Accuracy and Performance Evaluation of Quantum, Classical and Hybrid Solvers for the Max-Cut Problem

TL;DR

This study compares quantum, classical, and hybrid solvers for the Max-Cut problem, showing that hybrid and classical methods often outperform quantum approaches in solution quality and efficiency, especially for larger instances.

Contribution

It provides a comprehensive benchmark of quantum, classical, and hybrid solvers on Max-Cut instances, highlighting their relative strengths and weaknesses across different problem sizes.

Findings

Hybrid solver and SA achieve global optima on small instances.

SBM and slower SA perform well on larger, unknown instances.

Hybrid and SBM offer efficient computation times.

Abstract

This paper investigates the performance of quantum, classical, and hybrid solvers on the NP-hard Max-Cut and QUBO problems, examining their solution quality relative to the global optima and their computational efficiency. We benchmark the new fast annealing D-Wave quantum processing unit (QPU) and D-Wave Hybrid solver against the state-of-the-art classical simulated annealing algorithm (SA) and Toshiba's simulated bifurcation machine (SBM). Our study leverages three datasets encompassing 139 instances of the Max-Cut problem with sizes ranging from 100 to 10,000 nodes. For instances below 251 nodes, global optima are known and reported, while for larger instances, we utilize the best-known solutions from the literature. Our findings reveal that for the smaller instances where the global optimum is known, the Hybrid solver and SA algorithm consistently achieve the global optimum, outperforming the QPU. For larger instances where global optima are unknown, we observe that the SBM and the slower variant of SA deliver competitive solution quality, while the Hybrid solver and the faster variant of SA performed noticeably worse. Although computing time varies due to differing underlying hardware, the Hybrid solver and the SBM demonstrate both efficient computation times, while for SA reduction in computation time can be achieved at the expense of solution quality.