A particular ingredient that facilitated a lot of the recent progress in the field of complex quan- tum systems away from equilibrium was the ability to perform numerical simulations of the non- equilibrium dynamics, because the model systems of interest are generally not solvable otherwise. Particularly notable are tensor network algorithms, which today constitute the method of choice for the numerically exact simulation of quantum many-body dynamics in low dimensions. However, experimental advances on quantum simulators substantially increase the coherence times and push towards non-equilibrium dynamics in two spatial dimensions; thereby, they enter regimes in which tensor network methods face serious limitations.

A primary goal of my ongoing and future research is to develop novel computational techniques based on neural network quantum states to enable the versatile and efficient simulation of quantum many-body dynamics that is observed in modern quantum simulators. This idea was recently proposed in a pioneering work by Carleo and Troyer [Science 355, 602 (2017)]. While this work relied on the general representability theorems, we showed in a first analytical work specifically that at least in a perturbative regime time-evolved wave functions can efficiently be encoded in neural networks [1]. Subsequently, again in collaboration with Dr. Markus Heyl, I was able to overcome some severe limitations in the numerical approach to compute time evolution using neural network wave functions. With the resulting highly parallelized algorithm we demonstrated in paradigmatic test cases with generic parameters that this new approach outperforms state of the art methods for dynamics in two dimensions [2]. Moreover, supplementing the perturbative networks introduced in Ref. [1] with a time-dependent variational principle our collaboration of current and former members of the group of Markus Heyl most recently resulted in the first observation of an intriguing type of non-ergodic behavior in an interacting two-dimensional lattice gauge theory [3].

[1] M. Schmitt and M. Heyl, Quantum dynamics in transverse-field Ising models from classical networks, SciPost Phys. 4, 013 (2018)

[2] M. Schmitt and M. Heyl, Quantum many-body dynamics in two dimensions with artificial neural networks, arXiv:1912.08828

[3] P. Karpov, R. Verdel, Y.-P. Huang, M. Schmitt and M. Heyl, Disorder-free localization in an interacting two-dimensional lattice gauge theory, arXiv:2003.04901

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