  Quantum particles co-propagating on disordered lattices develop complex
non-classical correlations due to an interplay between quantum statistics,
inter-particle interactions, and disorder. Here we present a deep learning
algorithm based on Generative Adversarial Networks, capable of learning these
correlations and identifying the physical control parameters in a completely
unsupervised manner. After one-time training on a data set of unlabeled
examples, the algorithm can generate, without further calculations, a much
larger number of unseen yet physically correct new examples. Furthermore, the
knowledge distilled in the algorithm's latent space identifies disorder as the
relevant control parameter. This allows post-training tuning of the level of
disorder in the generated samples to values the algorithm was not explicitly
trained on. Finally, we show that a trained network can accelerate the learning
of new, more complex problems. These results demonstrate the ability of neural
networks to learn the rules of correlated quantum dynamics in an unsupervised
manner and offer a route to their use in quantum simulations and computation.
