Provably efficient machine learning for quantum many-body problems
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. Description Learning many-body behavior Predicting the properties of strongly interacting many-body quantum systems is notoriously difficult. One approach is to use quantum computers, but at the current stage of the technology, the most interesting problems are still out of reach. Huang et al. explored a different technique: using classical machine learning to learn from experimental data and then applying that knowledge to predict physical properties or classify phases of matter for specific types of many-body problems. The authors show that under certain conditions, the…
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