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Published September 23, 2022 | public
Journal Article

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.

Additional Information

The authors thank N. Bar-Gill, J. Carrasquilla, S. Chen, Y. Chen, A. Elben, M. Fishman, M. Fraas, S. Glancy, J. Haah, F. Kueng, J. McClean, S. Michalakis, J. Taylor, Y. Su, and T. Vidick for valuable input and inspiring discussions. H.-Y.H. thanks A. Elben for providing the code on the bond-alternating XXZ model. The numerical simulations were performed on AWS EC2 computing infrastructure using the software packages Itensors (92) and PastaQ (93). V.V.A. thanks O. Albert, H. Kandratsenia and R. Kandratsenia, as well as Ta. Albert and Th. Albert for providing daycare support throughout this work. Contributions to this work by NIST, an agency of the US government, are not subject to US copyright. Any mention of commercial products does not indicate endorsement by NIST. Funding: H.-Y.H. is supported by the J. Yang & Family Foundation and a Google PhD fellowship. V.V.A. acknowledges funding from NSF QLCI award no. OMA-2120757. J.P. acknowledges funding from the US Department of Energy Office of Science, Office of Advanced Scientific Computing Research (DE-NA0003525 and DE-SC0020290), and the National Science Foundation (PHY-1733907). The Institute for Quantum Information and Matter is an NSF Physics Frontiers Center.

Additional details

Created:
August 22, 2023
Modified:
October 23, 2023