Quantum many-body mixed phase space revealed by hybrid feedback control

Abstract Understanding how complex systems transition between order and chaos is a central challenge of non-equilibrium physics. Although weak perturbations of classical integrable systems give rise to a mixed phase space in which regular and chaotic trajectories coexist, analogous behaviour in interacting quantum many-body systems has been difficult to identify. Here we develop and experimentally implement a hybrid quantum–classical feedback protocol that autonomously discovers and stabilizes long-lived regular trajectories in a superconducting quantum processor. Each iteration combines short-time quantum evolution with classical optimization that projects the dynamics back onto a low-entanglement variational manifold, effectively distilling coherence from chaotic evolution. The stabilized trajectories reveal signatures of a quantum many-body mixed phase space emerging from nonlinear variational dynamics, without a direct analogue in few-body quantum systems described by a small number of effective degrees of freedom. Our results establish a framework for the algorithmic identification and control of coherent dynamics in quantum many-body systems.