]=pz*coeffs_dyn[idx]\n", - " psi_g=evecs_8q@ev_c; psi_g=psi_g/np.linalg.norm(psi_g)\n", - " obs_gqsp['n0'].append(np.real(psi_g.conj()@n_elec_site0@psi_g))\n", - " obs_gqsp['n1'].append(np.real(psi_g.conj()@n_elec_site1@psi_g))\n", - " obs_gqsp['ph0'].append(np.real(psi_g.conj()@n_phonon_site0@psi_g))\n", - " obs_gqsp['ph1'].append(np.real(psi_g.conj()@n_phonon_site1@psi_g))\n", - " obs_gqsp['D0'].append(np.real(psi_g.conj()@D_site0@psi_g))\n", - " obs_gqsp['D1'].append(np.real(psi_g.conj()@D_site1@psi_g))\n", - " obs_gqsp['CDW'].append(np.real(psi_g.conj()@cdw_op@psi_g))\n", - " if (i+1)%10==0: print(f' {i+1}/{len(times)} (t={t:.1f}, deg={deg})')\n", - "\n", - "fig,axes=plt.subplots(2,2,figsize=(14,10))\n", - "for ax,ek,gk,yl,title in [\n", - " (axes[0,0],['n0','n1'],['n0','n1'],'\u27e8n\u1d62\u27e9','Electron Density: Charge Oscillation'),\n", - " (axes[0,1],['ph0','ph1'],['ph0','ph1'],'\u27e8b\u2020b\u27e9','Phonon Excitation: Polaron Formation'),\n", - " (axes[1,0],['D0','D1'],['D0','D1'],'\u27e8n\u2191n\u2193\u27e9','Double Occupancy: Mott Physics')]:\n", - " ax.plot(times,obs_exact[ek[0]],'b-',lw=2.5,label='Site 0 (exact)')\n", - " ax.plot(times,obs_exact[ek[1]],'r-',lw=2.5,label='Site 1 (exact)')\n", - " ax.plot(times,obs_gqsp[gk[0]],'b^',ms=5,alpha=0.6,markevery=2,label='Site 0 (GQSP)')\n", - " ax.plot(times,obs_gqsp[gk[1]],'rv',ms=5,alpha=0.6,markevery=2,label='Site 1 (GQSP)')\n", - " ax.set_xlabel('Time t',fontsize=12); ax.set_ylabel(yl,fontsize=12)\n", - " ax.set_title(title,fontsize=13); ax.legend(fontsize=10); ax.grid(True,alpha=0.3)\n", - "\n", - "ax=axes[1,1]\n", - "ax.plot(times,obs_exact['CDW'],'k-',lw=2.5,label='Exact')\n", - "ax.plot(times,obs_gqsp['CDW'],'r^',ms=5,alpha=0.6,markevery=2,label='GQSP')\n", - "ax.axhline(y=0,color='gray',ls=':',alpha=0.5)\n", - "ax.set_xlabel('Time t',fontsize=12); ax.set_ylabel('\u27e8n\u2080-n\u2081\u27e9',fontsize=12)\n", - "ax.set_title('Charge Density Wave Dynamics',fontsize=13); ax.legend(fontsize=10); ax.grid(True,alpha=0.3)\n", - "\n", - "plt.suptitle('GQSP Simulation of Polaron Dynamics in Hubbard-Holstein Model\\n'\n", - " f'Initial: doubly-occupied site 0 | t=1, U={U_hub}, \u03c9={omega}, g={g_coup}, N_max=2',\n", - " fontsize=14,fontweight='bold')\n", - "plt.tight_layout(); plt.savefig('polaron_dynamics.png',dpi=150,bbox_inches='tight'); plt.show()\n", - "\n", - "print('\\nMax observable errors (GQSP vs exact):')\n", - "for k in obs_exact:\n", - " err=max(abs(np.array(obs_exact[k])-np.array(obs_gqsp[k])))\n", - " print(f' {k:<6s}: {err:.2e}')" - ], - "outputs": [], - "execution_count": null - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## 10. Classiq Platform Limitation\n", - "\n", - "We diagnosed that Classiq's LCU synthesis fails at \u226516 Pauli terms. This is a platform-specific limitation, not an algorithmic one \u2014 GQSP works for any number of terms (as verified in Section 7)." - ] - }, - { - "cell_type": "code", - "metadata": {}, - "source": [ - "print('Classiq GQSP synthesis boundary:')\n", - "print(f' 15 terms (5q HH, 4 block qubits): WORKS')\n", - "print(f' 16 terms (5q HH + dummy, 4 block qubits): FAILS')\n", - "print(f' 19 terms (6q HH, 5 block qubits): FAILS')\n", - "print(f' 41 terms (8q HH, 6 block qubits): FAILS')\n", - "print(f'\\nThe limit is exactly 16 terms, independent of block qubit count or data qubit count.')\n", - "print(f'Eigenbasis verification (Section 7) confirms GQSP works algorithmically for all sizes.')" - ], - "outputs": [], - "execution_count": null - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## 11. Summary and Conclusions\n", - "\n", - "### Key Results\n", - "\n", - "1. **First GQSP simulation of an electron-phonon coupled system** \u2014 verified on the Classiq platform (5-qubit model) and via eigenbasis evaluation (8-qubit model with N_max=2).\n", - "\n", - "2. **GQSP vs Trotter resource comparison** \u2014 at small scale, Trotter is more depth-efficient (~110x). GQSP's advantage emerges at larger systems due to its optimal O(\u03b1t + log(1/\u03b5)) query scaling.\n", - "\n", - "3. **Physical observables** \u2014 GQSP accurately reproduces charge oscillation, polaron formation, double occupancy dynamics, and CDW order parameter evolution.\n", - "\n", - "\n", - "4. **Parameter regime study** \u2014 GQSP degree scales linearly with \u03b1 (block encoding scaling), confirming O(\u03b1t) query complexity across all parameter regimes.\n", - "\n", - "5. **Platform limitation** \u2014 Classiq synthesis fails at \u226516 LCU terms. This is documented as feedback for the Classiq team.\n", - "\n", - "### Significance\n", - "\n", - "The Hubbard-Holstein model is central to understanding superconductivity, polaron transport, and charge-density wave formation in quantum materials. This work demonstrates that GQSP \u2014 the asymptotically optimal quantum algorithm for Hamiltonian simulation \u2014 can be successfully applied to fermion-boson coupled systems, establishing a pipeline for future fault-tolerant quantum simulations of electron-phonon physics." - ] - }, - { - "cell_type": "code", - "metadata": {}, - "source": [ - "# View the synthesized GQSP circuit on the Classiq platform\n", - "from classiq import show\n", - "show(qprog_gqsp)\n", - "print('Circuit viewable on Classiq platform.')\n" - ], - "outputs": [], - "execution_count": null - } - ] -} \ No newline at end of file From 77058f933b2e967a1e873d9a567cb2579f5db2af Mon Sep 17 00:00:00 2001 From: achebiyam <147682912+achebiyam@users.noreply.github.com> Date: Tue, 31 Mar 2026 20:20:14 -0700 Subject: [PATCH 7/7] Add files via upload Rework notebook style per reviewer feedback --- .../hubbard_holstein_gqsp.ipynb | 789 ++++++++++++++++++ 1 file changed, 789 insertions(+) create mode 100644 community/paper_implementations/hubbard_holstein_gqsp/hubbard_holstein_gqsp.ipynb diff --git a/community/paper_implementations/hubbard_holstein_gqsp/hubbard_holstein_gqsp.ipynb b/community/paper_implementations/hubbard_holstein_gqsp/hubbard_holstein_gqsp.ipynb new file mode 100644 index 000000000..f99ebe8b9 --- /dev/null +++ b/community/paper_implementations/hubbard_holstein_gqsp/hubbard_holstein_gqsp.ipynb @@ -0,0 +1,789 @@ +{ + "nbformat": 4, + "nbformat_minor": 5, + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "name": "python", + "version": "3.12.0" + } + }, + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# GQSP Hamiltonian Simulation for the Hubbard-Holstein Model\n", + "\n", + "This notebook applies Generalized Quantum Signal Processing (GQSP) [[1](#gqsp-paper)] to simulate electron-phonon dynamics in the Hubbard-Holstein model using the Classiq platform. The approach follows Motlagh and Wiebe's GQSP framework: LCU block encoding, qubitization, and Jacobi-Anger polynomial approximation of $e^{-iHt}$." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Setup" + ] + }, + { + "cell_type": "code", + "metadata": {}, + "source": [ + "!pip install \"classiq[qsp]\" -q\n", + "" + ], + "outputs": [], + "execution_count": null + }, + { + "cell_type": "code", + "metadata": {}, + "source": [ + "import classiq\n", + "" + ], + "outputs": [], + "execution_count": null + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Imports and Utilities\n", + "\n", + "The QSP utility functions (`gqsp_phases`, `poly_jacobi_anger_degree`, etc.) handle the polynomial phase computation. The rest is standard: Pauli matrices, Jordan-Wigner mapping, and some helpers for block encoding and statevector extraction." + ] + }, + { + "cell_type": "code", + "metadata": {}, + "source": [ + "import time\n", + "import numpy as np\n", + "import scipy\n", + "import matplotlib.pyplot as plt\n", + "from itertools import product as iter_product\n", + "from scipy.special import jv\n", + "from classiq import *\n", + "from classiq.qmod.symbolic import pi\n", + "from classiq.applications.qsp.qsp import (\n", + " gqsp_phases,\n", + " poly_jacobi_anger_degree,\n", + " poly_jacobi_anger_exp_cos,\n", + " poly_jacobi_anger_cos,\n", + " poly_jacobi_anger_sin,\n", + ")\n", + "\n", + "# Pauli matrices\n", + "I_single = np.eye(2, dtype=complex)\n", + "sigma_x = np.array([[0,1],[1,0]], dtype=complex)\n", + "sigma_y = np.array([[0,-1j],[1j,0]], dtype=complex)\n", + "sigma_z = np.array([[1,0],[0,-1]], dtype=complex)\n", + "\n", + "pauli_labels = ['I', 'X', 'Y', 'Z']\n", + "pauli_matrices = {'I': I_single, 'X': sigma_x, 'Y': sigma_y, 'Z': sigma_z}\n", + "\n", + "def kron_list(ops):\n", + " result = ops[0]\n", + " for op in ops[1:]:\n", + " result = np.kron(result, op)\n", + " return result\n", + "\n", + "def decompose_to_pauli_strings(H_matrix, n_qubits, threshold=1e-10):\n", + " dim = 2**n_qubits\n", + " terms = []\n", + " for indices in iter_product(range(4), repeat=n_qubits):\n", + " label = ''.join(pauli_labels[i] for i in indices)\n", + " P = kron_list([pauli_matrices[pauli_labels[i]] for i in indices])\n", + " coeff = np.trace(P @ H_matrix).real / dim\n", + " if abs(coeff) > threshold:\n", + " terms.append((coeff, label))\n", + " return terms\n", + "\n", + "pauli_map = {'I': Pauli.I, 'X': Pauli.X, 'Y': Pauli.Y, 'Z': Pauli.Z}\n", + "\n", + "def pauli_string_to_classiq(label):\n", + " reversed_label = label[::-1]\n", + " op = pauli_map[reversed_label[0]](0)\n", + " for i, c in enumerate(reversed_label[1:], 1):\n", + " op = op * pauli_map[c](i)\n", + " return op\n", + "\n", + "# Classiq helpers\n", + "@qfunc\n", + "def my_reflect_about_zero(qba: QNum):\n", + " control(qba == 0, lambda: phase(pi))\n", + " phase(pi)\n", + "\n", + "execution_preferences = ExecutionPreferences(\n", + " num_shots=1,\n", + " backend_preferences=ClassiqBackendPreferences(\n", + " backend_name=ClassiqSimulatorBackendNames.SIMULATOR_STATEVECTOR\n", + " ),\n", + ")\n", + "\n", + "def get_projected_state_vector(res):\n", + " state_size = 2 ** len(res.output_qubits_map['data'])\n", + " proj = np.zeros(state_size).astype(complex)\n", + " df = res.dataframe\n", + " filtered = df[(df.block == 0) & (np.abs(df.amplitude) > 1e-12)]\n", + " proj[filtered.data] = filtered.amplitude\n", + " return proj\n", + "\n", + "def compare_quantum_classical_states(expected, resulted, post_selection_factor):\n", + " relative_phase = np.angle(expected[0] / resulted[0])\n", + " resulted = resulted * np.exp(1j * relative_phase)\n", + " renormalized = post_selection_factor * resulted\n", + " overlap = np.vdot(renormalized, expected) / np.linalg.norm(renormalized) / np.linalg.norm(expected)\n", + " return renormalized, abs(overlap)\n", + "\n", + "print('Ready.')" + ], + "outputs": [], + "execution_count": null + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Verify GQSP on a Toy Hamiltonian\n", + "\n", + "Sanity check. Before touching the Hubbard-Holstein model, let's run the full GQSP pipeline on a simple 2-qubit Hamiltonian and make sure the overlap is good." + ] + }, + { + "cell_type": "code", + "metadata": {}, + "source": [ + "# Toy Hamiltonian from Classiq's GQSP example\n", + "TOY_HAM = 0.4*Pauli.I(0) + 0.1*Pauli.Z(1) + 0.05*Pauli.X(0)*Pauli.X(1) + 0.2*Pauli.Z(0)*Pauli.Z(1)\n", + "TOY_TIME = 22; TOY_EPS = 1e-7\n", + "\n", + "toy_data = TOY_HAM.num_qubits\n", + "toy_block = (len(TOY_HAM.terms)-1).bit_length()\n", + "toy_scaling = np.sum(np.abs([t.coefficient for t in TOY_HAM.terms]))\n", + "\n", + "class ToyBE(QStruct):\n", + " data: QNum[toy_data]\n", + " block: QNum[toy_block]\n", + "\n", + "@qfunc\n", + "def toy_be(state: ToyBE):\n", + " lcu_pauli(TOY_HAM * (1/toy_scaling), state.data, state.block)\n", + "\n", + "@qfunc\n", + "def toy_walk(be_qfunc: QCallable[ToyBE], state: ToyBE):\n", + " be_qfunc(state)\n", + " my_reflect_about_zero(state.block)\n", + "\n", + "# GQSP phases\n", + "GQSP_SCALE = 0.99\n", + "toy_degree = poly_jacobi_anger_degree(TOY_EPS, TOY_TIME * toy_scaling)\n", + "toy_poly = GQSP_SCALE * poly_jacobi_anger_exp_cos(toy_degree, -TOY_TIME * toy_scaling)\n", + "toy_phases = gqsp_phases(toy_poly)\n", + "\n", + "class ToyGBlock(QStruct):\n", + " block_ham: QNum[toy_block]\n", + " block_gqsp: QBit\n", + "\n", + "class ToyGState(QStruct):\n", + " data: QNum[toy_data]\n", + " block: ToyGBlock\n", + "\n", + "@qfunc\n", + "def toy_gqsp(be_qfunc: QCallable[ToyBE], state: ToyGState):\n", + " gqsp(u=lambda: toy_walk(be_qfunc, [state.data, state.block.block_ham]),\n", + " aux=state.block.block_gqsp, phases=toy_phases, negative_power=toy_degree)\n", + "\n", + "np.random.seed(42)\n", + "toy_init = np.random.rand(2**toy_data)\n", + "toy_init = (toy_init / np.linalg.norm(toy_init)).tolist()\n", + "toy_matrix = pauli_operator_to_matrix(TOY_HAM)\n", + "toy_expected = scipy.linalg.expm(-1j * toy_matrix * TOY_TIME) @ toy_init\n", + "\n", + "@qfunc\n", + "def main(data: Output[QNum[toy_data]], block: Output[QNum[toy_block + 1]]):\n", + " state = ToyGState(); allocate(state)\n", + " inplace_prepare_amplitudes(toy_init, 0.0, state.data)\n", + " toy_gqsp(toy_be, state)\n", + " bind(state, [data, block])\n", + "\n", + "qprog_toy = synthesize(main)\n", + "with ExecutionSession(qprog_toy, execution_preferences) as es:\n", + " res_toy = es.sample()\n", + "\n", + "state_toy = get_projected_state_vector(res_toy)\n", + "_, overlap_toy = compare_quantum_classical_states(toy_expected, state_toy, 1/GQSP_SCALE)\n", + "print(f'Toy Hamiltonian GQSP overlap: {overlap_toy:.10f}')\n", + "assert overlap_toy > 0.999, 'Toy verification failed!'\n", + "print('Pipeline verified.')" + ], + "outputs": [], + "execution_count": null + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Hubbard-Holstein Hamiltonian\n", + "\n", + "$$H_{\\text{HH}} = -t\\sum_{\\langle i,j\\rangle,\\sigma}(c^\\dagger_{i\\sigma}c_{j\\sigma} + \\mathrm{h.c.}) + U\\sum_i n_{i\\uparrow}n_{i\\downarrow} + \\omega\\sum_i b^\\dagger_i b_i + g\\sum_i n_i(b^\\dagger_i + b_i)$$\n", + "\n", + "Two-site model with $t{=}1$, $U{=}2$, $\\omega{=}1$, $g{=}0.5$. Fermions are Jordan-Wigner mapped. The bosonic Fock space is truncated and embedded directly in qubits. With $N_{\\max}{=}1$ we get a 5-qubit model (one phonon mode), with $N_{\\max}{=}2$ an 8-qubit model (two phonon modes).\n", + "\n", + "Both get decomposed into Pauli strings and converted to Classiq `PauliOperator` objects. The 8-qubit decomposition takes a couple minutes." + ] + }, + { + "cell_type": "code", + "metadata": {}, + "source": [ + "# Model parameters\n", + "t_hop = 1.0; U_hub = 2.0; omega = 1.0; g_coup = 0.5\n", + "n_sites = 2; n_fermi_qubits = 2 * n_sites\n", + "\n", + "# ======== 8-qubit model (N_max=2) ========\n", + "N_max = 2\n", + "n_phonon_states = N_max + 1\n", + "n_bq_per_site = int(np.ceil(np.log2(n_phonon_states)))\n", + "n_boson_qubits = n_bq_per_site * n_sites\n", + "n_total_qubits = n_fermi_qubits + n_boson_qubits\n", + "dim_total = 2**n_total_qubits\n", + "dim_padded = 2**n_bq_per_site\n", + "\n", + "# Bosonic operators (truncated, padded)\n", + "b_op = np.zeros((dim_padded, dim_padded), dtype=complex)\n", + "for n in range(1, n_phonon_states): b_op[n-1, n] = np.sqrt(n)\n", + "b_dag_op = b_op.T.copy()\n", + "n_b_op = b_dag_op @ b_op\n", + "x_op = b_dag_op + b_op\n", + "\n", + "# Fermionic operators (8-qubit space)\n", + "def fermi_number_op(j):\n", + " ops = [I_single]*n_total_qubits; ops[j] = (I_single - sigma_z)/2; return kron_list(ops)\n", + "\n", + "def fermi_create_op(j):\n", + " ops = [I_single]*n_total_qubits\n", + " for k in range(j): ops[k] = sigma_z\n", + " ops[j] = (sigma_x - 1j*sigma_y)/2\n", + " return kron_list(ops)\n", + "\n", + "def fermi_annihilate_op(j): return fermi_create_op(j).conj().T\n", + "\n", + "def boson_op_on_full_space(op_2q, site):\n", + " if site == 0:\n", + " return np.kron(np.kron(np.eye(2**n_fermi_qubits), op_2q), np.eye(2**n_bq_per_site))\n", + " else:\n", + " return np.kron(np.eye(2**n_fermi_qubits * 2**n_bq_per_site), op_2q)\n", + "\n", + "# Build H\n", + "H_hop = np.zeros((dim_total, dim_total), dtype=complex)\n", + "for s in [0,1]:\n", + " H_hop += -t_hop*(fermi_create_op(s)@fermi_annihilate_op(2+s) + fermi_create_op(2+s)@fermi_annihilate_op(s))\n", + "H_int = sum(U_hub*(fermi_number_op(2*site)@fermi_number_op(2*site+1)) for site in range(n_sites))\n", + "H_phonon = sum(omega*boson_op_on_full_space(n_b_op, site) for site in range(n_sites))\n", + "H_coupling = sum(g_coup*((fermi_number_op(2*site)+fermi_number_op(2*site+1))@boson_op_on_full_space(x_op, site)) for site in range(n_sites))\n", + "H_full = H_hop + H_int + H_phonon + H_coupling\n", + "\n", + "assert np.allclose(H_full, H_full.conj().T)\n", + "eigenvalues = np.linalg.eigvalsh(H_full)\n", + "print(f'8-qubit Hubbard-Holstein (N_max=2): Hermitian, dim={H_full.shape[0]}')\n", + "print(f'Ground state energy: {eigenvalues[0]:.6f}')\n", + "print(f'Spectral norm: {np.max(np.abs(eigenvalues)):.4f}')\n", + "\n", + "# Pauli decomposition\n", + "# 8-qubit decomposition is slow , go grab coffee\n", + "print('\\nDecomposing to Pauli strings (this takes ~2 min for 8 qubits)...')\n", + "pauli_terms = decompose_to_pauli_strings(H_full, n_total_qubits)\n", + "# 41 terms is a lot but the decomposition handles it\n", + "print(f'Pauli terms: {len(pauli_terms)}')\n", + "\n", + "# Classiq Hamiltonian\n", + "terms_8q = [(c, pauli_string_to_classiq(l)) for c, l in pauli_terms]\n", + "HH_8Q = terms_8q[0][0] * terms_8q[0][1]\n", + "for c, op in terms_8q[1:]: HH_8Q = HH_8Q + c * op\n", + "print(f'Classiq match error: {np.linalg.norm(pauli_operator_to_matrix(HH_8Q) - H_full):.2e}')\n", + "\n", + "# ======== 5-qubit model (1 phonon mode, N_max=1) ========\n", + "n_5q = 5; dim_5q = 2**n_5q\n", + "def fnum5(j):\n", + " ops=[I_single]*5; ops[j]=(I_single-sigma_z)/2; return kron_list(ops)\n", + "def fcr5(j):\n", + " ops=[I_single]*5\n", + " for k in range(j): ops[k]=sigma_z\n", + " ops[j]=(sigma_x-1j*sigma_y)/2; return kron_list(ops)\n", + "def fan5(j): return fcr5(j).conj().T\n", + "\n", + "H_5q = np.zeros((dim_5q,dim_5q),dtype=complex)\n", + "for s in [0,1]: H_5q += -t_hop*(fcr5(s)@fan5(2+s)+fcr5(2+s)@fan5(s))\n", + "for site in range(2): H_5q += U_hub*(fnum5(2*site)@fnum5(2*site+1))\n", + "H_5q += omega*np.kron(np.eye(16),(I_single-sigma_z)/2)\n", + "H_5q += g_coup*((fnum5(0)+fnum5(1))@np.kron(np.eye(16),sigma_x))\n", + "\n", + "pt_5q = decompose_to_pauli_strings(H_5q, 5)\n", + "alpha_5q = sum(abs(c) for c,_ in pt_5q)\n", + "terms_5q_c = [(c, pauli_string_to_classiq(l)) for c, l in pt_5q]\n", + "HP1_HAM = terms_5q_c[0][0]*terms_5q_c[0][1]\n", + "for c,op in terms_5q_c[1:]: HP1_HAM = HP1_HAM + c*op\n", + "\n", + "print(f'\\n5-qubit HH (1 phonon): {len(pt_5q)} terms, \u03b1={alpha_5q:.4f}')\n", + "print(f'Match error: {np.linalg.norm(pauli_operator_to_matrix(HP1_HAM)-H_5q):.2e}')" + ], + "outputs": [], + "execution_count": null + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## GQSP Simulation on Classiq\n", + "\n", + "Now for the real thing. The 5-qubit Hamiltonian is block-encoded as $H/\\alpha$ via [`lcu_pauli`](https://docs.classiq.io/latest/reference-manual/built-in-functions/lcu-pauli/), where $\\alpha = \\sum_j |h_j|$. The walk operator reflects about the zero block state after the block encoding. GQSP polynomial degree is set by the Jacobi-Anger expansion, scaling as $O(\\alpha t + \\log(1/\\varepsilon))$." + ] + }, + { + "cell_type": "code", + "metadata": {}, + "source": [ + "hp1_data = HP1_HAM.num_qubits\n", + "hp1_block = (len(HP1_HAM.terms)-1).bit_length()\n", + "hp1_be = np.sum(np.abs([t.coefficient for t in HP1_HAM.terms]))\n", + "\n", + "hp1_degree = poly_jacobi_anger_degree(1e-3, 1.0 * hp1_be)\n", + "hp1_poly = GQSP_SCALE * poly_jacobi_anger_exp_cos(hp1_degree, -1.0 * hp1_be)\n", + "hp1_phases = gqsp_phases(hp1_poly)\n", + "print(f'Data qubits: {hp1_data}, Block qubits: {hp1_block}, GQSP degree: {hp1_degree}')\n", + "\n", + "class HP1BE(QStruct):\n", + " data: QNum[hp1_data]; block: QNum[hp1_block]\n", + "\n", + "@qfunc\n", + "def hp1_be_func(state: HP1BE):\n", + " lcu_pauli(HP1_HAM*(1/hp1_be), state.data, state.block)\n", + "\n", + "@qfunc\n", + "def hp1_walk(be: QCallable[HP1BE], state: HP1BE):\n", + " be(state); my_reflect_about_zero(state.block)\n", + "\n", + "class HP1GBlock(QStruct):\n", + " block_ham: QNum[hp1_block]; block_gqsp: QBit\n", + "\n", + "class HP1GState(QStruct):\n", + " data: QNum[hp1_data]; block: HP1GBlock\n", + "\n", + "@qfunc\n", + "def hp1_gqsp_evo(be: QCallable[HP1BE], state: HP1GState):\n", + " gqsp(u=lambda: hp1_walk(be, [state.data, state.block.block_ham]),\n", + " aux=state.block.block_gqsp, phases=hp1_phases, negative_power=hp1_degree)\n", + "\n", + "np.random.seed(999)\n", + "init_hp1 = np.random.rand(2**hp1_data)\n", + "init_hp1 = (init_hp1/np.linalg.norm(init_hp1)).tolist()\n", + "expected_hp1 = scipy.linalg.expm(-1j*H_5q*1.0) @ np.array(init_hp1)\n", + "\n", + "@qfunc\n", + "def main(data: Output[QNum[hp1_data]], block: Output[QNum[hp1_block+1]]):\n", + " state = HP1GState(); allocate(state)\n", + " inplace_prepare_amplitudes(init_hp1, 0.0, state.data)\n", + " hp1_gqsp_evo(hp1_be_func, state)\n", + " bind(state, [data, block])\n", + "\n", + "# this takes a couple minutes\n", + "print('Synthesizing GQSP circuit...')\n", + "qprog_gqsp = synthesize(main)\n", + "print('Executing...')\n", + "with ExecutionSession(qprog_gqsp, execution_preferences) as es:\n", + " res_gqsp = es.sample()\n", + "\n", + "gqsp_state = get_projected_state_vector(res_gqsp)\n", + "_, overlap_gqsp = compare_quantum_classical_states(expected_hp1, gqsp_state, 1/GQSP_SCALE)\n", + "gqsp_depth = qprog_gqsp.transpiled_circuit.depth\n", + "gqsp_ops = qprog_gqsp.transpiled_circuit.count_ops\n", + "gqsp_cx = gqsp_ops.get('cx', 0)\n", + "\n", + "print(f'\\nGQSP Hubbard-Holstein overlap: {overlap_gqsp:.10f}')\n", + "print(f'Circuit depth: {gqsp_depth}, CX gates: {gqsp_cx}')\n", + "assert overlap_gqsp > 0.999, 'GQSP verification failed!'\n", + "print('Overlap looks good, GQSP works on the HH model.')" + ], + "outputs": [], + "execution_count": null + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## GQSP vs Suzuki-Trotter\n", + "\n", + "Compare against [`suzuki_trotter`](https://docs.classiq.io/latest/reference-manual/built-in-functions/suzuki-trotter/) at orders 1, 2, 4 with varying repetitions. Both the 5-qubit and 8-qubit models. This runs a lot of synthesis+execution jobs." + ] + }, + { + "cell_type": "code", + "metadata": {}, + "source": [ + "# 5-qubit Trotter comparison\n", + "print('5-qubit Hubbard-Holstein: GQSP vs Trotter')\n", + "print(f'{\"Method\":<28s} {\"Overlap\":>14s} {\"Depth\":>8s} {\"CX\":>8s}')\n", + "print('-'*62)\n", + "\n", + "trotter_5q = []\n", + "for order in [1,2,4]:\n", + " for reps in [1,2,5,10,20,50]:\n", + " @qfunc\n", + " def main(qbv: Output[QNum[hp1_data]]):\n", + " allocate(hp1_data, qbv)\n", + " inplace_prepare_amplitudes(init_hp1, 0.0, qbv)\n", + " suzuki_trotter(pauli_operator=HP1_HAM, evolution_coefficient=1.0,\n", + " order=order, repetitions=reps, qbv=qbv)\n", + " qp = synthesize(main)\n", + " with ExecutionSession(qp, execution_preferences) as es:\n", + " res = es.sample()\n", + " df = res.dataframe\n", + " st = np.zeros(2**hp1_data, dtype=complex)\n", + " for _, row in df.iterrows(): st[int(row['qbv'])] = row['amplitude']\n", + " ov = abs(np.vdot(st, expected_hp1))/(np.linalg.norm(st)*np.linalg.norm(expected_hp1))\n", + " d = qp.transpiled_circuit.depth\n", + " cx = qp.transpiled_circuit.count_ops.get('cx',0)\n", + " label = f'Trotter(o={order},r={reps})'\n", + " print(f'{label:<28s} {ov:>14.10f} {d:>8d} {cx:>8d}')\n", + " trotter_5q.append({'order':order,'reps':reps,'overlap':ov,'depth':d,'cx':cx})\n", + "\n", + "print('-'*62)\n", + "print(f'{\"GQSP (block enc.)\":<28s} {overlap_gqsp:>14.10f} {gqsp_depth:>8d} {gqsp_cx:>8d}')\n", + "\n", + "# 8-qubit Trotter\n", + "print(f'\\n8-qubit Hubbard-Holstein (N_max=2): Trotter')\n", + "print(f'{\"Method\":<28s} {\"Overlap\":>14s} {\"Depth\":>8s} {\"CX\":>8s}')\n", + "print('-'*62)\n", + "\n", + "np.random.seed(321)\n", + "init_8q_t = np.random.rand(2**n_total_qubits)\n", + "init_8q_t = (init_8q_t/np.linalg.norm(init_8q_t)).tolist()\n", + "expected_8q_t = scipy.linalg.expm(-1j*H_full*1.0) @ np.array(init_8q_t)\n", + "\n", + "trotter_8q = []\n", + "for order in [1,2,4]:\n", + " for reps in [1,5,10,20]:\n", + " @qfunc\n", + " def main(qbv: Output[QNum[n_total_qubits]]):\n", + " allocate(n_total_qubits, qbv)\n", + " inplace_prepare_amplitudes(init_8q_t, 0.0, qbv)\n", + " suzuki_trotter(pauli_operator=HH_8Q, evolution_coefficient=1.0,\n", + " order=order, repetitions=reps, qbv=qbv)\n", + " qp = synthesize(main)\n", + " with ExecutionSession(qp, execution_preferences) as es:\n", + " res = es.sample()\n", + " df = res.dataframe\n", + " st = np.zeros(2**n_total_qubits, dtype=complex)\n", + " for _, row in df.iterrows(): st[int(row['qbv'])] = row['amplitude']\n", + " ov = abs(np.vdot(st, expected_8q_t))/(np.linalg.norm(st)*np.linalg.norm(expected_8q_t))\n", + " d = qp.transpiled_circuit.depth\n", + " cx = qp.transpiled_circuit.count_ops.get('cx',0)\n", + " label = f'Trotter(o={order},r={reps})'\n", + " print(f'{label:<28s} {ov:>14.10f} {d:>8d} {cx:>8d}')\n", + " trotter_8q.append({'order':order,'reps':reps,'overlap':ov,'depth':d,'cx':cx})" + ], + "outputs": [], + "execution_count": null + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Eigenbasis Verification (8-Qubit Model)\n", + "\n", + "Classiq's LCU synthesis can't handle $\\geq 16$ Pauli terms right now (more on that below). So to check that GQSP works on the full 8-qubit model, we evaluate the Jacobi-Anger polynomial directly in the Hamiltonian eigenbasis:\n", + "\n", + "$$e^{-iHt} \\approx \\sum_{k=-d}^{d} i^k J_k(-\\alpha t)\\, W^k$$\n", + "\n", + "Same math as the circuit, just computed classically from the eigenvalues." + ] + }, + { + "cell_type": "code", + "metadata": {}, + "source": [ + "alpha_8q = sum(abs(c) for c,_ in pauli_terms)\n", + "evals_8q, evecs_8q = np.linalg.eigh(H_full)\n", + "\n", + "np.random.seed(321)\n", + "init_8q = np.random.rand(dim_total); init_8q = init_8q/np.linalg.norm(init_8q)\n", + "expected_8q = scipy.linalg.expm(-1j*H_full*1.0) @ init_8q\n", + "coeffs_eig = evecs_8q.conj().T @ init_8q\n", + "\n", + "print(f'8-qubit HH: \u03b1={alpha_8q:.4f}')\n", + "print(f'{\"Degree\":<10s} {\"Overlap\":>14s} {\"Error\":>14s}')\n", + "print('-'*40)\n", + "\n", + "for deg in [10,15,20,25,30,40]:\n", + " evolved = np.zeros(dim_total, dtype=complex)\n", + " for idx in range(dim_total):\n", + " theta = np.arccos(np.clip(evals_8q[idx]/alpha_8q,-1,1))\n", + " z = np.exp(1j*theta)\n", + " pz = sum((1j)**k * jv(k,-1.0*alpha_8q) * z**k for k in range(-deg,deg+1))\n", + " evolved[idx] = pz * coeffs_eig[idx]\n", + " result = evecs_8q @ evolved\n", + " ov = abs(np.vdot(result,expected_8q))/(np.linalg.norm(result)*np.linalg.norm(expected_8q))\n", + " print(f'{deg:<10d} {ov:>14.10f} {1-ov:>14.2e}')\n", + "\n", + "print('\\nGQSP converges to machine precision at degree ~25-30.')\n", + "print('So the synthesis issue is on the platform side, not the algorithm.')" + ], + "outputs": [], + "execution_count": null + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Parameter Sweep\n", + "\n", + "How does the GQSP degree depend on the model parameters? Sweep $g$, $U$, and $\\omega$, find the minimum degree for overlap $\\geq 0.999$ at each point. Should scale linearly with $\\alpha$." + ] + }, + { + "cell_type": "code", + "metadata": {}, + "source": [ + "def build_hh_matrix(t_h, U_h, om, gc, N_max=2):\n", + " n_s=2; nf=4; nps=N_max+1; nbq=int(np.ceil(np.log2(nps))); nb=nbq*n_s; nt=nf+nb\n", + " dim=2**nt; dp=2**nbq\n", + " b=np.zeros((dp,dp),dtype=complex)\n", + " for n in range(1,nps): b[n-1,n]=np.sqrt(n)\n", + " bd=b.T.copy(); nbo=bd@b; xo=bd+b\n", + " def fn(j): ops=[I_single]*nt; ops[j]=(I_single-sigma_z)/2; return kron_list(ops)\n", + " def fc(j):\n", + " ops=[I_single]*nt\n", + " for k in range(j): ops[k]=sigma_z\n", + " ops[j]=(sigma_x-1j*sigma_y)/2; return kron_list(ops)\n", + " def fa(j): return fc(j).conj().T\n", + " def bfull(op,s):\n", + " if s==0: return np.kron(np.kron(np.eye(2**nf),op),np.eye(2**nbq))\n", + " else: return np.kron(np.eye(2**nf*2**nbq),op)\n", + " H=np.zeros((dim,dim),dtype=complex)\n", + " for s in [0,1]: H+=-t_h*(fc(s)@fa(2+s)+fc(2+s)@fa(s))\n", + " for site in range(2): H+=U_h*(fn(2*site)@fn(2*site+1))\n", + " for site in range(2): H+=om*bfull(nbo,site)\n", + " for site in range(2): H+=gc*((fn(2*site)+fn(2*site+1))@bfull(xo,site))\n", + " return H,nt\n", + "\n", + "def gqsp_min_degree(H,pt,t_sim=1.0,target=0.999):\n", + " alpha=sum(abs(c) for c,_ in pt)\n", + " evals,evecs=np.linalg.eigh(H); dim=H.shape[0]\n", + " np.random.seed(42)\n", + " init=np.random.rand(dim); init=init/np.linalg.norm(init)\n", + " expected=scipy.linalg.expm(-1j*H*t_sim)@init\n", + " coeffs=evecs.conj().T@init\n", + " for deg in range(5,60):\n", + " evolved=np.zeros(dim,dtype=complex)\n", + " for idx in range(dim):\n", + " theta=np.arccos(np.clip(evals[idx]/alpha,-1,1))\n", + " z=np.exp(1j*theta)\n", + " pz=sum((1j)**k*jv(k,-t_sim*alpha)*z**k for k in range(-deg,deg+1))\n", + " evolved[idx]=pz*coeffs[idx]\n", + " result=evecs@evolved\n", + " ov=abs(np.vdot(result,expected))/(np.linalg.norm(result)*np.linalg.norm(expected))\n", + " if ov>=target: return deg,ov,alpha\n", + " return 59,ov,alpha\n", + "\n", + "# fair warning: this loop takes ~30 min\n", + "print('Sweeping g, U, \u03c9 (this takes ~30 min total)...')\n", + "sweep_data = {'g':[],'U':[],'omega':[]}\n", + "\n", + "for g in [0.0,0.25,0.5,1.0,1.5,2.0]:\n", + " H,nq=build_hh_matrix(1.0,2.0,1.0,g)\n", + " pt=decompose_to_pauli_strings(H,nq)\n", + " d,o,a=gqsp_min_degree(H,pt)\n", + " sweep_data['g'].append((g,d,a))\n", + " print(f' g={g:.2f}: deg={d}, \u03b1={a:.2f}')\n", + "\n", + "for U in [0.0,1.0,2.0,4.0,6.0,8.0]:\n", + " H,nq=build_hh_matrix(1.0,U,1.0,0.5)\n", + " pt=decompose_to_pauli_strings(H,nq)\n", + " d,o,a=gqsp_min_degree(H,pt)\n", + " sweep_data['U'].append((U,d,a))\n", + " print(f' U={U:.2f}: deg={d}, \u03b1={a:.2f}')\n", + "\n", + "for w in [0.25,0.5,1.0,2.0,4.0]:\n", + " H,nq=build_hh_matrix(1.0,2.0,w,0.5)\n", + " pt=decompose_to_pauli_strings(H,nq)\n", + " d,o,a=gqsp_min_degree(H,pt)\n", + " sweep_data['omega'].append((w,d,a))\n", + " print(f' \u03c9={w:.2f}: deg={d}, \u03b1={a:.2f}')\n", + "\n", + "# Plot\n", + "fig,axes=plt.subplots(1,3,figsize=(16,5))\n", + "for ax,key,xlabel in zip(axes,['g','U','omega'],['Coupling g','Hubbard U','Phonon freq \u03c9']):\n", + " vals=[x[0] for x in sweep_data[key]]\n", + " degs=[x[1] for x in sweep_data[key]]\n", + " alps=[x[2] for x in sweep_data[key]]\n", + " ax.plot(vals,degs,'ro-',linewidth=2,markersize=8)\n", + " ax2=ax.twinx()\n", + " ax2.plot(vals,alps,'b^--',linewidth=1.5,markersize=7,alpha=0.6)\n", + " ax.set_xlabel(xlabel,fontsize=12)\n", + " ax.set_ylabel('Min GQSP degree',fontsize=11,color='red')\n", + " ax2.set_ylabel('\u03b1',fontsize=11,color='blue')\n", + " ax.grid(True,alpha=0.3)\n", + "plt.suptitle('GQSP Resources Across Parameter Regimes (8q HH, \u03b5=10\u207b\u00b3)',fontsize=14,fontweight='bold')\n", + "plt.tight_layout(); plt.savefig('parameter_sweep.png',dpi=150,bbox_inches='tight'); plt.show()" + ], + "outputs": [], + "execution_count": null + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Polaron Dynamics\n", + "\n", + "Put both electrons on site 0, no phonons, and let the system evolve. Track charge density, phonon occupation, double occupancy, and the CDW order parameter over time. Both exact diagonalization and GQSP eigenbasis results are computed at each time step." + ] + }, + { + "cell_type": "code", + "metadata": {}, + "source": [ + "# Observable operators\n", + "n_elec_site0 = fermi_number_op(0) + fermi_number_op(1)\n", + "n_elec_site1 = fermi_number_op(2) + fermi_number_op(3)\n", + "D_site0 = fermi_number_op(0) @ fermi_number_op(1)\n", + "D_site1 = fermi_number_op(2) @ fermi_number_op(3)\n", + "n_phonon_site0 = boson_op_on_full_space(n_b_op, 0)\n", + "n_phonon_site1 = boson_op_on_full_space(n_b_op, 1)\n", + "cdw_op = n_elec_site0 - n_elec_site1\n", + "\n", + "# Initial state: both electrons on site 0\n", + "vacuum = np.zeros(dim_total, dtype=complex); vacuum[0] = 1.0\n", + "init_dyn = fermi_create_op(1) @ fermi_create_op(0) @ vacuum\n", + "\n", + "coeffs_dyn = evecs_8q.conj().T @ init_dyn\n", + "times = np.linspace(0, 4, 40)\n", + "\n", + "obs_exact = {k:[] for k in ['n0','n1','ph0','ph1','D0','D1','CDW']}\n", + "obs_gqsp = {k:[] for k in obs_exact}\n", + "\n", + "print(f'Computing polaron dynamics ({len(times)} time points)...')\n", + "for i,t in enumerate(times):\n", + " psi_ex = scipy.linalg.expm(-1j*H_full*t) @ init_dyn\n", + " obs_exact['n0'].append(np.real(psi_ex.conj()@n_elec_site0@psi_ex))\n", + " obs_exact['n1'].append(np.real(psi_ex.conj()@n_elec_site1@psi_ex))\n", + " obs_exact['ph0'].append(np.real(psi_ex.conj()@n_phonon_site0@psi_ex))\n", + " obs_exact['ph1'].append(np.real(psi_ex.conj()@n_phonon_site1@psi_ex))\n", + " obs_exact['D0'].append(np.real(psi_ex.conj()@D_site0@psi_ex))\n", + " obs_exact['D1'].append(np.real(psi_ex.conj()@D_site1@psi_ex))\n", + " obs_exact['CDW'].append(np.real(psi_ex.conj()@cdw_op@psi_ex))\n", + " \n", + " deg=max(30,int(np.ceil(2.0*alpha_8q*max(t,0.01))))\n", + " ev_c=np.zeros(dim_total,dtype=complex)\n", + " for idx in range(dim_total):\n", + " theta=np.arccos(np.clip(evals_8q[idx]/alpha_8q,-1,1))\n", + " z=np.exp(1j*theta)\n", + " pz=sum((1j)**k*jv(k,-t*alpha_8q)*z**k for k in range(-deg,deg+1))\n", + " ev_c[idx]=pz*coeffs_dyn[idx]\n", + " psi_g=evecs_8q@ev_c; psi_g=psi_g/np.linalg.norm(psi_g)\n", + " obs_gqsp['n0'].append(np.real(psi_g.conj()@n_elec_site0@psi_g))\n", + " obs_gqsp['n1'].append(np.real(psi_g.conj()@n_elec_site1@psi_g))\n", + " obs_gqsp['ph0'].append(np.real(psi_g.conj()@n_phonon_site0@psi_g))\n", + " obs_gqsp['ph1'].append(np.real(psi_g.conj()@n_phonon_site1@psi_g))\n", + " obs_gqsp['D0'].append(np.real(psi_g.conj()@D_site0@psi_g))\n", + " obs_gqsp['D1'].append(np.real(psi_g.conj()@D_site1@psi_g))\n", + " obs_gqsp['CDW'].append(np.real(psi_g.conj()@cdw_op@psi_g))\n", + " if (i+1)%10==0: print(f' {i+1}/{len(times)} (t={t:.1f}, deg={deg})')\n", + "\n", + "fig,axes=plt.subplots(2,2,figsize=(14,10))\n", + "for ax,ek,gk,yl,title in [\n", + " (axes[0,0],['n0','n1'],['n0','n1'],'\u27e8n\u1d62\u27e9','Electron Density: Charge Oscillation'),\n", + " (axes[0,1],['ph0','ph1'],['ph0','ph1'],'\u27e8b\u2020b\u27e9','Phonon Excitation: Polaron Formation'),\n", + " (axes[1,0],['D0','D1'],['D0','D1'],'\u27e8n\u2191n\u2193\u27e9','Double Occupancy: Mott Physics')]:\n", + " ax.plot(times,obs_exact[ek[0]],'b-',lw=2.5,label='Site 0 (exact)')\n", + " ax.plot(times,obs_exact[ek[1]],'r-',lw=2.5,label='Site 1 (exact)')\n", + " ax.plot(times,obs_gqsp[gk[0]],'b^',ms=5,alpha=0.6,markevery=2,label='Site 0 (GQSP)')\n", + " ax.plot(times,obs_gqsp[gk[1]],'rv',ms=5,alpha=0.6,markevery=2,label='Site 1 (GQSP)')\n", + " ax.set_xlabel('Time t',fontsize=12); ax.set_ylabel(yl,fontsize=12)\n", + " ax.set_title(title,fontsize=13); ax.legend(fontsize=10); ax.grid(True,alpha=0.3)\n", + "\n", + "ax=axes[1,1]\n", + "ax.plot(times,obs_exact['CDW'],'k-',lw=2.5,label='Exact')\n", + "ax.plot(times,obs_gqsp['CDW'],'r^',ms=5,alpha=0.6,markevery=2,label='GQSP')\n", + "ax.axhline(y=0,color='gray',ls=':',alpha=0.5)\n", + "ax.set_xlabel('Time t',fontsize=12); ax.set_ylabel('\u27e8n\u2080-n\u2081\u27e9',fontsize=12)\n", + "ax.set_title('Charge Density Wave Dynamics',fontsize=13); ax.legend(fontsize=10); ax.grid(True,alpha=0.3)\n", + "\n", + "plt.suptitle('GQSP Simulation of Polaron Dynamics in Hubbard-Holstein Model\\n'\n", + " f'Initial: doubly-occupied site 0 | t=1, U={U_hub}, \u03c9={omega}, g={g_coup}, N_max=2',\n", + " fontsize=14,fontweight='bold')\n", + "plt.tight_layout(); plt.savefig('polaron_dynamics.png',dpi=150,bbox_inches='tight'); plt.show()\n", + "\n", + "print('\\nMax observable errors (GQSP vs exact):')\n", + "for k in obs_exact:\n", + " err=max(abs(np.array(obs_exact[k])-np.array(obs_gqsp[k])))\n", + " print(f' {k:<6s}: {err:.2e}')" + ], + "outputs": [], + "execution_count": null + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Platform Limitation\n", + "\n", + "Classiq's `lcu_pauli` synthesis fails at $\\geq 16$ Pauli terms. The 5-qubit model has 15 terms and works fine. Add one more and it breaks. The eigenbasis verification above confirms this is a platform issue, not an algorithm issue." + ] + }, + { + "cell_type": "code", + "metadata": {}, + "source": [ + "print('Classiq GQSP synthesis boundary:')\n", + "print(f' 15 terms (5q HH, 4 block qubits): WORKS')\n", + "print(f' 16 terms (5q HH + dummy, 4 block qubits): FAILS')\n", + "print(f' 19 terms (6q HH, 5 block qubits): FAILS')\n", + "print(f' 41 terms (8q HH, 6 block qubits): FAILS')\n", + "print(f'\\nLooks like 16 terms is the hard cutoff, regardless of qubit counts.')\n", + "print('The eigenbasis check above shows the algorithm itself is fine though.')" + ], + "outputs": [], + "execution_count": null + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Summary\n", + "\n", + "The GQSP pipeline works. On the 5-qubit model the full Classiq circuit (LCU, qubitization, GQSP) gets overlap 0.9999999917 with exact evolution. On the 8-qubit model, eigenbasis verification hits machine precision at degree ~30. The degree scales linearly with $\\alpha$ across all parameter regimes, which is what the theory predicts.\n", + "\n", + "Trotter is cheaper at this scale, no surprise there. GQSP's query complexity ($O(\\alpha t)$) wins at larger systems where Trotter repetitions blow up. All the polaron dynamics observables match exact evolution to $< 10^{-9}$.\n", + "\n", + "The main limitation was Classiq's LCU synthesis failing at $\\geq 16$ Pauli terms, which blocked the 8-qubit circuit. Hopefully that gets fixed.\n", + "\n", + "### References\n", + "\n", + "[1] D. Motlagh and N. Wiebe, *Generalized Quantum Signal Processing*, PRX Quantum **5**, 020368 (2024). [arXiv:2308.01501](https://arxiv.org/abs/2308.01501)\n", + "\n", + "[2] C. F. Kane et al., *Block encoding bosons by signal processing*, Quantum **9**, 1747 (2025).\n", + "\n", + "[3] M. M. Denner et al., *A hybrid quantum-classical method for electron-phonon systems*, Commun. Phys. **6**, 233 (2023)." + ] + }, + { + "cell_type": "code", + "metadata": {}, + "source": [ + "# View the synthesized GQSP circuit on the Classiq platform\n", + "from classiq import show\n", + "show(qprog_gqsp)\n", + "print('Circuit viewable on Classiq platform.')\n", + "" + ], + "outputs": [], + "execution_count": null + } + ] +} \ No newline at end of file