Abstract
Mid-circuit measurements and feedback operations conditioned on their outcomes are essential primitives for realizing quantum error correction on modern quantum hardware. When incorporated into quantum many-body dynamics, these non-unitary operations can drive novel non-equilibrium phase transitions—both in the dynamics of individual quantum trajectories and in the ensemble-averaged quantum channel. The well-known measurement-induced entanglement transition belongs to the former category. In this talk, I will introduce a class of adaptive random-circuit models with feedback that exhibit phase transitions in both settings. By mapping the feedback-driven dynamics to classical stochastic processes, we show that the resulting absorbing-state transition falls into either the parity-conserving or directed-percolation universality class, depending on the feedback protocol. In the second part, I will present experimental results from a superconducting quantum processor featuring high-fidelity mid-circuit measurements and low-latency conditional feedback, where we directly observe the coexistence of measurement-induced entanglement and absorbing-state transitions.