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Quantum computing has attracted significant interest in the optimizationcommunity because it potentially can solve classes of optimization problemsfaster than conventional supercomputers. Several researchers proposed quantumcomputing methods, especially Quantum Interior Point Methods (QIPMs), to solveconvex optimization problems, such as Linear Optimization, SemidefiniteOptimization, and Second-order Cone Optimization problems. Most of them haveapplied a Quantum Linear System Algorithm at each iteration to compute a Newtonstep. However, using quantum linear solvers in QIPMs comes with manychallenges, such as having ill-conditioned systems and the considerable errorof quantum solvers. This paper investigates how one can efficiently use quantumlinear solvers in QIPMs. Accordingly, an Inexact Infeasible Quantum InteriorPoint Method is developed to solve linear optimization problems. We alsodiscuss how can we get an exact solution by Iterative Refinement withoutexcessive time of quantum solvers. Finally, computational results with QISKITimplementation of our QIPM using quantum simulators are analyzed.

Efficient Use of Quantum Linear System Algorithms in Interior Point Methods for Linear Optimization