Neural Quantum Simulation of Quantum Dynamics: Recent advances and limitations

Neural-network encodings of quantum states have been shown in recent years to be powerful tools to tackle the quantum many body problem. While several outstanding results have been shown, especially when tackling spin systems such as the J1-J2 model, simulating variational dynamics is proving to be much challenging. In this talk, I will discuss recent advances in simulating dynamics by using a multitude of approaches, ranging from repeated state compression approaches (pt-VMC), discussing global optimisation ones that yield the full solution with a single optimisation problem, and finishing with the variational representation of full 'Krylov-like' subspaces. Then, I will discuss our recent understanding of what is limiting those simulations, how this is related to the limits of Tensor Network methods, and what are the advantages of those neural-network based approaches.