Juan Carrasquilla - Vector Institute I will present a heuristic to simulate quantum circuits based on a probabilistic representation of the quantum state as the outcome distribution of a positive operator valued measure. In this language, unitary evolution translates into evolution of probability distributions subject to "somewhat" stochastic matrices, which are a generalization of stochastic matrices. I approximate the evolution of the quantum state using recurrent neural networks and transformers and provide a proof-of-principle demonstration of the approach on simple quantum circuits.