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Neural network representation of tensor network and chiral states

Huang, Yichen and Moore, Joel E. (2017) Neural network representation of tensor network and chiral states. . (Submitted) http://resolver.caltech.edu/CaltechAUTHORS:20170605-084735797

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Abstract

We study the representational power of a Boltzmann machine (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 quasi-local neural network representation for a chiral p-wave superconductor. This demonstrates the power of Boltzmann machines.


Item Type:Report or Paper (Discussion Paper)
Related URLs:
URLURL TypeDescription
https://arxiv.org/abs/1701.06246arXivDiscussion Paper
Additional Information: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-1125565) with support of the Gordon and Betty Moore Foundation (GBMF-2644). J.E.M. is supported by NSF DMR-1507141 and a Simons Investigatorship. Part of this work was presented on November 27, 2014 (Thanksgiving day!) at the Perimeter Institute for Theoretical Physics. Very recently, we became aware of some related papers [7, 9, 11], which studied the relationship between neural and tensor network states using different approaches. In particular, Theorem 2 and Corollary 3 are stronger than Theorem 3 in Ref. [11].
Group:IQIM, Institute for Quantum Information and Matter
Funders:
Funding AgencyGrant Number
Institute for Quantum Information and Matter (IQIM)UNSPECIFIED
NSFPHY-1125565
Gordon and Betty Moore FoundationGBMF-2644
NSFDMR-1507141
Simons FoundationUNSPECIFIED
Record Number:CaltechAUTHORS:20170605-084735797
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20170605-084735797
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:77938
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:05 Jun 2017 21:33
Last Modified:05 Jun 2017 21:33

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