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  Unifying neural-network quantum states and correlator product states via tensor networks

Clark, S. R. (2018). Unifying neural-network quantum states and correlator product states via tensor networks. Journal of Physics A, 51(13): 135301. doi:10.1088/1751-8121/aaaaf2.

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Item Permalink: http://hdl.handle.net/21.11116/0000-0001-AC09-4 Version Permalink: http://hdl.handle.net/21.11116/0000-0002-5023-C
Genre: Journal Article

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Clark_2018_J._Phys._A__Math._Theor._51_135301.pdf (Publisher version), 9MB
 
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https://dx.doi.org/10.1088/1751-8121/aaaaf2 (Publisher version)
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 Creators:
Clark, S. R.1, 2, Author              
Affiliations:
1Quantum Condensed Matter Dynamics, Condensed Matter Dynamics Department, Max Planck Institute for the Structure and Dynamics of Matter, Max Planck Society, ou_1938293              
2Department of Physics, University of Bath, ou_persistent22              

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 Abstract: Correlator product states (CPS) are a powerful and very broad class of states for quantum lattice systems whose (unnormalised) amplitudes in a fixed basis can be sampled exactly and efficiently. They work by gluing together states of overlapping clusters of sites on the lattice, called correlators. Recently Carleo and Troyer (2017 Science 355 602) introduced a new type sampleable ansatz called neural-network quantum states (NQS) that are inspired by the restricted Boltzmann model used in machine learning. By employing the formalism of tensor networks we show that NQS are a special form of CPS with novel properties. Diagramatically a number of simple observations become transparent. Namely, that NQS are CPS built from extensively sized GHZ-form correlators making them uniquely unbiased geometrically. The appearance of GHZ correlators also relates NQS to canonical polyadic decompositions of tensors. Another immediate implication of the NQS equivalence to CPS is that we are able to formulate exact NQS representations for a wide range of paradigmatic states, including superpositions of weighed-graph states, the Laughlin state, toric code states, and the resonating valence bond state. These examples reveal the potential of using higher dimensional hidden units and a second hidden layer in NQS. The major outlook of this study is the elevation of NQS to correlator operators allowing them to enhance conventional well-established variational Monte Carlo approaches for strongly correlated fermions.

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Language(s): eng - English
 Dates: 2018-01-232017-10-252018-01-292018-02-232018-04-03
 Publication Status: Published in print
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 Rev. Method: Peer
 Identifiers: DOI: 10.1088/1751-8121/aaaaf2
arXiv: 1710.03545
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Project name : SRC gratefully acknowledges support from the EPSRC under grant No. EP/P025110/1. Also SRC would like to thank Dieter Jaksch, Jonathan Coulthard, Michael Lubasch, Michael Pei, Sam Pearce, and Matthew Cook for helpful discussions. Note added. Shortly after this work appeared on the preprint arXiv related studies by Glasser et al [ 90 ] and Kaubruegger et al [ 91 ] on NQS representations of chiral topological states were submitted.
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Title: Journal of Physics A
  Other : Journal of Physics A: Mathematical and Theoretical
  Abbreviation : J. Phys. A
Source Genre: Journal
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Publ. Info: Bristol : IOP Pub.
Pages: - Volume / Issue: 51 (13) Sequence Number: 135301 Start / End Page: - Identifier: ISSN: 1751-8113
CoNE: /journals/resource/954925513480_2