Localization of quantum walk with classical randomness: Comparison between manual methods and supervised machine learning

Abstract

A transition of quantum walk induced by classical randomness changes the probability distribution of the walker from a two-peak structure to a single-peak one when the random parameter exceeds a critical value. We first establish the generality of the localization by showing its emergence in the presence of random rotation or translation. The transition point can be located manually by examining the probability distribution, momentum of inertia, and inverse participation ratio. As a comparison, we implement three supervised machine learning methods, the support vector machine (SVM), multi-layer perceptron neural network, and convolutional neural network with the same data and show they are able to identify the transition. While the SVM sometimes underestimate the exponents compared to the manual methods, the two neural-network methods show more deviation for the case with random translation due to the fluctuating probability distributions. Our work illustrates potentials and challenges facing machine learning of physical systems with mixed quantum and classical probabilities.