A comprehensive benchmark of an Ising machine on the Max-Cut problem

TL;DR

This paper benchmarks Fujitsu's Digital Annealer on large-scale Max-Cut problems formulated as QUBO, comparing its performance with other heuristics and quantum-classical approaches, demonstrating its competitiveness in solving large instances.

Contribution

It provides a comprehensive performance comparison of the Digital Annealer against other heuristics and quantum approaches on large Max-Cut QUBO instances.

Findings

Digital Annealer performs competitively on large graphs.

The benchmark includes over 2,000 graphs from MQLib.

Results show the extent of heuristic solutions for large QUBO problems.

Abstract

QUBO formulations of combinatorial optimization problems allow for solving them using various quantum heuristics. While large-scale quantum computations are currently still out of reach, we can already numerically test such QUBO formulations on a perhaps surprisingly large scale. In this work, we benchmark Fujitsu's Digital Annealer (DA) on the Max-Cut problem, which captures the main complexity of the QUBO problem. We make a comprehensive benchmark against leading other heuristic algorithms on graphs with up to 53,000 variables by focusing on the wall-clock time. Moreover, we compare the DA performance against published performance results of the D-Wave hybrid quantum-classical annealer and the recently proposed QIS3 heuristic. Based on performance statistics for over 2,000 graphs from the MQLib, we find that the DA yields competitive results. We hope that this benchmark demonstrates the extent to which large QUBO instances can be heuristically solved today, yielding consistent results across different solvers.