Periodic Reporting for period 4 - mlQuDyn (Machine learning quantum dynamics)
Okres sprawozdawczy: 2023-07-01 do 2025-06-30
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 has not only provided insights into fundamental open questions concerning the theoretical understanding of quantum many-body systems but also enhanced significantly the predictive power of quantum theory for experiments.
The central element of the approach utilized in mlQuDyn has been 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 have formed 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. Our research program has lifted the description and understanding of quantum many-body dynamics to a new level, impacting significantly both quantum theory as well as future experiments.
The central element of the approach utilized in mlQuDyn has been 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 have formed 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. Our research program has lifted the description and understanding of quantum many-body dynamics to a new level, impacting significantly both quantum theory as well as future experiments.
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.
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.
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 matter, as they have emerged as a current frontier in theoretical and experimental quantum physics research. These fundamental methodological advances have resulted from developing critical algorithmic improvements, which we demonstrated successfully for a set of so far inaccessible dynamical problems.
Based on the methodological advances we have been able to explore and uncover novel dynamical universal behavior far beyond what has been accessible in quantum theory before. In this way we have been able to 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 paradigmatic Kibble-Zurek mechanism to spectral functions of quantum magnets.
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 frontier 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.
Based on the methodological advances we have been able to explore and uncover novel dynamical universal behavior far beyond what has been accessible in quantum theory before. In this way we have been able to 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 paradigmatic Kibble-Zurek mechanism to spectral functions of quantum magnets.
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 frontier 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.