Solving Conic Programs over Sparse Graphs using a Variational Quantum Approach: The Case of the AC Optimal Power Flow

arXiv:2509.00341 · eess.SY, cs.LG, cs.SY, math.OC, quant-ph · Submitted 2025-08-30 · Read on arXiv

eess.SY, cs.LG, cs.SY, math.OC, quant-ph

Submitted: 2025-08-30

Updated: 2026-09-15

Comments: 21 pages, 7 figures, 2 tables, accepted for publication in Physical Review A (2026)

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Terminology

• Sparsity — 17× in this paper · explained in 4 episodes
• Benchmark — 4× in this paper · explained in 2 episodes
• Objective Function — 3× in this paper · explained in 2 episodes
• Quantum Circuits — 2× in this paper · explained in 2 episodes
• Robustness — 2× in this paper · explained in 5 episodes
• Verification — 2× in this paper · explained in 2 episodes
• Activation Function — 1× in this paper · explained in 1 episode
• Alignment — 1× in this paper · explained in 1 episode
• Application to the Optimal Power Flow — 1× in this paper
• Benchmarking — 1× in this paper · explained in 3 episodes
• Curse of Dimensionality — 1× in this paper · explained in 6 episodes
• Higher-order derivatives — 1× in this paper · explained in 2 episodes
• Physical Constraints — 1× in this paper · explained in 7 episodes
• Sample Complexity — 1× in this paper · explained in 15 episodes
• Variational Quantum Eigensolver (VQE) — 1× in this paper · explained in 5 episodes

Sources

• A Quantum Approximate Optimization Algorithm
• Quantum Computing for Power Flow Algorithms: Testing on real Quantum Computers
• Advancing Hybrid Quantum Neural Network for Alternative Current Optimal Power Flow
• Dynamic parameterized quantum circuits: expressive and barren-plateau free
• Quantum Recurrent Embedding Neural Network
• The Power Grid Library for Benchmarking AC Optimal Power Flow Algorithms
• PennyLane: Automatic differentiation of hybrid quantum-classical computations
• Handbook of Convergence Theorems for (Stochastic) Gradient Methods

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