Revisiting old combinatorial beasts in the quantum age: quantum annealing versus maximal matching

Abstract: This paper experimentally investigates the behavior of analog quantum computers such as commercialized by D-Wave when confronted to instances of the maximum cardinality matching problem 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 suggests that quantum annealing, at least as implemented in a D-Wave device, falls in the same pitfalls as simulated annealing and therefore suggest that there exist polynomial-time problems that such a machine cannot solve efficiently to optimality.