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Open quantum generalisation of Hopfield neural networks

P Rotondo, M Marcuzzi, J P Garrahan, I Lesanovsky, M Müller, Markus Muller

Journal of Physics A: Mathematical and Theoretical, Volume: 51, Issue: 11, Start page: 115301

Swansea University Author: Markus Muller

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DOI (Published version): 10.1088/1751-8121/aaabcb

Abstract

In this work, we propose a new framework to study how quantum effects may impact on the dynamics of neural networks. We consider neural network dynamics in terms of Markovian open quantum systems, which allows us to study both thermal and quantum coherent effects within the same framework. Specifica...

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Published in: Journal of Physics A: Mathematical and Theoretical
ISSN: 1751-8113 1751-8121
Published: 2018
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URI: https://cronfa.swan.ac.uk/Record/cronfa40130
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first_indexed 2018-05-12T19:27:44Z
last_indexed 2019-06-18T20:29:26Z
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spelling 2019-06-18T16:51:40.3163810 v2 40130 2018-05-12 Open quantum generalisation of Hopfield neural networks 9b2ac559af27c967ece69db08b83762a Markus Muller Markus Muller true false 2018-05-12 FGSEN In this work, we propose a new framework to study how quantum effects may impact on the dynamics of neural networks. We consider neural network dynamics in terms of Markovian open quantum systems, which allows us to study both thermal and quantum coherent effects within the same framework. Specifically, we propose and study an open quantum generalisation of the paradigmatic Hopfield neural network model. We determine its phase diagram and encounter a qualitatively new non-equilibrium phase. This novel phase is characterised by limit cycles corresponding to high-dimensional stationary manifolds, which can be understood as generalisations of storage patterns to the quantum domain. Journal Article Journal of Physics A: Mathematical and Theoretical 51 11 115301 1751-8113 1751-8121 Neural Networks, Open Quantum Systems 14 2 2018 2018-02-14 10.1088/1751-8121/aaabcb http://iopscience.iop.org/article/10.1088/1751-8121/aaabcb COLLEGE NANME Science and Engineering - Faculty COLLEGE CODE FGSEN Swansea University 2019-06-18T16:51:40.3163810 2018-05-12T16:58:42.7438303 Faculty of Science and Engineering School of Biosciences, Geography and Physics - Physics P Rotondo 1 M Marcuzzi 2 J P Garrahan 3 I Lesanovsky 4 M Müller 5 Markus Muller 6 0040130-12052018170426.pdf opQnet-final-submission.pdf 2018-05-12T17:04:26.4170000 Output 3568494 application/pdf Accepted Manuscript true 2019-02-14T00:00:00.0000000 12 month embargo. true eng
title Open quantum generalisation of Hopfield neural networks
spellingShingle Open quantum generalisation of Hopfield neural networks
Markus Muller
title_short Open quantum generalisation of Hopfield neural networks
title_full Open quantum generalisation of Hopfield neural networks
title_fullStr Open quantum generalisation of Hopfield neural networks
title_full_unstemmed Open quantum generalisation of Hopfield neural networks
title_sort Open quantum generalisation of Hopfield neural networks
author_id_str_mv 9b2ac559af27c967ece69db08b83762a
author_id_fullname_str_mv 9b2ac559af27c967ece69db08b83762a_***_Markus Muller
author Markus Muller
author2 P Rotondo
M Marcuzzi
J P Garrahan
I Lesanovsky
M Müller
Markus Muller
format Journal article
container_title Journal of Physics A: Mathematical and Theoretical
container_volume 51
container_issue 11
container_start_page 115301
publishDate 2018
institution Swansea University
issn 1751-8113
1751-8121
doi_str_mv 10.1088/1751-8121/aaabcb
college_str Faculty of Science and Engineering
hierarchytype
hierarchy_top_id facultyofscienceandengineering
hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
hierarchy_parent_title Faculty of Science and Engineering
department_str School of Biosciences, Geography and Physics - Physics{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Biosciences, Geography and Physics - Physics
url http://iopscience.iop.org/article/10.1088/1751-8121/aaabcb
document_store_str 1
active_str 0
description In this work, we propose a new framework to study how quantum effects may impact on the dynamics of neural networks. We consider neural network dynamics in terms of Markovian open quantum systems, which allows us to study both thermal and quantum coherent effects within the same framework. Specifically, we propose and study an open quantum generalisation of the paradigmatic Hopfield neural network model. We determine its phase diagram and encounter a qualitatively new non-equilibrium phase. This novel phase is characterised by limit cycles corresponding to high-dimensional stationary manifolds, which can be understood as generalisations of storage patterns to the quantum domain.
published_date 2018-02-14T03:51:05Z
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score 11.036116

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