Quantum accelerated approach to the thermal state of classical spin systems with applications to pattern-retrieval in the Hopfield neural network

TL;DR

This paper investigates whether quantum effects can accelerate the convergence of spin systems to their thermal states, demonstrating potential speedups in pattern retrieval within Hopfield neural networks through a novel quantum dissipative approach.

Contribution

The paper introduces a quantum dissipative dynamics framework that interpolates between classical and quantum regimes, enabling faster thermalization of spin systems and improved pattern retrieval in neural networks.

Findings

Quantum dynamics can accelerate convergence to thermal states.

A transformation allows interpolation between classical and quantum regimes.

Potential speedup in pattern retrieval in Hopfield networks.

Abstract

We explore the question as to whether quantum effects can yield a speedup of the non-equilibrium evolution of spin systems towards a classical thermal state. In our approach we exploit the fact that the thermal state of a spin system can be mapped onto a node-free quantum state whose coefficients are given by thermal weights. This perspective permits the construction of a dissipative -- yet quantum -- dynamics which encodes in its stationary state the thermal state of the original problem. We show for the case of an all-to-all connected Ising spin model that an appropriate transformation of this dissipative dynamics allows to interpolate between a regime in which the order parameter obeys the classical equations of motion under Glauber dynamics, to a quantum regime with an accelerated approach to stationarity. We show that this effect enables in principle a speedup of pattern retrieval in a Hopfield neural network.