Benchmarking D-Wave Quantum Annealers: Spectral Gap Scaling of Maximum Cardinality Matching Problems

Quantum computing, in particular Quantum Annealing (QA), provides a theoretically promising alternative to classical methods for solving combinatorially difficult optimization problems. In particular, QA is suitable for problems that can be formulated as a Quadratic Unconstrained Binary Optimization (QUBO) problem, such as SAT, graph colouring and travelling salesman. With commercially available QA hardware, like that offered by D-Wave Systems (D-Wave), reaching scales capable of tackling real world problems, it is timely to assess and benchmark the performance of this current generation of hardware. This paper empirically investigates the performance of D-Wave’s 2000Q (2048 qubits) and Advantage (5640 qubits) quantum annealers in solving a specific instance of the maximum cardinality matching problem, building on the results of a prior paper that investigated the performance of earlier QA hardware from D-Wave. We find that the Advantage quantum annealer is able to produce optimal solutions to larger problem instances than the 2000Q. We further consider the problem’s structure and its implications for suitability to QA by utilising the Landau-Zener formula to explore the potential scaling of the diabatic transition probability. We propose a method to investigate the behaviour of minimum energy gaps for scalable problems deployed to quantum annealers. We find that the minimum energy gap for our target QA problem does not scale favourably. This behaviour raises questions as to the suitability of this problem for benchmarking QA hardware, as it potentially lacks the nuance required to identify meaningful performance improvements between generations.