Controlling nonergodicity in quantum many-body systems by reinforcement learning

Abstract: Finding optimal control strategies to suppress quantum thermalization for arbitrarily initial states, the so-called quantum nonergodicity control, is important for quantum information science and technologies. Previous control methods largely relied on theoretical model of the target quantum system, but invertible model approximations and inaccuracies can lead to control failures. We develop a model-free and deep-reinforcement learning (DRL) framework for quantum nonergodicity control. It is a machine-learning method with the unique focus on balancing exploration and exploitation strategies to maximize the cumulative rewards so as to preserve the initial memory in the time-dependent nonergodic metrics over a long stretch of time. We use the paradigmatic one-dimensional tilted Fermi-Hubbard system to demonstrate that the DRL agent can efficiently learn the quantum many-body system solely through the interactions with the environment. The optimal policy obtained by the DRL provides broader control scenarios for managing nonergodicity in the phase diagram as compared to, e.g., the specific protocol for Wannier-Stark localization. The continuous control protocols and observations are experimentally feasible. The model-free nature of DRL and its versatile search space for control functions render promising nonergodicity control in more complex quantum many-body systems.