Universal Kardar-Parisi-Zhang scaling in noisy hybrid quantum circuits

Abstract

Measurement-induced phase transitions (MIPTs) 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, which can qualitatively modify or even destroy certain entanglement structure, needs to be considered in analyzing a system with MIPT. In this Letter, we investigate the effect of quantum noise modeled by a reset quantum channel acting on each site with a probability $q$ on MIPT. Based on the numerical results from Clifford circuits, we show that the quantum noise can qualitatively change the entanglement properties---the entanglement obeys ``area law'' instead of ``volume law'' with a measurement rate $p<{p}_{c}$. In the noise-induced area law phase, the entanglement exhibits a novel ${q}^{\ensuremath{-}1/3}$ power-law scaling. Using an analytic mapping from the quantum model to a classical statistical model, we further show that the area law entanglement is the consequence of noise-driven symmetry-breaking field, and the ${q}^{\ensuremath{-}1/3}$ scaling can be understood as the result of Kardar-Parisi-Zhang fluctuations of directed polymer with an effective length scale ${L}_{\mathrm{eff}}\ensuremath{\sim}{q}^{\ensuremath{-}1}$ in a random environment.