Neural network enhanced hybrid quantum many-body dynamics

Computing dynamical properties in quantum many-body systems represents one of the paradigmatic open problems in theoretical condensed matter physics. Despite the existence of different techniques both in real-time and frequency space, computational limitations often dramatically constrain the physical regimes in which quantum many- body dynamics can be solved. Here we show [1] that the combination of machine learning methods and complementary many-body tensor network techniques substantially decreases the computational cost of quantum many-body dynamics. We demonstrate that combining kernel polynomial techniques [2] and real-time evolution, together with deep neural networks, allows to compute dynamical quantities faithfully. We show that this hybrid neural-network many-body algorithm can efficiently extrapolate dynamics in the presence of numerical noise, learning to detect defective data and correcting it. Ultimately, our results provide a starting point towards adversarial neural-network algorithms for predicting quantum many-body dynamics that could potentially solve computationally expensive many-body systems in a more efficient manner.

[1] R. Koch and J. L. Lado, in preparation (2021)
[2] W. Alexander, et al. "The kernel polynomial method." Rev. Mod. Physik 78.1 (2006): 275.