CavityVQE

Variational Quantum Eigensolver for the Jaynes-Cummings model, implemented in NVIDIA CUDA-Q.

Finds the ground-state energy of a two-level atom coupled to a single cavity photon mode — a foundational quantum optics system — using a hardware-efficient ansatz and COBYLA optimisation on CUDA-Q's statevector simulator.

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Key Results

Metric	Value
Model	Jaynes-Cummings (RWA, 1-photon Fock truncation)
Qubits	2
Ansatz	Hardware-efficient, 2 reps, 6 parameters
Framework	NVIDIA CUDA-Q (qpp-cpu / nvidia backends)
VQE energy	converges to exact GS within ~1e-4
Vacuum Rabi splitting	reproduced at resonance (gap ≈ 2g)

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Physics

The Jaynes-Cummings Hamiltonian (rotating-wave approximation, ℏ = 1):

H = ωc·a†a + ω0/2·σz + g·(a†σ⁻ + a·σ⁺)

Qubit encoding (2-qubit, Fock truncation N=1):

H = ωc/2·(I − Z₀) + ω0/2·Z₁ + g/2·(X₀X₁ + Y₀Y₁)

At resonance (ωc = ω0), the dressed states split by ±g — the vacuum Rabi splitting.

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Project Structure

CavityVQE/
├── hamiltonian/
│   └── jaynes_cummings.py   # JC → cudaq.SpinOperator + exact diagonalisation
├── circuits/
│   └── ansatz.py            # Hardware-efficient CUDA-Q kernel
├── vqe/
│   └── runner.py            # VQE loop: cudaq.observe + COBYLA
├── analysis/
│   └── plots.py             # Convergence, Rabi splitting, spectrum plots
├── tests/                   # pytest suite (Hamiltonian + VQE integration)
├── notebooks/
│   └── walkthrough.ipynb    # End-to-end demo with 4 charts
├── config.py                # All parameters, env-var overridable
└── run.py                   # CLI entrypoint

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Quickstart

pip install -r requirements.txt

# Run VQE with default parameters (qpp-cpu, no GPU needed)
python run.py

# Override coupling strength and ansatz depth
python run.py --g 0.2 --reps 3

# Run with GPU backend (requires NVIDIA GPU + cudaq[nvidia])
python run.py --backend nvidia

# Run full sweep with Rabi splitting plot
python run.py --sweep --save plots/

# Run tests
pytest tests/ -v

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Notebooks

Open notebooks/walkthrough.ipynb for a step-by-step demo covering:

1. Hamiltonian construction and exact eigenvalues
2. Ansatz circuit diagram
3. VQE convergence
4. Vacuum Rabi splitting sweep
5. Off-resonance detuning scan

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Configuration

All parameters are set in config.py and overridable via environment variables:

Variable	Default	Description
CAVITY_FREQ	1.0	ωc — cavity frequency
ATOM_FREQ	1.0	ω0 — atomic transition frequency
COUPLING	0.1	g — light-matter coupling
N_PHOTON_MAX	1	Fock space truncation
BACKEND	qpp-cpu	CUDA-Q simulator backend
MAX_ITERATIONS	200	COBYLA max iterations

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Stack

• NVIDIA CUDA-Q — quantum kernel execution and statevector simulation
• NumPy / SciPy — classical optimisation (COBYLA) and exact diagonalisation
• Matplotlib — results visualisation

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References

• Kandala, A. et al. "Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets." Nature 549, 242–246 (2017). https://doi.org/10.1038/nature23879
• Jaynes, E. T. & Cummings, F. W. "Comparison of quantum and semiclassical radiation theories with application to the beam maser." Proc. IEEE 51, 89–109 (1963).

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