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Provably efficient machine learning for quantum many-body problems

Huang, Hsin-Yuan and Kueng, Richard and Torlai, Giacomo and Albert, Victor V. and Preskill, John (2022) Provably efficient machine learning for quantum many-body problems. Science, 377 (6613). Art. No. abk3333. ISSN 0036-8075. doi:10.1126/science.abk3333.

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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.

Item Type:Article
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URLURL TypeDescription ItemDiscussion Paper InCaltech News
Huang, Hsin-Yuan0000-0001-5317-2613
Kueng, Richard0000-0002-8291-648X
Torlai, Giacomo0000-0001-8478-4436
Albert, Victor V.0000-0002-0335-9508
Preskill, John0000-0002-2421-4762
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.
Group:Institute for Quantum Information and Matter
Funding AgencyGrant Number
J. Yang Family and FoundationUNSPECIFIED
Google PhD FellowshipUNSPECIFIED
Department of Energy (DOE)DE-NA0003525
Department of Energy (DOE)DE-SC0020290
Issue or Number:6613
Record Number:CaltechAUTHORS:20221207-387978400.2
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:118259
Deposited By: Research Services Depository
Deposited On:10 Jan 2023 23:04
Last Modified:28 Feb 2023 20:26

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