Universal KPZ scaling in noisy hybrid quantum circuits

TL;DR

This paper demonstrates that quantum noise can induce a universal area law entanglement phase in noisy hybrid quantum circuits, characterized by a KPZ scaling law, altering the typical entanglement behavior.

Contribution

It reveals a universal KPZ scaling law in the entanglement of noisy quantum circuits and connects quantum noise effects to classical statistical models.

Findings

Quantum noise induces an area law entanglement phase.

Entanglement exhibits a $q^{-1/3}$ power-law scaling.

Theoretical mapping to KPZ fluctuations explains the scaling law.

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 of ``volume 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 the ``area 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.