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 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 $L_{\mathrm{eff}}\sim q^{-1}$ in a random environment.

4.5 pages + references + supplemental, 4 figures

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Cited by in corpus (29)

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• Zero-temperature entanglement membranes in quantum circuits
• Symmetry Breaking Dynamics in Quantum Many-Body Systems
• Statistical Mechanics of Monitored Dissipative Random Circuits
• Boundary sensitive Lindbladians and relaxation dynamics
• Gapless Symmetry-Protected Topological States in Measurement-Only Circuits
• Ancilla quantum measurements on interacting chains: Sensitivity of entanglement dynamics to the type and concentration of detectors
• Measurement-Induced Entanglement Phase Transition in Free Fermion Systems
• Universal Stochastic Equations of Monitored Quantum Dynamics
• Subsystem Information Capacity in Random Circuits and Hamiltonian Dynamics
• Fate of non-Hermitian free fermions with Wannier-Stark ladder
• Protect Measurement-Induced Phase Transition from Noise
• KPZ fluctuations in finite volume
• Delocalization of skin steady states
• Quantum feedback induced entanglement relaxation and dynamical phase transition in monitored free fermion chains with Wannier-Stark ladder
• Phase transitions induced by standard and predetermined measurements in transmon arrays
• Variational post-selection for ground states and thermal states simulation
• Coherent Information Phase Transition in a Noisy Quantum Circuit
• Random Quantum Circuits with Time-Reversal Symmetry
• Measurement-Driven Transitions between Area Law Phases
• Relaxation Critical Dynamics in Measurement-induced Phase Transitions
• Multipartite Greenberger-Horne-Zeilinger Entanglement in Monitored Random Clifford Circuits
• Entanglement Growth from Entangled States: A Unified Perspective on Entanglement Generation and Transport
• Noisy Monitored Quantum Circuits