A benchmarking study of quantum algorithms for combinatorial optimization

IF 6.6 1区物理与天体物理 Q1 PHYSICS, APPLIED

npj Quantum Information Pub Date : 2024-06-22 DOI:10.1038/s41534-024-00856-3

Krishanu Sankar, Artur Scherer, Satoshi Kako, Sam Reifenstein, Navid Ghadermarzy, Willem B. Krayenhoff, Yoshitaka Inui, Edwin Ng, Tatsuhiro Onodera, Pooya Ronagh, Yoshihisa Yamamoto

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Abstract

We study the performance scaling of three quantum algorithms for combinatorial optimization: measurement-feedback coherent Ising machines (MFB-CIM), discrete adiabatic quantum computation (DAQC), and the Dürr–Høyer algorithm for quantum minimum finding (DH-QMF) that is based on Grover’s search. We use MaxCut problems as a reference for comparison, and time-to-solution (TTS) as a practical measure of performance for these optimization algorithms. For each algorithm, we analyze its performance in solving two types of MaxCut problems: weighted graph instances with randomly generated edge weights attaining 21 equidistant values from −1 to 1; and randomly generated Sherrington–Kirkpatrick (SK) spin glass instances. We empirically find a significant performance advantage for the studied MFB-CIM in comparison to the other two algorithms. We empirically observe a sub-exponential scaling for the median TTS for the MFB-CIM, in comparison to the almost exponential scaling for DAQC and the proven \(\widetilde{{{{\mathcal{O}}}}}\left(\sqrt{{2}^{n}}\right)\) scaling for DH-QMF. We conclude that the MFB-CIM outperforms DAQC and DH-QMF in solving MaxCut problems.

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组合优化量子算法基准研究

我们研究了三种用于组合优化的量子算法的性能缩放：测量反馈相干伊辛机（MFB-CIM）、离散绝热量子计算（DAQC）以及基于格罗弗搜索的量子最小值查找杜尔-霍耶算法（DH-QMF）。我们将 MaxCut 问题作为比较的参考，并将求解时间（TTS）作为衡量这些优化算法性能的实用指标。对于每种算法，我们都分析了其在解决两类 MaxCut 问题时的性能：加权图实例，随机生成的边权重达到 21 个从 -1 到 1 的等距值；以及随机生成的 Sherrington-Kirkpatrick（SK）旋转玻璃实例。我们根据经验发现，与其他两种算法相比，所研究的 MFB-CIM 具有显著的性能优势。我们根据经验观察到，MFB-CIM 的中位 TTS 呈亚指数缩放，而 DAQC 几乎呈指数缩放，DH-QMF 则呈已证实的 \(\widetilde{{{{\mathcal{O}}}}}\left(\sqrt{2}^{n}\}right)\) 缩放。我们的结论是，在解决 MaxCut 问题时，MFB-CIM 的性能优于 DAQC 和 DH-QMF。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

npj Quantum Information Computer Science-Computer Science (miscellaneous)

CiteScore

13.70

自引率

3.90%

发文量

130

审稿时长

29 weeks

期刊介绍： The scope of npj Quantum Information spans across all relevant disciplines, fields, approaches and levels and so considers outstanding work ranging from fundamental research to applications and technologies.