English

A Faster Quantum Algorithm for Semidefinite Programming via Robust IPM Framework

Quantum Physics 2023-02-08 v2

Abstract

This paper studies a fundamental problem in convex optimization, which is to solve semidefinite programming (SDP) with high accuracy. This paper follows from the existing robust SDP-based interior point method analysis due to [Huang, Jiang, Song, Tao and Zhang, FOCS 2022]. While, the previous work only provides an efficient implementation in the classical setting. This work provides a novel quantum implementation. We give a quantum second-order algorithm with high-accuracy in both the optimality and the feasibility of its output, and its running time depending on log(1/ϵ)\log(1/\epsilon) on well-conditioned instances. Due to the limitation of quantum itself or first-order method, all the existing quantum SDP solvers either have polynomial error dependence or low-accuracy in the feasibility.

Keywords

Cite

@article{arxiv.2207.11154,
  title  = {A Faster Quantum Algorithm for Semidefinite Programming via Robust IPM Framework},
  author = {Baihe Huang and Shunhua Jiang and Zhao Song and Runzhou Tao and Ruizhe Zhang},
  journal= {arXiv preprint arXiv:2207.11154},
  year   = {2023}
}