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Computational complexity of three-dimensional Ising spin glass: Lessons from D-wave annealer

Hao Zhang1,* and Alex Kamenev1,2

  • *Contact author : hao.zhang.quantum@gmail.com
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Phys. Rev. Research 7, 033098 – Published 28 July, 2025

DOI: https://doi.org/10.1103/3bkn-v5rd

Abstract

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 2N2/3, 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 2N/β with β≈103. 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<β3, annealing devices provide most efficient way to find an exact ground state.

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Phys. Rev. Research 7, 033098– Published 28 July, 2025
  • Received 14 January 2025
  • Accepted 9 July 2025
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