Measurement induced phase transitions in quantum raise and peel models

We present a quantum circuit model which emulates the interface growth of the classical raise-and-peel model. Our model consists of Clifford unitary gates interspersed with projective measurements, applied according to prescribed feedback rules. We numerically find via large-scale simulations that, depending on the feedback rules, the system may undergo several measurement-induced entanglement transitions, including continuous transitions within a universality class not previously observed in hybrid random Clifford systems as well as a first-order transition.