Provably efficient machine learning for quantum many-body problems

Published

September 23, 2022

Author(s)

Hsin-Yuan Huang, Richard Kueng, Giacomo Torlai, Victor Albert, John Preskill

Abstract

Classical machine learning (ML) provides a potentially powerful approach to solving challenging quantum many-body problems that arise in physics and chemistry, but the advantages of ML over more traditional classical methods have not been firmly established. Here we prove that a classical ML algorithm, after learning from data obtained in quantum experiments, can accurately predict expectation values of local operators in ground states of gapped local Hamiltonians. In contrast, under widely accepted complexity theory assumptions, 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 of matter. Our arguments rely heavily on the concept of a classical shadow, a succinct classical description of a many-body quantum state that can be constructed in feasible quantum experiments and can be used to predict many properties of the state. Extensive numerical experiments validate our theoretical results in a variety of scenarios, including Rydberg atom systems, 2D random Heisenberg models, symmetry-protected topological phases, and topologically ordered phases.

Citation

Physics Arxiv

Pub Type

Journals

Download Paper

https://doi.org/10.1126/science.abk3333

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Citation

Huang, H. , Kueng, R. , Torlai, G. , Albert, V. and Preskill, J. (2022), Provably efficient machine learning for quantum many-body problems, Physics Arxiv, [online], https://doi.org/10.1126/science.abk3333, https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=932594 (Accessed April 29, 2024)