  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.
