Temporal Griffiths effects and ultrafast criticality in monitored quantum circuits

We investigate quantum circuits with temporally random measurement rates, uncovering a rich dynamical phase diagram that deviates significantly from conventional measurement-driven transitions. Our primary discovery is that any spatially-uniform randomness in the measurement rate destabilizes the typical volume-law entangled phase, leading to the emergence of novel temporal Griffiths regions. This destabilization gives rise to a new phase marked by sub-volume steady-state entanglement scaling. At the critical point, we identify striking ultrafast dynamics, reflected in an activated scaling relation t^Ψ_τ ~ log(L), corresponding to a vanishing space-time dynamical exponent z→0. This behavior can be understood as a space-time rotation of the infinite-randomness fixed point seen in spatially random models. Through extensive numerical simulations of stabilizer circuits, we analyze information propagation and entanglement dynamics, offering a comprehensive physical understanding of this novel phase diagram and its criticality.