Speedup of high-order unconstrained binary optimization using quantum Z2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}

Abstract

An important and difficult problem in optimization is the high-order unconstrained binary optimization, which can represent many optimization problems more efficiently than quadratic unconstrained binary optimization, but how to quickly solve it has remained difficult. Here, we present an approach by mapping the high-order unconstrained binary optimization to quantum Z2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\mathbb{Z}}}_{2}$$\end{document} lattice gauge theory and propose the gauged local quantum annealing, which is the local quantum annealing protected by the gauge symmetry. We present the quantum algorithm and its corresponding quantum-inspired classical algorithm for this problem and achieve algorithmic speedup by using gauge symmetry. By running the quantum-inspired classical algorithm, we demonstrate that the gauged local quantum annealing reduces the computational time by one order of magnitude from that of the local quantum annealing. The authors propose a quantum annealing scheme for solving a higher-order unconstrained binary optimization problem by mapping it to a quantum Z2 lattice gauge theory on a dual graph. This scheme is shown to achieve a speed-up of at least one order of magnitude in finding the ground state compared to other methods.