QuantumGrid — Quantum-Classical Hybrid for Energy Optimization

Unit commitment — scheduling power generators on/off to meet demand at minimum cost — is NP-hard and central to grid operations. Quantum optimization (QAOA, VQE) offers a potential path for combinatorial problems of this type. This project implements both quantum and classical solvers on the same real-data instances, providing an honest assessment of where quantum approaches currently stand and where they break down.

PennyLane QAOA VQE Google OR-Tools ENTSO-E API PyTorch

Key questions this project answers

At what problem size does QAOA/VQE match classical MILP quality?
How does solution quality degrade as generators exceed simulator qubit capacity?
What's the optimization landscape? (convergence, local minima)
How sensitive is QUBO performance to constraint penalty weights?
Can VQE capture continuous OPF better than discretized QAOA?

Technical approach

Data: Real load and generation data from ENTSO-E Transparency Platform (France/Germany, hourly resolution, 1 year).
QUBO encoding: Unit commitment binary decisions encoded as Ising Hamiltonian. Constraints embedded as quadratic penalty terms.
QAOA: p-layer alternating cost/mixer unitaries optimized with COBYLA. PennyLane default.qubit simulator.
VQE: Hardware-efficient ansatz with Ry/Rz rotations + CNOT entanglement for continuous OPF relaxation.
Classical baselines: MILP via OR-Tools (exact), simulated annealing (heuristic), greedy priority list (fast heuristic).
Scaling study: N = 4 to 20 generators, T = 6 to 48 hours, QAOA layers p = 1 to 5.

Scaling benchmarks

All solvers run on the same problem instances derived from ENTSO-E data.

Problem size	MILP (exact)	Sim. Annealing	QAOA	VQE
4 gen, 6h	—	—	—	—
8 gen, 12h	—	—	—	—
12 gen, 24h	—	—	—	—
16 gen, 24h	—	—	—	N/A
20 gen, 48h	—	—	N/A	N/A

Cost in $/MWh. N/A = exceeds simulator capacity. Results from real benchmark runs.

QAOA circuit structure

Python · PennyLane QAOA cost layer

@qml.qnode(dev)
def qaoa_circuit(gammas, betas, cost_h, n_layers):
    # Equal superposition
    for i in range(n_qubits):
        qml.Hadamard(wires=i)

    # Alternating cost + mixer layers
    for p in range(n_layers):
        qml.ApproxTimeEvolution(cost_h, gammas[p], 1)
        for i in range(n_qubits):
            qml.RX(2 * betas[p], wires=i)

    return qml.expval(cost_h)

System diagram

flowchart TB Data["ENTSO-E Grid Data
Load, generation, costs"] --> UC["Unit Commitment
MILP formulation"] UC --> QUBO["QUBO Encoding
Binary → Ising Hamiltonian"] QUBO --> QAOA["QAOA Solver
PennyLane circuit"] QUBO --> VQE["VQE Solver
Variational ansatz"] UC --> MILP["MILP Solver
OR-Tools (exact)"] UC --> SA["Simulated Annealing
Classical heuristic"] QAOA --> Compare["Benchmark
Cost, time, quality"] VQE --> Compare MILP --> Compare SA --> Compare style QAOA fill:#eff6ff,stroke:#2563eb,color:#0f172a style VQE fill:#eff6ff,stroke:#2563eb,color:#0f172a style MILP fill:#eff6ff,stroke:#2563eb,color:#0f172a style SA fill:#eff6ff,stroke:#2563eb,color:#0f172a