Entanglement Dynamics in Hybrid Quantum Circuits

The central philosophy of statistical mechanics (stat-mech) and random-matrix theory complex systems are that while individual instances essentially intractable to simulate, the properties random ensembles obey simple universal “laws.” This same promises powerful methods for studying dynamics quantum information in ideal noisy circuits—for which classical description circuits is expected be generically intractable. Here, we review recent progress understanding circuits, through a stat-mech lens. We begin by reviewing discoveries features entanglement growth, operator spreading, thermalization, chaos unitary their relation problems surface growth hydrodynamics. then explore monitored can loosely thought as arising from an environment monitoring system, exhibit new types measurement-induced phases criticality. Throughout, attempt give pedagogical introduction various technical highlight emerging connections between concepts stat-mech, information, communication theory.