My PhD thesis presents three applications of machine learning to condensed matter theory. Firstly, I will explain how the problem of detecting phase transitions can be rephrased as an image classification task, paving the way to the automatic mapping of phase diagrams. I tested the reliability of this approach and showed its limits for models exhibiting a many-body localized phase in 1 and 2 dimensions. Secondly, I will introduce a variational representation of quantum many-body ground-states in the form of neural-networks and show our results on a constrained model of hardcore bosons in 2d using variational and projection methods. In particular, we confirmed the phase diagram obtained independently earlier and extends its validity to larger system sizes. Moreover we also established the ability of neural-network quantum states to approximate accurately solid and liquid bosonic phases of matter. Finally, I will present a new approach to quantum error correction based on the same techniques used to conceive the best Go game engine. We showed that efficient correction strategies can be uncovered with evolutionary optimization algorithms, competitive with gradient-based optimization techniques. In particular, we found that shallow neural-networks are competitive with deep neural-networks.
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