Measurement-induced criticality in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi mathvariant="double-struck">Z</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:math> -symmetric quantum automaton circuits

We study entanglement dynamics in hybrid ${\mathbb{Z}}_{2}$-symmetric quantum automaton circuits subject to local composite measurements. show that there exists an phase transition from a volume-law critical by varying the measurement rate $p$. By analyzing underlying classical bit-string dynamics, we demonstrate point belongs parity-conserving universality class. further with $p&gt;{p}_{c}$ is related diffusion-annihilation process and protected measurement. give interpretation of entropy terms two-species particle model identify coefficient front logarithmic scaling as persistent coefficient. The behavior observed at $p\ensuremath{\ge}{p}_{c}$ associated dynamical exponents are also confirmed purification dynamics.