# Open quantum generalisation of Hopfield neural networks

## TL;DR

This paper introduces a quantum extension of Hopfield neural networks using open quantum systems, revealing a new non-equilibrium phase with limit cycles that generalize classical memory patterns.

## Contribution

It presents the first open quantum generalisation of Hopfield networks, analyzing their phase diagram and discovering a novel quantum-induced non-equilibrium phase.

## Key findings

- Quantum fluctuations induce a new non-equilibrium phase.
- The phase diagram reveals limit cycles as quantum analogues of memory patterns.
- The framework unifies thermal and quantum effects in neural network dynamics.

## 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 celebrated 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.