Measurement-induced phase transitions in (d+1) -dimensional stabilizer circuits

The interplay between unitary dynamics and local quantum measurements results in unconventional nonunitary dynamical phases and transitions. In this paper we investigate the dynamics of (d+1)-dimensional hybrid stabilizer circuits, for d=1,2,3. We characterize the measurement-induced phases and their transitions using large-scale numerical simulations focusing on entanglement measures, purification dynamics, and wave-function structure. Our findings demonstrate the measurement-induced transition in (d+1) spatiotemporal dimensions is conformal and has critical properties close to the percolation transition in (d+1) spatial dimensions.