Open quantum generalisation of Hopfield neural networks

Rotondo, Pietro and Marcuzzi, Matteo and Garrahan, Juan P. and Lesanovsky, Igor and Müller, M. (2018) Open quantum generalisation of Hopfield neural networks. Journal of Physics A: Mathematical and Theoretical, 51 (11). 115301/1-115301/11. ISSN 1751-8121

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Abstract

We propose a new framework to understand how quantum effects may impact on the dynamics of neural networks. We implement the dynamics of neural networks in terms of Markovian open quantum systems, which allows us to treat thermal and quantum coherent effects on the same footing. In particular, we propose an open quantum generalisation of the Hopfield neural network, the simplest toy model of associative memory. We determine its phase diagram and show that quantum fluctuations give rise to a qualitatively new non-equilibrium phase. This novel phase is characterised by limit cycles corresponding to high-dimensional stationary manifolds that may be regarded as a generalisation of storage patterns to the quantum domain.

Item Type: Article
Keywords: neural networks; statistical physics of disordered systems; open quantum systems
Schools/Departments: University of Nottingham, UK > Faculty of Science > School of Physics and Astronomy
Identification Number: https://doi.org/10.1088/1751-8121/aaabcb
Depositing User: Eprints, Support
Date Deposited: 08 Mar 2018 11:56
Last Modified: 09 Mar 2018 09:29
URI: http://eprints.nottingham.ac.uk/id/eprint/50332

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