A Benchmarking Study of Quantum Algorithms for Combinatorial Optimization

TL;DR

This study compares three quantum algorithms for combinatorial optimization, finding that measurement-feedback coherent Ising machines (MFB-CIM) outperform others in solving MaxCut problems, with better scaling and practical performance.

Contribution

The paper provides an empirical benchmarking of MFB-CIM, DAQC, and DH-QMF algorithms on MaxCut problems, highlighting the superior performance of MFB-CIM.

Findings

MFB-CIM shows significant performance advantage over DAQC and DH-QMF.

MFB-CIM exhibits sub-exponential scaling in median TTS.

DAQC and DH-QMF scale almost exponentially and as square root of 2^n, respectively.

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.