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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 (2021) Provably efficient machine learning for quantum many-body problems. . (Unpublished) https://resolver.caltech.edu/CaltechAUTHORS:20220104-233146603

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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 more 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 in finite spatial dimensions, after learning from data obtained by measuring other Hamiltonians in the same quantum phase of matter. 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 are based 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 be used to predict many properties of the state. Extensive numerical experiments corroborate our theoretical results in a variety of scenarios, including Rydberg atom systems, 2D random Heisenberg models, symmetry-protected topological phases, and topologically ordered phases.


Item Type:Report or Paper (Discussion Paper)
Related URLs:
URLURL TypeDescription
http://arxiv.org/abs/2106.12627arXivDiscussion Paper
ORCID:
AuthorORCID
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:Attribution 4.0 International (CC BY 4.0). The authors thank Nir Bar-Gill, Juan Carrasquilla, Sitan Chen, Yifan Chen, Matthew Fishman, Scott Glancy, Jeongwan Haah, Felix Kueng, Jarrod McClean, Spiros Michalakis, Jacob Taylor, Yuan Su, and Thomas Vidick for valuable input and inspiring discussions. HH thanks Andreas Elben for providing the code on bond-alternating XXZ model. The numerical simulations were performed on AWS EC2 computing infra-structure, using the software packages ITensors [65] and PastaQ [64]. HH is supported by the J. Yang & Family Foundation. JP acknowledges funding from the U.S. Department of Energy Office of Science, Office of Advanced Scientific Computing Research, (DE-NA0003525, DE-SC0020290), and the National Science Foundation (PHY-1733907). The Institute for Quantum Information and Matter is an NSF Physics Frontiers Center. 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. VVA thanks Olga Albert, Halina and Ryhor Kandratsenia, as well as Tatyana and Thomas Albert for providing daycare support throughout this work.
Group:Institute for Quantum Information and Matter, AWS Center for Quantum Computing
Funders:
Funding AgencyGrant Number
J. Yang Family and FoundationUNSPECIFIED
Department of Energy (DOE)DE-NA0003525
Department of Energy (DOE)DE-SC0020290
NSFPHY-1733907
Record Number:CaltechAUTHORS:20220104-233146603
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20220104-233146603
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:112704
Collection:CaltechAUTHORS
Deposited By: George Porter
Deposited On:11 Jan 2022 17:06
Last Modified:11 Jan 2022 17:06

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