具有最优查询复杂度的定点量子连续搜索算法

IF 6.4 1区 物理与天体物理 Q1 PHYSICS, MULTIDISCIPLINARY
Shan Jin, Yuhan Huang, Shaojun Wu, Guanyu Zhou, Chang-Ling Zou, Luyan Sun, Xiaoting Wang
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引用次数: 0

摘要

连续搜索问题(Continuous search problem, csp)涉及在连续域中寻找解决方案,经常出现在优化、物理和工程等领域。与离散搜索问题不同,csp需要在无限空间中导航,这给计算带来了独特的挑战。在这项工作中,我们提出了一种利用连续变量来解决这些挑战的定点量子搜索算法,实现了二次加速。受离散搜索结果的启发,我们设法建立了任意量子搜索csp查询复杂性的下界,证明了我们的方法的最优性。此外,我们还演示了如何针对特定问题设计量子搜索oracle的内部结构。此外,我们开发了一个通用框架,将该算法应用于一系列问题类型,包括涉及连续变量的优化和特征值问题。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Fixed-point quantum continuous search algorithm with optimal query complexity

Continuous search problems (CSPs), which involve finding solutions within a continuous domain, frequently arise in fields such as optimization, physics, and engineering. Unlike discrete search problems, CSPs require navigating an uncountably infinite space, presenting unique computational challenges. In this work, we propose a fixed-point quantum search algorithm that leverages continuous variables to address these challenges, achieving a quadratic speedup. Inspired by the discrete search results, we manage to establish a lower bound on the query complexity of arbitrary quantum search for CSPs, demonstrating the optimality of our approach. In addition, we demonstrate how to design the internal structure of the quantum search oracle for specific problems. Furthermore, we develop a general framework to apply this algorithm to a range of problem types, including optimization and eigenvalue problems involving continuous variables.

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来源期刊
Science China Physics, Mechanics & Astronomy
Science China Physics, Mechanics & Astronomy PHYSICS, MULTIDISCIPLINARY-
CiteScore
10.30
自引率
6.20%
发文量
4047
审稿时长
3 months
期刊介绍: Science China Physics, Mechanics & Astronomy, an academic journal cosponsored by the Chinese Academy of Sciences and the National Natural Science Foundation of China, and published by Science China Press, is committed to publishing high-quality, original results in both basic and applied research. Science China Physics, Mechanics & Astronomy, is published in both print and electronic forms. It is indexed by Science Citation Index. Categories of articles: Reviews summarize representative results and achievements in a particular topic or an area, comment on the current state of research, and advise on the research directions. The author’s own opinion and related discussion is requested. Research papers report on important original results in all areas of physics, mechanics and astronomy. Brief reports present short reports in a timely manner of the latest important results.
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