Machine learning of quantum walk with classical randomness

Quantum walk exhibits a two-peak probability distribution, in contrast to the single-peak distribution of classical random walk. By introducing classical randomness into the coin operator or translation operator of a quantum walk, the distribution changes from the two-peak structure to the single-peak one as the randomness crosses a critical value. We implement three manual methods based on the distribution, moment of inertia, and inverse participation ratio, and three supervised machine-learning methods, including the support vector machine (SVM), multi-layer perceptron neural network, and convolutional neural network, to locate the transition point. While the SVM predicts a scaling exponent slightly smaller than the manual methods, the two neural-network based methods show more prominent deviations for the case with random translation. The results highlight challenges of machine learning of systems mixing quantum and classical probabilities.