Exploring quantum localization with machine learning

TL;DR

This paper presents a novel neural network architecture that efficiently classifies quantum wave functions by their localization properties, enabling scalable analysis of quantum systems approaching the semiclassical limit.

Contribution

The authors introduce a versatile quantum phase space-based neural network that accurately classifies wave functions of any dimension with interpretability and computational efficiency.

Findings

Effective classification of wave functions by localization

Scalable analysis near the semiclassical limit

Model interpretability of quantum localization patterns

Abstract

We introduce an efficient neural network (NN) architecture for classifying wave functions in terms of their localization. Our approach integrates a versatile quantum phase space parametrization leading to a custom 'quantum' NN, with the pattern recognition capabilities of a modified convolutional model. This design accepts wave functions of any dimension as inputs and makes accurate predictions at an affordable computational cost. This scalability becomes crucial to explore the localization rate at the semiclassical limit, a long standing question in the quantum scattering field. Moreover, the physical meaning built in the model allows for the interpretation of the learning process