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 undergoes one of three distinct measurement-induced phase transitions, including continuous transitions within two universality classes which have not been previously observed in quantum hybrid systems as well as a first-order transition.