On Computational Complexity of 3D Ising Spin Glass: Lessons from D-Wave Annealer

Hao Zhang, Alex Kamenev

Published 2025-01-02Version 1

Finding an exact ground state of a 3D Ising spin glass is proven to be an NP-hard problem. There is a widespread belief that this statement implies an exponential scaling, $\sim 2^{N/\beta}$, of necessary computational efforts (classical or quantum), with the number of spins, $N$. Yet, what is a factor $\beta$ here and are there any fundamental limits on how large it can be? Here we report results of extensive experimentation with D-Wave 3D annealer with $N\leq 5627$. We found exact ground states (in a probabilistic sense) for typical realizations of 3D spin glasses with the efficiency, characterized by $\beta\approx 10^{3}$. We argue that with a further improvement of annealing protocols, post-processing algorithms and device noise reduction, $\beta$ can be increased even further. We provide a theoretical argumentation for this observation based on statistical analysis of low energy states.