Implement QFT Section IV.1 simulation

[Tatgithub02]

Issue

Closes #580

What This Does

Implements the QFT simulation from Section IV.1 of the paper
Simulating Quantum Field Theories on Gate-Based Quantum Computers
by Gayathree M. Vinod and Anil Shaji.

Reproduces Fig. 2 — the oscillatory dynamics of a fermion transitioning
into a fermion-plus-boson pair in a 1+1D Yukawa theory on a 12-qubit register.

Implementation Details

Physics Setup:

• 12 qubits: 3 fermionic modes (Jordan–Wigner), 3 antifermion modes (JW), 3 bosonic modes (2 qubits each)
• Hamiltonian: 2257 Pauli strings
• Initial state: |f⟩₂ (K=2, Q=1); Tracked state: |f⟩₁⊗|φ⟩₁ (K=2, Q=1)

Simulations:

1. Exact evolution — SciPy expm_multiply (reference)
2. Gate-based — Classiq Suzuki–Trotter (order=1, repetitions=10)

Results

✓ Exact evolution reproduces paper Fig. 2:

• Peak population: 0.2249 (paper reports ~0.225)
• Period: 0.131 m_π⁻¹
• P(t=0.2): 0.2238

✓ Closed-form Rabi validation:

• Max deviation from exact: 4×10⁻¹⁴ (two-level system is exact)

✓ Conservation laws verified:

• [H, K] = 0 (momentum conserved)
• [H, Q] = 0 (charge conserved)

✓ Gate-based Trotter simulation:

• Circuit: 12 qubits, ~54k gates, ~19k CNOTs
• Matches exact within validated window (t ≤ 0.2)

Files Included

• qft_simulation.ipynb (46 cells, ~15–20 min runtime)
• qft_simulation.qmod (~1.2 MB, compiled model)

Testing

pip install "classiq==1.19.1" numpy scipy matplotlib
jupyter notebook qft_simulation.ipynb
# Kernel → Restart & Run All

Checklist

• Notebook runs with classiq==1.19.1
• Files in research/qft_simulation/
• File names unique and descriptive
• Required files included: .ipynb, .qmod
• Paper link included
• Will run pre-commit before commit

Key Assumptions

1. α_n renormalization: Uses authors' reference-code convention (required for Fig. 2)
2. Mode cutoff N_max=3: Matches Section IV.1
3. Coefficient rounding: 4 decimals (negligible perturbation)

References

• G. M. Vinod and A. Shaji, arXiv:2401.04496
• Classiq documentation: https://docs.classiq.io/

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[github-actions]

🔥 New notebook just dropped!

@amir-naveh , @TomerGoldfriend — come check out this shiny new addition to our repo.

[Tatgithub02]

@NadavClassiq please review the PR

[TomerGoldfriend]

Thank you @Tatgithub02 for this contribution. We will review it :-).
There are some test failures:

1. Could you please rebase your branch on the most updated main? This shall resolve the second test (this is due to a bug in our workflow that we fixed recently)
2. There are some lint error, could you please run pre-commit and commit again?

pip install pre-commit
pre-commit install

Let us know if you have any questions.

[Tatgithub02]

Thank you @Tatgithub02 for this contribution. We will review it :-). There are some test failures:

1. Could you please rebase your branch on the most updated main? This shall resolve the second test (this is due to a bug in our workflow that we fixed recently)
2. There are some lint error, could you please run pre-commit and commit again?

pip install pre-commit
pre-commit install

Let us know if you have any questions.

Thanks @TomerGoldfriend ! I've rebased onto the latest main and run pre-commit with the lint fixes committed. Let me know if anything else comes up.