Benchmark Study of Quantum Algorithms for Combinatorial Optimization: Unitary versus Dissipative

• URL: http://arxiv.org/abs/2105.03528v1
• Date: Fri, 7 May 2021 22:35:02 GMT
• Title: Benchmark Study of Quantum Algorithms for Combinatorial Optimization: Unitary versus Dissipative
• Authors: Krishanu Sankar, Artur Scherer, Satoshi Kako, Sam Reifenstein, Navid Ghadermarzy, Willem B. Krayenhoff, Yoshitaka Inui, Edwin Ng, Tatsuhiro Onodera, Pooya Ronagh, and Yoshihisa Yamamoto
• Abstract summary: We study the performance scaling of three quantum algorithms for optimization. MFB-CIM, discrete adiabatic quantum computation (DAQC), and the D"urr-Hoyer algorithm for quantum minimum finding (DH-QMF)
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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 our reference for comparison, and time-to-solution (TTS) as a practical measure of performance for these optimization algorithms. We empirically observe a $\Theta(2^{\sqrt{n}})$ scaling for the median TTS for MFB-CIM, in comparison to the exponential scaling with the exponent $n$ for DAQC and the provable $\widetilde{\mathcal O}\left(\sqrt{2^n}\right)$ scaling for DH-QMF. We conclude that these scaling complexities result in a dramatic performance advantage for MFB-CIM in comparison to the other two algorithms for solving MaxCut problems.

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