Noise-induced phase transitions in hybrid quantum circuits Quantum noises inherent to real physical systems can significantly impact the physics of hybrid quantum circuits with local random unitaries and mid-circuit measurements. Quantum noises with size-independent occurrence probabilities can lead to the disappearance of a measurement-induced entanglement phase transition and the emergence of a single area-law phase. In this work, we investigate the effects of quantum noises with size-dependent probabilities $ q = p/L^{\alpha} $, where $ \alpha $ is the scaling exponent. We identify a noise-induced entanglement phase transition from a volume law to a power (area) law in the presence (absence) of measurements when $ \alpha = 1 $. Using an effective statistical model, we reveal that the phase transition is first-order, arising from the competition between two types of spin configurations and shares the same analytical understanding as the noise-induced coding transition. This unified picture deepens the understanding of the connection between entanglement behavior and information protection capacity. When $ \alpha \neq 1 $, one spin configuration always dominates regardless of $ p $, and the phase transition disappears. We highlight the difference between the effects of size-dependent bulk noise and boundary noises. Our analytical predictions are validated with extensive numerical results from stabilizer circuit simulations. The presence of quantum noises in real experimental quantum systems introduces environmental coupling, which can disrupt entanglement phase transitions. In the effective statistical model for random quantum circuits, quantum noises can be treated as symmetry-breaking fields that result in the disappearance of the entanglement phase transition and a single area-law entanglement phase regardless of the measurement probability. The MIPT from a power law phase to an area law phase with fixed quantum noises at the spatial boundaries has been investigated, which can be regarded as a special case of quantum noises with size-dependent probabilities $ q = 2/L $. Additionally, the effects of quantum noises or T gates in the bulk with size-dependent probabilities $ q = p/L $ have been explored in the context of random circuit sampling and non-stabilizerness transition. However, the investigation of the entanglement phase transition in the MIPT setup with bulk quantum noises of size-dependent probability is lacking. Moreover, the entanglement structures and critical behaviors associated with quantum noises of size-dependent probabilities, as well as the influence of different choices of scaling exponents $ \alpha $, are also worth studying. The entanglement structure and information protection capacity are closely related. From the perspective of information protection, a spatial boundary and a temporal boundary noise-induced coding transition both occur. Below a finite critical probability of boundary noise, the encoded information can be protected after a hybrid evolution of time $ O(L) $. On the contrary, if the probability of boundary noise exceeds this critical value, the information will be destroyed by quantum noises. A similar noise-induced coding transition is anticipated in the presence of bulk quantum noise with probability $ q = p/L $, but the differencesNoise-induced phase transitions in hybrid quantum circuits Quantum noises inherent to real physical systems can significantly impact the physics of hybrid quantum circuits with local random unitaries and mid-circuit measurements. Quantum noises with size-independent occurrence probabilities can lead to the disappearance of a measurement-induced entanglement phase transition and the emergence of a single area-law phase. In this work, we investigate the effects of quantum noises with size-dependent probabilities $ q = p/L^{\alpha} $, where $ \alpha $ is the scaling exponent. We identify a noise-induced entanglement phase transition from a volume law to a power (area) law in the presence (absence) of measurements when $ \alpha = 1 $. Using an effective statistical model, we reveal that the phase transition is first-order, arising from the competition between two types of spin configurations and shares the same analytical understanding as the noise-induced coding transition. This unified picture deepens the understanding of the connection between entanglement behavior and information protection capacity. When $ \alpha \neq 1 $, one spin configuration always dominates regardless of $ p $, and the phase transition disappears. We highlight the difference between the effects of size-dependent bulk noise and boundary noises. Our analytical predictions are validated with extensive numerical results from stabilizer circuit simulations. The presence of quantum noises in real experimental quantum systems introduces environmental coupling, which can disrupt entanglement phase transitions. In the effective statistical model for random quantum circuits, quantum noises can be treated as symmetry-breaking fields that result in the disappearance of the entanglement phase transition and a single area-law entanglement phase regardless of the measurement probability. The MIPT from a power law phase to an area law phase with fixed quantum noises at the spatial boundaries has been investigated, which can be regarded as a special case of quantum noises with size-dependent probabilities $ q = 2/L $. Additionally, the effects of quantum noises or T gates in the bulk with size-dependent probabilities $ q = p/L $ have been explored in the context of random circuit sampling and non-stabilizerness transition. However, the investigation of the entanglement phase transition in the MIPT setup with bulk quantum noises of size-dependent probability is lacking. Moreover, the entanglement structures and critical behaviors associated with quantum noises of size-dependent probabilities, as well as the influence of different choices of scaling exponents $ \alpha $, are also worth studying. The entanglement structure and information protection capacity are closely related. From the perspective of information protection, a spatial boundary and a temporal boundary noise-induced coding transition both occur. Below a finite critical probability of boundary noise, the encoded information can be protected after a hybrid evolution of time $ O(L) $. On the contrary, if the probability of boundary noise exceeds this critical value, the information will be destroyed by quantum noises. A similar noise-induced coding transition is anticipated in the presence of bulk quantum noise with probability $ q = p/L $, but the differences