Phase diagram of quantum generalized Potts-Hopfield neural networks
We introduce and analyze an open quantum generalization of the q-state Potts-Hopfield neural network (NN), which is an associative memory model based on multi-level classical spins. The dynamics of this many-body system is formulated in terms of a Markovian master equation of Lindblad type, which al...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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IOP Publishing
2022-01-01
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| Series: | New Journal of Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1088/1367-2630/ac5490 |
| _version_ | 1797748508675014656 |
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| author | Eliana Fiorelli Igor Lesanovsky Markus Müller |
| author_facet | Eliana Fiorelli Igor Lesanovsky Markus Müller |
| author_sort | Eliana Fiorelli |
| collection | DOAJ |
| description | We introduce and analyze an open quantum generalization of the q-state Potts-Hopfield neural network (NN), which is an associative memory model based on multi-level classical spins. The dynamics of this many-body system is formulated in terms of a Markovian master equation of Lindblad type, which allows to incorporate both probabilistic classical and coherent quantum processes on an equal footing. By employing a mean field description we investigate how classical fluctuations due to temperature and quantum fluctuations effectuated by coherent spin rotations affect the ability of the network to retrieve stored memory patterns. We construct the corresponding phase diagram, which in the low temperature regime displays pattern retrieval in analogy to the classical Potts-Hopfield NN. When increasing quantum fluctuations, however, a limit cycle phase emerges, which has no classical counterpart. This shows that quantum effects can qualitatively alter the structure of the stationary state manifold with respect to the classical model, and potentially allow one to encode and retrieve novel types of patterns. |
| first_indexed | 2024-03-12T16:06:47Z |
| format | Article |
| id | doaj.art-a4ce5a21abf24094ab5b2b298651747c |
| institution | Directory Open Access Journal |
| issn | 1367-2630 |
| language | English |
| last_indexed | 2024-03-12T16:06:47Z |
| publishDate | 2022-01-01 |
| publisher | IOP Publishing |
| record_format | Article |
| series | New Journal of Physics |
| spelling | doaj.art-a4ce5a21abf24094ab5b2b298651747c2023-08-09T14:21:00ZengIOP PublishingNew Journal of Physics1367-26302022-01-0124303301210.1088/1367-2630/ac5490Phase diagram of quantum generalized Potts-Hopfield neural networksEliana Fiorelli0Igor Lesanovsky1https://orcid.org/0000-0001-9660-9467Markus Müller2https://orcid.org/0000-0002-2813-3097Institute for Theoretical Nanoelectronics (PGI-2) , Forschungszentrum Jülich, 52428 Jülich, Germany; Institute for Quantum Information, RWTH Aachen University , 52056 Aachen, GermanySchool of Physics and Astronomy, University of Nottingham , Nottingham, NG7 2RD, United Kingdom; Centre for the Mathematics and Theoretical Physics of Quantum Non-equilibrium Systems, University of Nottingham , Nottingham NG7 2RD, United Kingdom; Institut für Theoretische Physik, Universität Tübingen , Auf der Morgenstelle 14, 72076 Tübingen, GermanyInstitute for Theoretical Nanoelectronics (PGI-2) , Forschungszentrum Jülich, 52428 Jülich, Germany; Institute for Quantum Information, RWTH Aachen University , 52056 Aachen, GermanyWe introduce and analyze an open quantum generalization of the q-state Potts-Hopfield neural network (NN), which is an associative memory model based on multi-level classical spins. The dynamics of this many-body system is formulated in terms of a Markovian master equation of Lindblad type, which allows to incorporate both probabilistic classical and coherent quantum processes on an equal footing. By employing a mean field description we investigate how classical fluctuations due to temperature and quantum fluctuations effectuated by coherent spin rotations affect the ability of the network to retrieve stored memory patterns. We construct the corresponding phase diagram, which in the low temperature regime displays pattern retrieval in analogy to the classical Potts-Hopfield NN. When increasing quantum fluctuations, however, a limit cycle phase emerges, which has no classical counterpart. This shows that quantum effects can qualitatively alter the structure of the stationary state manifold with respect to the classical model, and potentially allow one to encode and retrieve novel types of patterns.https://doi.org/10.1088/1367-2630/ac5490open quantum systemsquantum neural networksdisordered systems |
| spellingShingle | Eliana Fiorelli Igor Lesanovsky Markus Müller Phase diagram of quantum generalized Potts-Hopfield neural networks New Journal of Physics open quantum systems quantum neural networks disordered systems |
| title | Phase diagram of quantum generalized Potts-Hopfield neural networks |
| title_full | Phase diagram of quantum generalized Potts-Hopfield neural networks |
| title_fullStr | Phase diagram of quantum generalized Potts-Hopfield neural networks |
| title_full_unstemmed | Phase diagram of quantum generalized Potts-Hopfield neural networks |
| title_short | Phase diagram of quantum generalized Potts-Hopfield neural networks |
| title_sort | phase diagram of quantum generalized potts hopfield neural networks |
| topic | open quantum systems quantum neural networks disordered systems |
| url | https://doi.org/10.1088/1367-2630/ac5490 |
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