  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 with the exponent close to the ``growth exponent''
of 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
that exhibit similar sublinear power-law scaling. We give an interpretation of
these results by mapping them to various quantities in a classical particle
model. We demonstrate that the subleading correction term of the entanglement
entropy and the sublinear power-law scaling of the contiguous code distance in
the volume-law phase are both the emergent phenomena of the hybrid random
dynamics. Finally, we show that this classical particle dynamics itself has a
type of error correction ability and can dynamically generate a classical
linear code.
