A preconditioned inexact infeasible quantum interior point method for linear optimization
提出一种基于最优分割估计的预条件非精确不可行量子内点法，将线性系统条件数对对偶间隙倒数的依赖从二次降至线性，在精度和维度上优于其他同类方法。
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.