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.

我们研究了用于组合优化的三种量子算法的性能扩展：测量反馈相干伊辛机 (MFB-CIM)、离散绝热量子计算 (DAQC) 和用于量子最小值发现的 Dürr–Høyer 算法 (DH-QMF)，即基于格罗弗的搜索。我们使用 MaxCut 问题作为比较的参考，并使用解决时间 (TTS) 作为这些优化算法性能的实际衡量标准。对于每种算法，我们分析其在解决两类 MaxCut 问题中的性能：具有随机生成的边权重的加权图实例，获得从 -1 到 1 的 21 个等距值；以及随机生成的 Sherrington–Kirkpatrick (SK) 自旋玻璃实例。我们凭经验发现，与其他两种算法相比，所研究的 MFB-CIM 具有显着的性能优势。与 DAQC 的近指数缩放和经过验证的 \(\widetilde{{{{\mathcal{O}}}}}\left( \sqrt{{2}^{n}}\right)\) DH-QMF 的缩放。我们得出的结论是，MFB-CIM 在解决 MaxCut 问题方面优于 DAQC 和 DH-QMF。