Phase diagram of quantum generalized Potts-Hopfield neural networks

Fiorelli, Eliana; Lesanovsky, Igor; Müller, Markus

Abstract

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.

Citation

Fiorelli, E., Lesanovsky, I., & Müller, M. (2022). Phase diagram of quantum generalized Potts-Hopfield neural networks. New Journal of Physics, 24(3), Article 033012. https://doi.org/10.1088/1367-2630/ac5490

• Journal Article Type: Article
• Acceptance Date: Feb 11, 2022
• Online Publication Date: Mar 10, 2022
• Publication Date: 2022-03
• Deposit Date: Feb 23, 2022
• Publicly Available Date: Feb 23, 2022
• Journal: New Journal of Physics
• Electronic ISSN: 1367-2630
• Publisher: IOP Publishing
• Peer Reviewed: Peer Reviewed
• Volume: 24
• Issue: 3
• Article Number: 033012
• DOI: https://doi.org/10.1088/1367-2630/ac5490
• Keywords: open quantum systems, quantum neural networks, disordered systems
• Public URL: https://nottingham-repository.worktribe.com/output/7474433
• Publisher URL: https://iopscience.iop.org/article/10.1088/1367-2630/ac5490