Entanglement structure in the volume-law phase of hybrid quantum automaton circuits

We study entanglement fluctuations and quantum error correction in the weakly monitored volume-law phase of automaton circuits subject to repeated local measurements. numerically observe that entropy exhibits strong fluctuation with exponent close ``growth exponent'' Kardar-Parisi-Zhang (KPZ) universality class, same as other random studied previously. also investigate dynamically generated code purification process show this model has different contiguous distances for two types errors exhibit similar sublinear power-law scaling. give an interpretation these results by mapping them various quantities a classical particle model. demonstrate subleading term scaling distance are both emergent phenomena hybrid dynamics. Finally, we dynamics itself type ability can generate linear code.