Periodic Reporting for period 3 - mlQuDyn (Machine learning quantum dynamics) Reporting period: 2022-01-01 to 2023-06-30 Summary of the context and overall objectives of the project A key scope of quantum many-body theory is the identification of universal behavior in quantum matter. 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. However, the theoretical description of such nonequilibrium quantum states has remained a key challenge. Within the mlQuDyn project it is the central goal to progress at this intriguing frontier using a crossdisciplinary approach at the interface between quantum many-body theory and machine learning. The enhanced understanding obtained within this research program will not only provide insights into fundamental open questions concerning the theoretical understanding of quantum many-body systems but also enhance the predictive power of quantum theory for experiments.The central element of the approach utilized in mlQuDyn 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. Work performed from the beginning of the project to the end of the period covered by the report and main results achieved so far The key goal of the project mlQuDyn is to take the theoretical understanding and predictive power of quantum many-body theory to a new level by a crossdisciplinary approach at the interface between quantum dynamics and machine learning. Concretely, this means to provide a new route to the outstanding challenge of solving Schrödinger’s equation, the fundamental equation of quantum mechanics, for systems composed out of many particles in the regime of two spatial dimensions by means of artificial neural networks. In this context we have achieved central progress along various axes.This progress includes technological advances in the context of novel powerful machine learning methods for the description of the dynamics in interacting quantum matter. As a key result within the mlQuDyn we have identified critical algorithmic improvements making our machine learning approaches competitive or even superior to state of the art computational methods. This has allowed us to target physical questions which have so far been out of reach. For instance we have been able to verify for the first time the universal dynamical behavior in celebrated quantum Kibble-Zurek mechanism for interacting quantum matter beyond one spatial dimension, the phase-ordering kinetics of the so-called many-body localized spin glass order, or disorder-free localization in interacting two-dimensional quantum matter. Overall, these examples demonstrate that we have been able to explore yet inaccessible theoretical phenomena and universal dynamical behavior in quantum matter. In quite some parts we have been able to go even beyond what has been initially planned and the developments have exceeded our own expectations. Progress beyond the state of the art and expected potential impact (including the socio-economic impact and the wider societal implications of the project so far) Within mlQuDyn we have shifted the frontier of dynamics in interacting quantum matter for quantum theory beyond state of the art approaches in particular concerning two-dimensional quantum systems. These fundamental methodological advances have resulted from developing critical algorithmic improvements, which we demonstrated successfully for a set of paradigmatic cases.Based on the methodological advances we have been able to explore and uncover novel dynamical universal behavior beyond what has been accessible before in quantum theory. For the remaining duration of mlQuDyn, we expect that these advances will provide access to fundamental open questions and outstanding challenges in the field of dynamics in interacting quantum matter. This includes a broad range of dynamical phenomena ranging from the emergence of hydrodynamics in the long-time evolution of nonequilibrium quantum matter to spectral functions of frustrated magnets in the regime of linear response.It is essential to recognize that the dynamics of quantum matter in two dimensions is not only central for theoretical considerations. Such systems rather constitute the key scope at the experimental front such as in the context of Rydberg atom arrays. Consequently, we expect that our advances will facilitate also collaborations with experimental teams to fully exploit the advanced predictive power of quantum theory obtained from mlQuDyn. Spatiotemporal build-up of many-body localized spin-glass order in a random quantum Ising model.
