Laboratoire de Physique Théorique
Toulouse - UMR 5152

I will present 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 [1]. I tested the reliability of this approach and showed its limits for models exhibiting a many-body localized phase in 1 and 2 dimensions [2,3]. Secondly, I will introduce a variational representation of quantum many-body ground-states in the form of neural-networks [4] 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 [5] 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 [6,7]. We showed that efficient correction strategies can be uncovered with evolutionary optimization algorithms [8], competitive with gradient-based optimization techniques. In particular, we found that shallow neural-networks are competitive with deep neural-networks.

[1] Carrasquilla, J., Melko, R.G., 2017. Machine learning phases of matter. Nature Physics 13, 431–434.

[2] TH, Alet, F., 2019. Neural network setups for a precise detection of the many-body localization transition : Finite-size scaling and limitations. Phys. Rev. B 100, 224202.

[3] TH, Lan, Z., Meyer, G., Alet, F., 2020. Transition to a many-body localized regime in a two-dimensional disordered quantum dimer model. Phys. Rev. Research 2, 033154.

[4] Carleo, G., Troyer, M., 2017. Solving the quantum many-body problem with artificial neural networks. Science 355, 602–606.

[5] Tay, T., Motrunich, O.I., 2010. Study of a hard-core boson model with ring-only interactions. Physical Review Letters 105.

[6] Silver, D. et al., 2016. Mastering the game of Go with deep neural networks and tree search. Nature 529, 484–489.

[7] Sweke, R., Kesselring, M.S., van Nieuwenburg, E.P.L., Eisert, J., 2018. Reinforcement Learning Decoders for Fault-Tolerant Quantum Computation. arxiv

[8] Stanley, K.O., Miikkulainen, R., 2002. Evolving neural networks through augmenting topologies. Evol. Comput. 10, 99–127.