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 constrained update rules. We numerically find via large-scale simulations that, depending on the constrained update rules, the system may undergo several measurement-induced entanglement transitions, including continuous transitions, as well as a second phase transition which we interpret using a biased random walk picture.