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Neural tensor contractions and the expressive power of deep neural quantum states

Sharir, Or and Shashua, Amnon and Carleo, Giuseppe (2022) Neural tensor contractions and the expressive power of deep neural quantum states. Physical Review B, 106 (20). Art. No. 205136. ISSN 2469-9950. doi:10.1103/physrevb.106.205136.

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We establish a direct connection between general tensor networks and deep feed-forward artificial neural networks. The core of our results is the construction of neural-network layers that efficiently perform tensor contractions and that use commonly adopted nonlinear activation functions. The resulting deep networks feature a number of edges that closely match the contraction complexity of the tensor networks to be approximated. In the context of many-body quantum states, this result establishes that neural-network states have strictly the same or higher expressive power than practically usable variational tensor networks. As an example, we show that all matrix product states can be efficiently written as neural-network states with a number of edges polynomial in the bond dimension and depth that is logarithmic in the system size. The opposite instead does not hold true, and our results imply that there exist quantum states that are not efficiently expressible in terms of matrix product states or projected entangled pair states but that are instead efficiently expressible with neural network states.

Item Type:Article
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URLURL TypeDescription
Sharir, Or0000-0003-4957-8957
Carleo, Giuseppe0000-0002-8887-4356
Additional Information:This research was supported by the ERC (European Research Council) and the ISF (Israel Science Foundation).Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.
Funding AgencyGrant Number
European Research Council (ERC)UNSPECIFIED
Israel Science FoundationUNSPECIFIED
Issue or Number:20
Record Number:CaltechAUTHORS:20230203-893210800.19
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:119014
Deposited By: Research Services Depository
Deposited On:24 Feb 2023 20:49
Last Modified:24 Feb 2023 20:49

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