Exploring quantum localization with machine learning

Abstract

We introduce an efficient neural network (NN) architecture for classifying wave functions in terms of their localization (probability concentration) in a specific region of the quantum phase space. 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 –i.e. at large Hilbert space dimensions $N={(2\pi ħ)}^{-1}$– 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.