This study investigates the effects of both temporally uncorrelated and correlated quantum noises on entanglement generation and information protection in noisy hybrid quantum circuits. The research reveals that entanglement within the system scales as $ q^{-1/3} $ for both types of noise, where $ q $ is the noise probability. This scaling arises from the Kardar-Parisi-Zhang (KPZ) fluctuation with an effective length scale $ L_{eff} \sim q^{-1} $. The information protection timescales for steady states are found to scale as $ q^{-1/2} $ for temporally uncorrelated noise and $ q^{-2/3} $ for correlated noise. The former corresponds to the Hayden-Preskill protocol, while the latter is a direct consequence of KPZ fluctuations. The study uses extensive numerical simulations with the stabilizer formalism to support these findings. The results contribute to a deeper understanding of the interplay between quantum noises and measurement-induced phase transitions, and provide new insights into the effects of Markovian and non-Markovian noises on quantum computation. The study also demonstrates that the presence of quantum noises can be treated as a symmetry-breaking field in the effective statistical model, leading to a single area-law entanglement phase and the disappearance of MIPT with infinitesimal noise strength. The findings highlight the differences in the effects of temporally correlated and uncorrelated quantum noises on information protection, which are crucial for quantum error correction and mitigation. The study also shows that the information protection process can be understood as a Hayden-Preskill protocol, where the steady state is regarded as a black hole and the encoded information is destroyed by throwing it into the black hole. The timescale of information protection corresponds to the time required for a quantum noise with probability $ q $ to appear in the light cone of the encoded information with area $ O(t^2) $, resulting in a timescale of $ q^{-1/2} $. The study also provides a comprehensive analytical understanding of the impacts of quantum noises with different temporal correlations on entanglement generation and information protection, showing that the mutual information satisfies the scaling $ q^{-1/3} $ for both types of noise, while the timescale of information protection for temporally uncorrelated and correlated noise is $ q^{-1/2} $ and $ q^{-2/3} $, respectively. The results are supported by numerical simulations and are consistent with theoretical predictions. The study also highlights the importance of understanding the effects of quantum noises on information protection in noisy hybrid quantum circuits, which is essential for quantum error correction and mitigation.This study investigates the effects of both temporally uncorrelated and correlated quantum noises on entanglement generation and information protection in noisy hybrid quantum circuits. The research reveals that entanglement within the system scales as $ q^{-1/3} $ for both types of noise, where $ q $ is the noise probability. This scaling arises from the Kardar-Parisi-Zhang (KPZ) fluctuation with an effective length scale $ L_{eff} \sim q^{-1} $. The information protection timescales for steady states are found to scale as $ q^{-1/2} $ for temporally uncorrelated noise and $ q^{-2/3} $ for correlated noise. The former corresponds to the Hayden-Preskill protocol, while the latter is a direct consequence of KPZ fluctuations. The study uses extensive numerical simulations with the stabilizer formalism to support these findings. The results contribute to a deeper understanding of the interplay between quantum noises and measurement-induced phase transitions, and provide new insights into the effects of Markovian and non-Markovian noises on quantum computation. The study also demonstrates that the presence of quantum noises can be treated as a symmetry-breaking field in the effective statistical model, leading to a single area-law entanglement phase and the disappearance of MIPT with infinitesimal noise strength. The findings highlight the differences in the effects of temporally correlated and uncorrelated quantum noises on information protection, which are crucial for quantum error correction and mitigation. The study also shows that the information protection process can be understood as a Hayden-Preskill protocol, where the steady state is regarded as a black hole and the encoded information is destroyed by throwing it into the black hole. The timescale of information protection corresponds to the time required for a quantum noise with probability $ q $ to appear in the light cone of the encoded information with area $ O(t^2) $, resulting in a timescale of $ q^{-1/2} $. The study also provides a comprehensive analytical understanding of the impacts of quantum noises with different temporal correlations on entanglement generation and information protection, showing that the mutual information satisfies the scaling $ q^{-1/3} $ for both types of noise, while the timescale of information protection for temporally uncorrelated and correlated noise is $ q^{-1/2} $ and $ q^{-2/3} $, respectively. The results are supported by numerical simulations and are consistent with theoretical predictions. The study also highlights the importance of understanding the effects of quantum noises on information protection in noisy hybrid quantum circuits, which is essential for quantum error correction and mitigation.