Universal KPZ scaling in noisy hybrid quantum circuits

Abstract: Measurement-induced phase transitions (MIPT) have attracted increasing attention due to the rich phenomenology of entanglement structures and their relation with quantum information processing. Since physical systems are unavoidably coupled to environment, quantum noise needs be considered in analyzing a system with MIPT, which may qualitatively modify or even destroy certain entanglement structure of the system. In this Letter, we investigate the effect of quantum noise modeled by reset quantum channel acting on each site with probability $q$ on MIPT. Based on the numerical results from the Clifford circuits, we show that the quantum noise can qualitatively change the entanglement properties - the entanglement obeys area law'' instead ofvolume law'' with projective measurement rate $p<p_{c}$. In the quantum noise induced area law'' phase, the entanglement exhibits a novel $q^{-1/3}$ power-law scaling. Using an analytic mapping of the quantum model to a classical statistical model, we further show that thearea law'' entanglement is the consequence of the noise-driven symmetry-breaking field and the $q^{-1/3}$ scaling can be understood as the result of Kardar-Parisi-Zhang (KPZ) fluctuations of the directed polymer with an effective length scale $L_{\rm{eff}} \sim q^{-1}$ in a random environment.