Phase diagram of quantum generalized Potts-Hopfield neural networks

TL;DR

This paper introduces a quantum generalization of the Potts-Hopfield neural network, analyzing how quantum and classical fluctuations influence memory retrieval and revealing a novel limit cycle phase induced by quantum effects.

Contribution

It develops a quantum version of the Potts-Hopfield neural network using Lindblad dynamics and explores how quantum fluctuations modify the phase diagram and memory retrieval capabilities.

Findings

Classical pattern retrieval persists at low temperatures.

Quantum fluctuations induce a new limit cycle phase.

Quantum effects can enable encoding of novel patterns.

Abstract

We introduce and analyze an open quantum generalization of the q-state Potts-Hopfield neural network, 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 neural network. 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.