Periodic Reporting for period 3 - mlQuDyn (Machine learning quantum dynamics)
Periodo di rendicontazione: 2022-01-01 al 2023-06-30
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.
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.
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.