Open quantum generalisation of Hopfield neural networks
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 pr...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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IOP
2018
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| Online Access: | https://eprints.nottingham.ac.uk/50332/ |
| _version_ | 1848798223622209536 |
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| author | Rotondo, Pietro Marcuzzi, Matteo Garrahan, Juan P. Lesanovsky, Igor Müller, M. |
| author_facet | Rotondo, Pietro Marcuzzi, Matteo Garrahan, Juan P. Lesanovsky, Igor Müller, M. |
| author_sort | Rotondo, Pietro |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | 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. |
| first_indexed | 2025-11-14T20:16:21Z |
| format | Article |
| id | nottingham-50332 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-14T20:16:21Z |
| publishDate | 2018 |
| publisher | IOP |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-503322019-02-14T04:30:17Z https://eprints.nottingham.ac.uk/50332/ Open quantum generalisation of Hopfield neural networks Rotondo, Pietro Marcuzzi, Matteo Garrahan, Juan P. Lesanovsky, Igor Müller, M. 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. IOP 2018-03-16 Article PeerReviewed application/pdf en https://eprints.nottingham.ac.uk/50332/1/opQnet.pdf Rotondo, Pietro, Marcuzzi, Matteo, Garrahan, Juan P., 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 neural networks; statistical physics of disordered systems; open quantum systems http://iopscience.iop.org/article/10.1088/1751-8121/aaabcb/meta doi:10.1088/1751-8121/aaabcb doi:10.1088/1751-8121/aaabcb |
| spellingShingle | neural networks; statistical physics of disordered systems; open quantum systems Rotondo, Pietro Marcuzzi, Matteo Garrahan, Juan P. Lesanovsky, Igor Müller, M. Open quantum generalisation of Hopfield neural networks |
| title | 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_short | Open quantum generalisation of Hopfield neural networks |
| title_sort | open quantum generalisation of hopfield neural networks |
| topic | neural networks; statistical physics of disordered systems; open quantum systems |
| url | https://eprints.nottingham.ac.uk/50332/ https://eprints.nottingham.ac.uk/50332/ https://eprints.nottingham.ac.uk/50332/ |