This paper investigates the effects of quantum noises on entanglement generation and information protection in noisy hybrid quantum circuits. The authors present a comprehensive theoretical analysis, focusing on both temporally uncorrelated and correlated quantum noises. They find that entanglement within the system follows a $q^{-1/2}$ scaling for both types of noise, where $q$ is the noise probability. The scaling arises from the Kardar-Parisi-Zhang (KPZ) fluctuation with an effective length scale $L_{\text{eff}} \sim q^{-1}$. Additionally, the information protection timescales of the steady states are explored, showing $q^{-1/2}$ and $q^{-2/3}$ scaling for temporally uncorrelated and correlated noises, respectively. The former scaling is interpreted as a Hayden-Preskill protocol, while the latter is a direct consequence of KPZ fluctuations. Extensive numerical simulations using the stabilizer formalism support these theoretical findings. The study not only deepens the understanding of the interplay between quantum noises and measurement-induced phase transitions but also provides new insights into the effects of Markovian and non-Markovian noises on quantum computation.This paper investigates the effects of quantum noises on entanglement generation and information protection in noisy hybrid quantum circuits. The authors present a comprehensive theoretical analysis, focusing on both temporally uncorrelated and correlated quantum noises. They find that entanglement within the system follows a $q^{-1/2}$ scaling for both types of noise, where $q$ is the noise probability. The scaling arises from the Kardar-Parisi-Zhang (KPZ) fluctuation with an effective length scale $L_{\text{eff}} \sim q^{-1}$. Additionally, the information protection timescales of the steady states are explored, showing $q^{-1/2}$ and $q^{-2/3}$ scaling for temporally uncorrelated and correlated noises, respectively. The former scaling is interpreted as a Hayden-Preskill protocol, while the latter is a direct consequence of KPZ fluctuations. Extensive numerical simulations using the stabilizer formalism support these theoretical findings. The study not only deepens the understanding of the interplay between quantum noises and measurement-induced phase transitions but also provides new insights into the effects of Markovian and non-Markovian noises on quantum computation.