Quantum Algorithms for Optimal Power Flow
Sajad Fathi Hafshejani, Md Mohsin Uddin, David Neufeld, Daya Gaur, Robert Benkoczi
TL;DR
The paper investigates quantum approaches to Optimal Power Flow (OPF) by embedding HHL and VQLS into a Step-Controlled Primal-Dual Interior Point Method (SC-PDIPM) and using left preconditioning to manage ill-conditioning. The methods are evaluated on small MATPOWER DC-OPF and AC-OPF cases, showing that quantum solvers can achieve solutions of comparable quality to classical solvers, with preconditioning mitigating growth in the condition number and reducing iterations. The results highlight potential quantum advantages in OPF when combined with classical preconditioning, though practical scalability is limited by current qubit counts and numerical stability. The work provides a concrete hybrid framework and points to hardware-based validation and scaling as key future steps, including exploring more efficient quantum preconditioners and larger power-system benchmarks. It leverages the linear-system structure $A x = b$ inherent in OPF subproblems, noting the complexity of HHL scales as $\tilde{O}(\log(N) s^{2} \kappa^{2} / \epsilon)$ and that VQLS can be trained to approximate the same solution within the quantum-classical loop.
Abstract
This paper explores the use of quantum computing, specifically the use of HHL and VQLS algorithms, to solve optimal power flow problem in electrical grids. We investigate the effectiveness of these quantum algorithms in comparison to classical methods. The simulation results presented here which substantially improve the results in [1] indicate that quantum approaches yield similar solutions and optimal costs compared to classical methods, suggesting the potential use case of quantum computing for power system optimization.