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.