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Neural Network Representation of Tensor Network and Chiral States

Huang, Yichen and Moore, Joel E. (2021) Neural Network Representation of Tensor Network and Chiral States. Physical Review Letters, 127 (17). Art. No. 170601. ISSN 0031-9007. doi:10.1103/PhysRevLett.127.170601.

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We study the representational power of Boltzmann machines (a type of neural network) in quantum many-body systems. We prove that any (local) tensor network state has a (local) neural network representation. The construction is almost optimal in the sense that the number of parameters in the neural network representation is almost linear in the number of nonzero parameters in the tensor network representation. Despite the difficulty of representing (gapped) chiral topological states with local tensor networks, we construct a quasilocal neural network representation for a chiral p-wave superconductor. These results demonstrate the power of Boltzmann machines.

Item Type:Article
Related URLs:
URLURL TypeDescription Paper
Huang, Yichen0000-0002-8496-9251
Additional Information:© 2021 American Physical Society. Received 20 July 2021; accepted 20 September 2021; published 18 October 2021. The authors would like to thank Xie Chen for collaboration in the early stages of this project. Y. H. acknowledges funding provided by the Institute for Quantum Information and Matter, an NSF Physics Frontiers Center (NSF Grant PHY-1733907) with support of the Gordon and Betty Moore Foundation (GBMF-2644). J. E. M. is supported by NSF DMR-1507141, DMR-1918065 and a Simons Investigatorship.
Group:Institute for Quantum Information and Matter
Funding AgencyGrant Number
Institute for Quantum Information and Matter (IQIM)UNSPECIFIED
Gordon and Betty Moore FoundationGBMF-2644
Simons FoundationUNSPECIFIED
Issue or Number:17
Record Number:CaltechAUTHORS:20170605-084735797
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:77938
Deposited By: Tony Diaz
Deposited On:05 Jun 2017 21:33
Last Modified:04 Nov 2021 16:03

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