Optimal power flow solution via noise-resilient quantum interior-point methods

Abstract

This paper presents quantum interior-point methods (QIPMs) tailored to tackle the DC optimal power flow (OPF) 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, we utilized a noise-tolerant quantum IPM. This approach provides high-quality OPF solutions even in scenarios where inexact solutions to the linear equation systems result in approximated Newton’s direction. To enhance performance in cases of slow convergence and uphold the feasibility of OPF upon convergence, we propose a classically augmented noise-tolerant QIPM. This technique is designed to expedite convergence relative to classical IPM while maintaining the accuracy of the solution. The proposed QIPM variants are studied through comprehensive simulations and error analyses on 3-bus, 5-bus, 118-bus, and 300-bus systems. By modeling the errors and incorporating quantum computer noise, we simulate the algorithms on Qiskit and classical computers to better understand their effectiveness and feasibility under realistic conditions.