Physics-inspired optimization for quadratic unconstrained problems using a digital annealer

The Fujitsu Digital Annealer is designed to solve fully connected quadratic unconstrained binary optimization (QUBO) problems. It is implemented on application-specific CMOS hardware and currently solves problems of up to 1024 variables using a parallel-trial algorithm based on simulated annealing. We compare the performance of the Digital Annealer to simulated annealing and parallel tempering Monte Carlo with isoenergetic cluster moves on different spin-glass problems. Our results show that the Digital Annealer currently exhibits a time-to-solution speedup of roughly two orders of magnitude for fully connected spin-glass problems, over the single-core implementations of simulated annealing and parallel tempering Monte Carlo used in this study. This, however, is not the case for sparse two-dimensional problems. We also benchmarked an early implementation of the Parallel Tempering Digital Annealer. Our results suggest an improved scaling over the other algorithms for fully-connected problems of average difficulty with bimodal disorder. The use of specialized hardware paired with fast algorithms thus allows for a more detailed study of statistical physics Hamiltonians in the near future.