Benchmarking Quantum Annealing Against “Hard” Instances of the Bipartite Matching Problem

This paper experimentally investigates the behavior of analog quantum computers as commercialized by D-Wave when confronted to instances of the maximum cardinality matching problem which is specifically designed to be hard to solve by means of simulated annealing. We benchmark a D-Wave “Washington” (2X) with 1098 operational qubits on various sizes of such instances and observe that for all but the most trivially small of these it fails to obtain an optimal solution. Thus, our results suggest that quantum annealing, at least as implemented in a D-Wave device, falls in the same pitfalls as simulated annealing and hence provides additional evidences suggesting that there exist polynomial-time problems that such a machine cannot solve efficiently to optimality. Additionally, we investigate the extent to which the qubits interconnection topologies explains these latter experimental results. In particular, we provide evidences that the sparsity of these topologies which, as such, lead to QUBO problems of artificially inflated sizes can partly explain the aforementioned disappointing observations. Therefore, this paper hints that denser interconnection topologies are necessary to unleash the potential of the quantum annealing approach.