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

Understanding the transition between order and chaos is a fundamental challenge in physics. While classical systems often exhibit a mixed phase space—where regular and chaotic trajectories coexist—the existence of an analogous structure in interacting quantum many-body systems has remained elusive. This study investigates whether such a mixed phase space can be identified and controlled in a programmable superconducting quantum processor.

The authors implement a hybrid quantum-classical feedback protocol on a 24-qubit superconducting processor. The system is modeled as an interacting Su-Schrieffer-Heeger (SSH) ladder, which can be tuned between integrable and chaotic regimes. The protocol alternates between short-time quantum evolution and classical optimization, which projects the system's state back onto a low-entanglement variational manifold. By measuring the subsystem imbalance—a proxy for state fidelity—the researchers map the dynamics across the variational parameter space, effectively creating a quantum many-body version of a Poincare section.

The study demonstrates that the hybrid feedback protocol can successfully isolate and stabilize coherent, periodic trajectories within a sea of chaotic evolution. The experimental results show a clear contrast: initial states within the identified regular islands exhibit long-lived, coherent oscillations with pronounced revivals, while states in the chaotic regions thermalize rapidly. This confirms the existence of a quantum many-body mixed phase space, which arises from the nonlinear geometry of the variational manifold and many-body correlations, rather than from a conventional classical limit.