  We experimentally study the performance of a programmable quantum annealing
processor, the D-Wave One (DW1) with up to 108 qubits, on maximum
satisfiability problem with 2 variables per clause (MAX 2-SAT) problems. We
consider ensembles of random problems characterized by a fixed clause density,
an order parameter which we tune through its critical value in our experiments.
We demonstrate that the DW1 is sensitive to the critical value of the clause
density. The DW1 results are verified and compared with akmaxsat, an exact,
state-of-the-art algorithm. We study the relative performance of the two
solvers and how they correlate in terms of problem hardness. We find that the
DW1 performance scales more favorably with problem size and that problem
hardness correlation is essentially non-existent. We discuss the relevance and
limitations of such a comparison.
