  Adiabatic quantum optimization offers a new method for solving hard
optimization problems. In this paper we calculate median adiabatic times (in
seconds) determined by the minimum gap during the adiabatic quantum
optimization for an NP-hard Ising spin glass instance class with up to 128
binary variables. Using parameters obtained from a realistic superconducting
adiabatic quantum processor, we extract the minimum gap and matrix elements
using high performance Quantum Monte Carlo simulations on a large-scale
Internet-based computing platform. We compare the median adiabatic times with
the median running times of two classical solvers and find that, for the
considered problem sizes, the adiabatic times for the simulated processor
architecture are about 4 and 6 orders of magnitude shorter than the two
classical solvers' times. This shows that if the adiabatic time scale were to
determine the computation time, adiabatic quantum optimization would be
significantly superior to those classical solvers for median spin glass
problems of at least up to 128 qubits. We also discuss important additional
constraints that affect the performance of a realistic system.
