Learning to stabilize nonequilibrium phases of matter with active feedback using partial information

Abstract Recent advances in quantum computing experiments have enabled new pathways for feedback control. Here, we investigate the role of information in interactive quantum many-body dynamics to engineer out-of-equilibrium phases of matter. To this end, we train reinforcement learning agents to prevent entanglement spreading in $(1{+}1)$-dimensional stabilizer circuits with up to $128$ qubits. We find that, above an information threshold, agents learn stochastic near-optimal strategies that prevent the system from reaching volume-law entangled states and instead stabilize area-law scaling. These strategies rely on bottlenecks that divide the system and cap the entanglement in the steady state. Crucially, learned strategies are inherently out of equilibrium, require real-time active feedback, and could not be reproduced by simple human-designed control rules. This work establishes the foundations for information-driven individual control of many interacting quantum degrees of freedom, demonstrating the capabilities of reinforcement learning to stabilize and uncover novel critical properties of many-body nonequilibrium steady states.