Noisy induced entanglement transition in one-dimensional random quantum circuits

TL;DR

This paper investigates how noise affects entanglement in one-dimensional random quantum circuits, revealing a transition from area law to volume law entanglement at a critical noise level, with implications for quantum device performance.

Contribution

It introduces a detailed analysis of entanglement transition in noisy 1D quantum circuits using negativity and finite-size scaling, highlighting universal properties.

Findings

Entanglement transition occurs at a critical error rate p_c≈0.056.

Logarithmic negativity effectively characterizes entanglement evolution.

Finite-size scaling reveals universal dynamic properties.

Abstract

Random quantum circuit is a minimally structured model to study the entanglement dynamics of many-body quantum systems. In this paper, we considered a one-dimensional quantum circuit with noisy Haar-random unitary gates using density matrix operator and tensor contraction methods. It is shown that the entanglement evolution of the random quantum circuits is properly characterized by the logarithmic entanglement negativity. By performing exact numerical calculations, we found that, as the physical error rate is decreased below a critical value $p_c\approx 0.056$, the logarithmic entanglement negativity changes from the area law to the volume law, giving rise to an entanglement transition. The critical exponent of the correlation length can be determined from the finite-size scaling analysis, revealing the universal dynamic property of the noisy intermediate-scale quantum devices.