Provably efficient machine learning for quantum many-body problems

TLDR

Classical machine learning offers a potentially powerful approach to solving challenging quantum many-body problems in physics and chemistry, but its advantages over traditional methods have not been firmly established. The authors prove that classical ML algorithms can efficiently predict ground‑state properties of gapped Hamiltonians after learning from other Hamiltonians in the same quantum phase, and can efficiently classify a wide range of quantum phases, whereas classical algorithms that do not learn from data cannot achieve the same guarantee. Numerical experiments on Rydberg atom systems, two‑dimensional random Heisenberg models, symmetry‑protected topological phases, and topologically ordered phases corroborate the theoretical results.

Abstract

Classical machine learning (ML) provides a potentially powerful approach to solving challenging quantum many-body problems in physics and chemistry. However, the advantages of ML over traditional methods have not been firmly established. In this work, we prove that classical ML algorithms can efficiently predict ground-state properties of gapped Hamiltonians after learning from other Hamiltonians in the same quantum phase of matter. By contrast, under a widely accepted conjecture, classical algorithms that do not learn from data cannot achieve the same guarantee. We also prove that classical ML algorithms can efficiently classify a wide range of quantum phases. Extensive numerical experiments corroborate our theoretical results in a variety of scenarios, including Rydberg atom systems, two-dimensional random Heisenberg models, symmetry-protected topological phases, and topologically ordered phases.