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 quantum automaton circuits subject to repeated local measurements. We numerically observe that the entanglement entropy exhibits strong fluctuation belonging to the Kardar-Parisi-Zhang (KPZ) universality class, the same as other local random circuits studied previously. We also investigate the dynamically generated quantum error correction code in the purification process and show that this model has different contiguous code distances for two types of errors. We give an interpretation of these results by mapping them to various quantities in a classical particle model. Finally, we show that this classical particle dynamics itself has a type of error correction ability, and can dynamically generate a classical linear code.