Optimal Power Flow Solutions via Noise-Resilient Quantum-Inspired Interior-Point Methods

Abstract: This paper presents three quantum interior-point methods (QIPMs) tailored to tackle the DC optimal power flow (DCOPF) problem using noisy intermediate-scale quantum devices. The optimization model is redefined as a linearly constrained quadratic optimization. By incorporating the Harrow-Hassidim-Lloyd (HHL) quantum algorithm into the IPM framework, Newton's direction is determined through the resolution of linear equation systems. To mitigate the impact of HHL error and quantum noise on Newton's direction calculation, we present a noise-tolerant quantum IPM (NT-QIPM) approach. This approach provides high-quality OPF solutions even in scenarios where inexact solutions to the linear equation systems result in approximated Newton's directions. Moreover, to enhance performance in cases of slow convergence and uphold the feasibility of OPF outcomes upon convergence, we propose a hybrid strategy, classically augmented NT-QIPM. This technique is designed to expedite convergence relative to classical IPM while maintaining the solution accuracy. The efficacy of the proposed quantum IPM variants is studied through comprehensive simulations and error analyses on 3-bus, 5-bus, 118-bus, and 300-bus systems, highlighting their potential and promise in addressing challenging OPF scenarios. By modeling the errors and incorporating quantum computer noise, we simulate the proposed algorithms on both Qiskit and classical computers to gain a deeper understanding of the effectiveness and feasibility of our methods under realistic conditions.