Accessing theoretically the ground state of interacting quantum matter is a long-standing challenge, especially for complex two-dimensional systems. Recent developments have highlighted the potential to solve the quantum many-body problem by means of so-called neural quantum states. The enabling idea of this approach is to harness the power of machine learning by encoding the many-body wave function into an artificial neural network. In this talk, I will aim at introducing the main idea and central developments of this computational approach. In particular, I will outline one of the critical limitations, which until recently has prohibited the training of modern large-scale deep network architectures. I will show how this key limitation has been now resolved through the so-called minimum-step stochastic reconfiguration method. I will demonstrate for paradigmatic frustrated quantum magnets that this enables the neural quantum states method to reach regimes and accuracies beyond what is accessible by other computational approaches. Further, I will highlight the recent results on solving the real-time dynamics of correlated quantum matter, which has allowed us to verify for instance for the first time the quantum Kibble-Zurek mechanism for interacting quantum many-body systems in two spatial dimensions.
