This thesis lies at the intersection of quantum machine learning and tensor network methods, focusing on the simulation, benchmarking, and control of many-body quantum systems.
This thesis is devoted to the application of tensor-network methods to problems in quantum many-body physics in one and two dimensions and in machine learning. It contributes to the theory of infinite dimensional tensor networks giving rise to critical or fractional quantum Hall lattice models. The power of artificial neural networks at representing such states is investigated both analytically and numerically, and connections with tensor networks are uncovered, with applications both in the study of quantum states and in machine learning.