Open quantum generalisation of Hopfield neural networks

Rotondo, Pietro; Marcuzzi, Matteo; Garrahan, Juan P.; Lesanovsky, Igor; Müller, M.

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.

Citation

Rotondo, P., Marcuzzi, M., Garrahan, J. P., Lesanovsky, I., & Müller, M. (2018). Open quantum generalisation of Hopfield neural networks. Journal of Physics A: Mathematical and Theoretical, 51(11), Article 115301. https://doi.org/10.1088/1751-8121/aaabcb

• Journal Article Type: Article
• Acceptance Date: Jan 30, 2018
• Online Publication Date: Feb 14, 2018
• Publication Date: Mar 16, 2018
• Deposit Date: Mar 8, 2018
• Publicly Available Date: Feb 15, 2019
• Journal: Journal of Physics A: Mathematical and Theoretical
• Print ISSN: 1751-8113
• Electronic ISSN: 1751-8121
• Publisher: IOP Publishing
• Peer Reviewed: Peer Reviewed
• Volume: 51
• Issue: 11
• Article Number: 115301
• DOI: https://doi.org/10.1088/1751-8121/aaabcb
• Keywords: neural networks; statistical physics of disordered systems; open quantum systems
• Public URL: https://nottingham-repository.worktribe.com/output/920226
• Publisher URL: http://iopscience.iop.org/article/10.1088/1751-8121/aaabcb/meta