Computational complexity of three-dimensional Ising spin glass: Lessons from D-wave annealer - Hao Zhang; Alex Kamenev (Physical Review Research)
Finding an exact ground state of a three-dimensional (3D) Ising spin glass is proven to be an NP-hard problem (i.e., at least as hard as any problem in the nondeterministic polynomial-time (NP) class). Given validity of the exponential time hypothesis, its computational complexity was proven to be no less than 2^{N^{2/3}}, where N is the total number of spins. Here, we report results of extensive experimentation with D-Wave 3D annealer with N≤5627. We found exact ground states (in a probabilistic sense) for typical realizations of 3D spin glasses with the efficiency, which scales as 2^{N/β} with β≈10^{3}. Based on statistical analysis of low-energy states, we argue that with an improvement of annealing protocols and device noise reduction, β can be increased even further. This suggests that, for N<β^{3}, annealing devices provide most efficient way to find an exact ground state.