Machine learning quantum dynamics
A key scope of quantum many-body theory is the identification of universal behavior in quantum matter, where macroscopic properties become independent of microscopic details. In recent years the quest for phases with novel universal properties has been revolutionized by forcing systems out of equilibrium, which has opened up a universe of unexplored phenomena and new dynamical paradigms. These developments not only hold the promise to theoretically uncover unrecognized universal dynamical behavior, but are also driven by the enormous advances in quantum simulators such as ultra-cold atoms, which have nowadays achieved unique capabilities in generating and probing such nonequilibrium quantum states. Still, their theoretical description is facing severe challenges. It is the aim of this proposal to take the theoretical understanding and predictive power of quantum many-body theory to a new level by an crossdisciplinary approach at the interface between quantum dynamics and machine learning. 

The central element of this approach is to encode time-evolved quantum states into artificial neural networks, which have been remarkably successful in storing and recognizing complex structures in computer science. In order to reach the main goal we have identified three main challenges which form the core of the program: (i) to design efficient artificial network structures based on fundamental principles of quantum many-body systems such as locality and causality; (ii) to utilize concepts of many-body theory and statistical physics to understand the physical properties of artificial neural networks; (iii) to explore fundamental but yet inaccessible dynamical quantum phenomena and universal behavior in quantum dynamics. The successfully conducted research program will lift the description and understanding of quantum many-body dynamics to a new level, impacting significantly both quantum theory as well as future experiments.