Teacher-student learning for a binary perceptron with quantum fluctuations

TL;DR

This paper investigates how quantum fluctuations can improve the generalisation performance of a binary perceptron by enabling the efficient finding of robust solutions, validated through theoretical analysis and quantum Monte Carlo simulations.

Contribution

It introduces a teacher-student learning framework for binary perceptrons with quantum fluctuations and demonstrates improved generalisation performance over classical models.

Findings

Quantum fluctuations lead to better generalisation performance.

Quantum Monte Carlo simulations validate theoretical predictions.

Deviations occur at low transverse field strength and high pattern ratio due to ergodicity violations.

Abstract

We analysed the generalisation performance of a binary perceptron with quantum fluctuations using the replica method. An exponential number of local minima dominate the energy landscape of the binary perceptron. Local search algorithms often fail to identify the ground state of a binary perceptron. In this study, we considered the teacher-student learning method and computed the generalisation error of a binary perceptron with quantum fluctuations. Due to the quantum fluctuations, we can efficiently find robust solutions that have better generalisation performance than the classical model. We validated our theoretical results through quantum Monte Carlo simulations. We adopted the replica symmetry (RS) ansatz assumption and static approximation. The RS solutions are consistent with our simulation results, except for the relatively low strength of the transverse field and high pattern ratio. These deviations are caused by the violation of ergodicity and static approximation. After accounting for the deviation between the RS solutions and numerical results, the enhancement of generalisation performance with quantum fluctuations holds.