Measurement-induced criticality in $\mathbb{Z}_2$-symmetric quantum automaton circuits

Understand

We study entanglement dynamics in hybrid $\mathbb{Z}_2$-symmetric quantum automaton circuits subject to local composite measurements.

• We show that there exists an entanglement phase transition from a volume law phase to a critical phase by varying the measurement rate $p$.
• By analyzing the underlying classical bit string dynamics, we demonstrate that the critical point belongs to parity-conserving universality class.
• We further show that the critical phase with $p>p_c$ is related to the diffusion-annihilation process and is protected by the $\mathbb{Z}_2$-symmetric measurement.