量子退火法线性方程求解算法的收敛率

Pub Date : 2024-06-13 DOI:10.1134/s0965542524700325

S. B. Tikhomirov, V. S. Shalgin

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引用次数: 0

摘要

摘要研究了利用量子计算机按照量子退火原理求解线性方程 \(ax = b\) 的各种迭代算法。假定计算机产生的结果由玻尔兹曼分布描述，得到了这些算法收敛的条件，并对其收敛速率进行了估计。研究还考虑了这种方法在使用无限量量子比特和少量量子比特的算法中的应用。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

Convergence Rate of Algorithm for Solving Linear Equations by Quantum Annealing

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Convergence Rate of Algorithm for Solving Linear Equations by Quantum Annealing

Abstract

Various iterative algorithms for solving the linear equation \(ax = b\) using a quantum computer operating on the principle of quantum annealing are studied. Assuming that the result produced by the computer is described by the Boltzmann distribution, conditions under which these algorithms converge are obtained and an estimate of their convergence rate is provided. Application of this approach for algorithms that use an infinite number of qubits and a small number of qubits is considered.

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