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Quantum annealing is getting increasing attention in combinatorialoptimization. The quantum processing unit by D-Wave is constructed toapproximately solve Ising models on so-called Chimera graphs. Ising models areequivalent to quadratic unconstrained binary optimization (QUBO) problems andmaximum cut problems on the associated graphs. We have tailored branch-and-cutas well as semidefinite programming algorithms for solving Ising models forChimera graphs to provable optimality and use the strength of these approachesfor comparing our solution values to those obtained on the current quantumannealing machine D-Wave 2000Q. This allows for the assessment of the qualityof solutions produced by the D-Wave hardware. It has been a matter ofdiscussion in the literature how well the D-Wave hardware performs at itsnative task, and our experiments shed some more light on this issue.

Performance of a Quantum Annealer for Ising Ground State Computations on Chimera Graphs