Stabilizer simulations of measurement- and feedback-induced entanglement transition in the probabilistic control of chaos

In recent work on measurement-induced phase transitions, measurements interspersed with unitary evolution leads to a dynamical phase transition where entanglement is volume-law for low rates of measurements and area-law for high measurement rates. However, naive post-selection arguments estimate that viewing the transition experimentally requires more than the lifetime of the universe. Inspired by a classical model in the theory of chaotic dynamics in which a system's dynamics can be "controlled" (a classical dynamic phase transition), we construct dynamics within stabilizer circuits that experience control onto a specific state while also experiencing a similar entanglement transition. In this "quantum Bernoulli map," the transition into the phase in which entanglement is lost is heralded by an operator that acts as an order parameter for the transition. As such, an experiment could probe this transition without post-selection. We present data on larger system sizes than can be accomplished with exact methods, building on our previous work on a similar model.