Quantum Hopfield Model

TL;DR

This paper explores how quantum fluctuations influence the behavior of Hopfield neural networks in a transverse field, revealing that quantum effects mimic thermal fluctuations in their impact on macroscopic network properties.

Contribution

It demonstrates that the phase diagram of the quantum Hopfield model resembles the classical one, highlighting the role of quantum fluctuations similar to thermal effects.

Findings

Quantum fluctuations affect the phase diagram similarly to thermal fluctuations.

The phase diagram in the quantum model resembles the classical Hopfield model.

Quantum effects can be understood as analogous to temperature in neural networks.

Abstract

The Hopfield model in a transverse field is investigated in order to clarify how quantum fluctuations affect the macroscopic behavior of neural networks. Using the Trotter decomposition and the replica method, we find that the $\alpha$ (the ratio of the number of stored patterns to the system size)-$\Delta$ (the strength of the transverse field) phase diagram of this model in the ground state resembles the $\alpha$-$T$ phase diagram of the Hopfield model quantitatively, within the replica-symmetric and static approximations. This fact suggests that quantum fluctuations play quite similar roles to thermal fluctuations in neural networks as long as macroscopic properties are concerned.