The key goal of the project mlQuDyn has been 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. In the following, we would like to highlight the three most important contributions, while emphasizing that overall many further important results have been achieved.
We have been able to verify for the first time the theoretically proposed universal dynamical behavior in the celebrated quantum Kibble-Zurek mechanism for interacting quantum matter beyond one spatial dimension. This work has been published in Science Advances.
Based on the advances achieved during the execution of the mlQuDyn project, we have been able to provide the theoretical data to construct for the first time so-called wave function networks for quantum many-body states. We have shown that these networks can becomes scale-free in the vicinity of continuous phase transitions, lifting the concept of universality to a new level
A further milestone in our project mlQuDyn has been the invention of what we called the minimum-step stochastic reconfiguration algorithm (minSR), which has been published in Nature Physics. With minSR we have revolutionized the training of the underlying artificial neural networks, pushing our method to a new level. Now it has become possible to numerically solve some of the most challenging quantum many-body problems such as frustrated quantum magnets at an unprecedented level.
Overall, these examples demonstrate that we have been able to push quantum theory to so far inaccessible regimes, which even goes beyond what has been initially planned exceeding our own initial expectations.
