Machine learning techniques have been recently proposed as a way to efficiently represent certain quantum states with applications in state tomography and ground state estimation. In this talk, we present a practically usable deep architecture for representing and sampling from probability distributions of quantum states. Our representation is based on variational autoencoders, a type of generative model in the form of a neural network. We show that this model is able to learn efficient representations of states that are easy to simulate classically and can compress states that are not classically tractable. Specifically, we consider the learnability of a class of quantum states that are provably hard to sample for classical computers, but not for quantum ones, under plausible computational complexity assumptions. The good level of compression achieved for hard states suggests these methods can be suitable for characterising states of the size expected in NISQ devices.