Quantum Optimization for Optimal Power Flow: CVQLS-Augmented Interior Point Method

Abstract

This paper presents a quantum-enhanced optimization approach for solving optimal power flow (OPF) by integrating the interior point method (IPM) with a coherent variational quantum linear solver (CVQLS). The objective is to explore the applicability of quantum computing to power systems optimization and address the associated challenges. A comparative analysis of state-of-the-art quantum linear solvers - Harrow-Hassidim-Lloyd (HHL), variational quantum linear solver (VQLS), and CVQLS - revealed that CVQLS is most suitable for OPF due to its stability with ill-conditioned matrices, such as the Hessian in IPM. To ensure high-quality solutions, prevent suboptimal convergence, and avoid the barren plateau problem, we propose a quantum circuit parameter initialization technique along with a method to guide the IPM along the central path. Moreover, we design an ansatz tailored for OPF, optimizing the expressibility and trainability of the quantum circuit to ensure efficient convergence and robustness in solving quantum OPF. Various optimizers are also tested for quantum circuit parameter optimization to select the best one. We evaluate our approaches on multiple systems to show their effectiveness in providing reliable OPF solutions. Simulations for the 2-bus system are conducted on a commercial IBMQ quantum device, while simulations for the other larger cases are performed using the IBM quantum simulator. While promising, CVQLS is limited by current quantum hardware, especially for larger systems. We use a quantum noise simulator to test scalability.