Power of deep convolutional recurrent networks in predicting the dynamics of random quantum circuits

Machine learning has shown significant breakthroughs in the field of quantum computing in particular deep neural networks exhibited remarkable power in enhancing quantum many-body dynamical simulations. In this work, we study the connection between the power of data-driven deep networks in learning the dynamics of physical observables of quantum many-body systems and the way that quantum information scramble with a focus on the random quantum circuits. In particular, utilizing convolutional recurrent neural networks we study how the extrapolation power of the neural network in time and system size where the network has not been trained is correlated with the localization of quantum information in the system. We illustrate integrability can be used as a figure of merit to identify the power of deep neural networks in extrapolating the predictions.