Operational Quantum Annealers are Cursed by their Qubits Interconnection Topologies

Recent experimental works have studied how the quantum annealing approach, as implemented in D-Wave devices, deals with pathological instances of the (polynomial) bipartite matching problem known to be hard for classical simulated annealing algorithms and shown that the quantum approach also performed rather poorly on such instances. In this paper, 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.