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

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, multi-layer perceptron neural network, and convolutional neural network with the same data and show that they can identify the transition and produce comparable exponents of the localization except for the case with random translation, where the two neural-network methods tend to underestimate the exponent due to the complicated probability distributions in the transition regime. Our work illustrates potentials and challenges facing machine learning of physical systems with mixed quantum and classical probabilities.Comment: 12 pages, 6 figure