An introduction to variational quantum algorithms for combinatorial optimization problems

IF 4.4 3区 管理学 Q1 OPERATIONS RESEARCH & MANAGEMENT SCIENCE Annals of Operations Research Pub Date : 2024-09-13 DOI:10.1007/s10479-024-06253-5
Camille Grange, Michael Poss, Eric Bourreau
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Abstract

Noisy intermediate-scale quantum computers are now readily available, motivating many researchers to experiment with Variational Quantum Algorithms. Among them, the Quantum Approximate Optimization Algorithm is one of the most popular one studied by the combinatorial optimization community. In this tutorial, we provide a mathematical description of the class of Variational Quantum Algorithms, assuming no previous knowledge of quantum physics from the readers. We introduce precisely the key aspects of these hybrid algorithms on the quantum side (parametrized quantum circuit) and the classical side (guiding function, optimizer). We devote a particular attention to QAOA, detailing the quantum circuits involved in that algorithm, as well as the properties satisfied by its possible guiding functions. Finally, we discuss the recent literature on QAOA, highlighting several research trends.

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组合优化问题的变分量子算法简介
目前,噪声中等规模的量子计算机已经很容易获得,这促使许多研究人员开始尝试变量子算法。其中,量子近似优化算法是组合优化领域研究的最热门算法之一。在本教程中,我们假定读者不具备量子物理知识,对变量量子算法类进行了数学描述。我们将精确介绍这些混合算法在量子侧(参数化量子电路)和经典侧(引导函数、优化器)的关键方面。我们特别关注 QAOA,详细介绍了该算法所涉及的量子电路,以及其可能的指导函数所满足的特性。最后,我们讨论了有关 QAOA 的最新文献,强调了几个研究趋势。
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来源期刊
Annals of Operations Research
Annals of Operations Research 管理科学-运筹学与管理科学
CiteScore
7.90
自引率
16.70%
发文量
596
审稿时长
8.4 months
期刊介绍: The Annals of Operations Research publishes peer-reviewed original articles dealing with key aspects of operations research, including theory, practice, and computation. The journal publishes full-length research articles, short notes, expositions and surveys, reports on computational studies, and case studies that present new and innovative practical applications. In addition to regular issues, the journal publishes periodic special volumes that focus on defined fields of operations research, ranging from the highly theoretical to the algorithmic and the applied. These volumes have one or more Guest Editors who are responsible for collecting the papers and overseeing the refereeing process.
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