Noise-induced phase transitions in hybrid quantum circuits

The presence of quantum noises inherent to real physical systems can strongly impact the physics in hybrid quantum circuits with local random unitaries and mid-circuit measurements. The quantum noises with a size-independent occurring probability 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 $\alpha$ represents the scaling exponent. We have identified a noise-induced entanglement phase transition from a volume law to a power (area) law in the presence (absence) of measurements as $p$ increases when $\alpha=1$. With the help of an effective statistical model, we reveal that the phase transition is of 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 further deepens the understanding of the connection between entanglement behavior and the capacity of information protection. When $\alpha \neq 1$, one spin configuration always dominates regardless of $p$ and thus the phase transition disappears. Moreover, we highlight the difference between the effects of size-dependent bulk noise and boundary noises. We validate our analytical predictions with extensive numerical results from stabilizer circuit simulations.