A preconditioned inexact infeasible quantum interior point method for linear optimization

TL;DR

This paper introduces a preconditioned inexact infeasible quantum interior point method that improves the conditioning of linear systems in quantum optimization, leading to faster and more accurate solutions for linear programming.

Contribution

It develops a novel preconditioning technique for quantum interior point methods, reducing the condition number dependence from quadratic to linear in the duality gap.

Findings

Improved condition number dependence from quadratic to linear.

Enhanced accuracy dependence compared to existing methods.

Better scalability with problem dimension.

Abstract

Quantum Interior Point Methods (QIPMs) have been attracting significant interests recently due to their potential of solving optimization problems substantially faster than state-of-the-art conventional algorithms. In general, QIPMs use Quantum Linear System Algorithms (QLSAs) to substitute classical linear system solvers. However, the performance of QLSAs depends on the condition numbers of the linear systems, which are typically proportional to the square of the reciprocal of the duality gap in QIPMs. To improve conditioning, a preconditioned inexact infeasible QIPM (II-QIPM) based on optimal partition estimation is developed in this work. We improve the condition number of the linear systems in II-QIPMs from quadratic dependence on the reciprocal of the duality gap to linear, and obtain better dependence with respect to the accuracy when compared to other II-QIPMs. Our method also attains better dependence with respect to the dimension when compared to other inexact infeasible Interior Point Methods.