A Benchmarking Study of Quantum Algorithms for Combinatorial Optimization

• URL: http://arxiv.org/abs/2105.03528v2
• Date: Fri, 17 Jan 2025 06:08:17 GMT
• Title: A Benchmarking Study of Quantum Algorithms for Combinatorial Optimization
• Authors: Krishanu Sankar, Artur Scherer, Satoshi Kako, Sam Reifenstein, Navid Ghadermarzy, Willem B. Krayenhoff, Yoshitaka Inui, Edwin Ng, Tatsuhiro Onodera, Pooya Ronagh, Yoshihisa Yamamoto,
• Abstract summary: We study the performance scaling of three quantum algorithms for optimization: measurement-feedback coherent Ising machines (MFB-CIM), discrete adiabatic quantum computation (DAQC), and the D"urr-Hoyer algorithm for quantum minimum finding (DH-QMF) 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.
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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 D\"urr-Hoyer 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 $\widetilde{O}\left(\sqrt{2^n}\right)$ scaling for DH-QMF. We conclude that the MFB-CIM outperforms DAQC and DH-QMF in solving MaxCut problems.

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