Machine Learning to Tailor Correlated States of Matter

• Applicants: Dr. Marin Bukov; Dr. Markus Schmitt
• Subject Area: Theoretical Condensed Matter Physics ; Optics, Quantum Optics and Physics of Atoms, Molecules and Plasmas
• Term: since 2024
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 544919793

The possibility to precisely manipulate and control artificial quantum systems constitutes the foundation of emerging quantum technologies. Rapid development in experimental capabilities is opening up unprecedented opportunities to exploit quantum resources for computation, scientific simulation, and sensing. Of particular interest for the field of correlated quantum matter is the emulation of theoretical models using microscopic degrees of freedom, that inherently behave quantum mechanically. However, our understanding of how to manipulate such systems using external drives is in its infancy, especially in the presence of strong interactions. We propose to overcome some of the current limitations by combining techniques from machine learning with ideas from quantum many-body physics. We will develop (1) simulation methods for periodically driven systems based on neural quantum states (NQS), and (2) a new interpretable framework for tensor-networks-based reinforcement learning (RL). To optimize control of quantum matter. In a final exploratory part of the project we will merge both efforts for NQS-based RL. At the heart of both parts of the project lies the idea to utilize suited compressed state representations, which will be key to reach large enough system sizes, where many-body effects become apparent. Floquet engineering by periodic drives is widely used to stabilize interesting states of matter in quantum simulators. Due to their capability to incorporate arbitrary neighborhood relations of physical degrees of freedom and to represent highly entangled states, NQS are a promising candidate to simulate real time dynamics in the presence of Floquet drives. Within the proposed project, we will pioneer the development of NQS techniques that incorporate the structure imposed by periodic drives in order to. Open up the notoriously difficult realms of two spatial dimensions (2D) and late times for numerical investigation. This will be instrumental to understand heating and state preparation in 2D quantum simulators, and it will allow us to investigate exotic states like discrete time crystals or Floquet-engineered topological states of matter. In the second part of the project, we relax the periodicity constraint on the control fields and consider manipulation by general control protocols. This poses the central challenge to identify optimal strategies out of exponentially many possibilities, where the power of RL comes into play. In combination with tensor networks, this will on the one hand render learning to control large-scale quantum many-body simulators feasible - a largely uncharted territory for non-integrable systems without exact analytical solutions. On the other hand, tensor networks impose physically interpretable structure, which can help us to reveal the principles underlying optimal control protocols, for example otherwise hard to identify effective degrees of freedom.

• DFG Programme: Research Grants