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

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.