Quantum Power Flow: a HHL-based implementation

A transparent, end-to-end reproduction of the five-bus Quantum Power Flow (QPF) study by Feng, Zhou, and Zhang, implemented with modern Qiskit and Qiskit Aer.

F. Feng, Y. Zhou, and P. Zhang, “Quantum Power Flow,” arXiv:2104.04888, 2021.

The repository reconstructs the paper’s fast-decoupled AC power-flow model, implements a custom Harrow–Hassidim–Lloyd (HHL) circuit, and reproduces every reported experiment: the normal and stressed operating cases, the finite phase-register precision ablation, and the 5,000-sample correlated stochastic power-flow study. Every assumption, inferred parameter, and numerical discrepancy relative to the paper is documented.

Everything in this section is regenerated end-to-end by one command, qpf-reproduce all (see Quickstart).

Normal loading (the paper’s Test I): this repo’s quantum and classical solvers both track the paper’s published iteration history.

Stressed loading (the paper’s Test II): solid lines are this repo’s classical solver, dashed lines the quantum solver; both converge to the same endpoint near the solvability boundary. This reproduction converges in 32 updates where the paper reports 34; the difference is analyzed in docs/reconstruction_notes.md.

5,000 random loading scenarios with correlated Gaussian injections (the paper’s stochastic experiment), solved with the quantum solver.

Machine-readable metrics are in results/diagnostics/reproduction_metrics.json. Assumptions, reconstructed parameters, and every difference from the paper: docs/reconstruction_notes.md and docs/limitations_and_interpretation.md.

Each fast-decoupled iteration writes the state update as two constant-matrix linear systems, B′(VΔθ) = ΔP/V and B″ΔV = ΔQ/V, and hands them to a custom HHL solver. The reduced matrices are iteration-independent, so the expensive circuit parts, phase estimation and the reciprocal rotation, are built once and reused across iterations.

flowchart TD
    A["AC mismatch: ΔP, ΔQ at current V, θ"] --> B["Right-hand sides ΔP/V, ΔQ/V"]
    B --> C["Amplitude-encode b"]
    C --> D["Quantum phase estimation on fixed B′ / B″"]
    D --> E["Controlled reciprocal rotation"]
    E --> F["Inverse QPE + ancilla postselection"]
    F --> G["Classical scale and sign recovery"]
    G --> H["Update V, θ"]
    H --> I{"Converged?"}
    I -->|no| A
    I -->|yes| J["Voltages, angles, branch flows"]
    R["Built once, reused across iterations"] -.-> D
    R -.-> E

Equation-by-equation map from the paper to the code: docs/algorithm_mapping.md.

Python 3.10–3.13 is supported. The archived reproduction used Python 3.13.5, Qiskit 2.5.0, and Qiskit Aer 0.17.2.

git clone https://github.com/TravisCao/quantum-power-flow.git
cd quantum-power-flow

python -m venv .venv
source .venv/bin/activate                 # Windows: .venv\Scripts\activate
python -m pip install --upgrade pip
python -m pip install -e '.[dev]'

Reproduce every experiment (deterministic, stressed, precision-ablation, and stochastic) and write figures, tables, and diagnostics under results/:

qpf-reproduce all --output results

Equivalent script entry point: python scripts/reproduce_all.py. The omitted-line-parameter inference can be repeated independently with python scripts/infer_missing_line_data.py.

Run the verification suite:

ruff check src tests scripts
pytest -q

The primary assumptions are exposed in configs/paper_case5.yaml, including:

• five-bus topology and bus injections;
• slack-bus voltage;
• reconstructed common branch impedance;
• convergence tolerance;
• four-qubit phase register and phase scale;
• stochastic sample count, seed, target correlation, and marginal standard deviation.

The stressed operating case is defined separately in configs/stressed_case5.yaml.

quantum-power-flow/
├── configs/                  # Normal and stressed five-bus cases
├── docs/                     # Algorithm mapping, reconstruction, limitations
├── notebooks/                # Guided paper-reproduction notebook
├── paper/                    # Citation and links to the original article
├── results/
│   ├── diagnostics/          # Circuit statistics and machine-readable metrics
│   ├── figures/              # Reproduced plots (committed; regenerated by the CLI)
│   └── tables/               # Iteration traces and Monte Carlo samples
├── scripts/                  # Reproduction and parameter-inference entry points
├── src/qpf_repro/
│   ├── quantum/hhl.py        # Custom modern-Qiskit HHL implementation
│   ├── powerflow.py          # Fast-decoupled and Newton–Raphson solvers
│   ├── network.py            # Y-bus, injections, line flows, B′/B″ matrices
│   ├── stochastic.py         # Correlated stochastic power flow
│   └── experiments/          # End-to-end paper experiment runner
└── tests/                    # Physics, circuit, and regression tests

notebooks/reproduce_paper.ipynb is a guided lab designed for students without prior quantum-computing or linear-algebra experience: the five-bus application, classical and HHL-simulation comparisons, demand and quantum-precision controls, and the constructed Qiskit circuit.

uv pip install --python .venv/bin/python -e '.[notebook]'
.venv/bin/jupyter lab notebooks/reproduce_paper.ipynb

Reproduction corrections, numerical cross-checks, and alternative quantum linear-system backends are welcome. Please read CONTRIBUTING.md before opening a pull request.

The implementation is released under the MIT License. The original paper remains subject to its authors’ and publisher’s terms; its PDF is linked rather than redistributed.