A Faster Quantum Algorithm for Semidefinite Programming via Robust IPM Framework

• URL: http://arxiv.org/abs/2207.11154v1
• Date: Fri, 22 Jul 2022 15:51:02 GMT
• Title: A Faster Quantum Algorithm for Semidefinite Programming via Robust IPM Framework
• Authors: Baihe Huang, Shunhua Jiang, Zhao Song, Runzhou Tao, Ruizhe Zhang
• Abstract summary: This paper studies a fundamental problem in convex optimization, which is to solve semidefinite programming (SDP) with high accuracy. We give a quantum second-order algorithm with high-accuracy in both the optimality and the feasibility of its output.
• Score: 14.531920189937495
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: This paper studies a fundamental problem in convex optimization, which is to solve semidefinite programming (SDP) with high accuracy. This paper follows from 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 $\log(1/\epsilon)$ 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.

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