Work

Emergence of Generic Entanglement Structure in Doped Matchgate Circuits

Year: 2025

Type: article

Abstract: Free fermionic Gaussian, also known as matchgate, random circuits exhibit atypical behavior compared to generic interacting systems. They produce anomalously slow entanglement growth, characterized by diffusive scaling S(t)∼sqrt[t], and evolve into volume-law entangled states at late times, S∼N, which are highly unstable under measurements. Here, we investigate how doping such circuits with non-Gaussian resources (gates) restores entanglement structures of typical dynamics. We demonstrate that ballistic entanglement growth S(t)∼t is recovered after injecting an extensive total amount of non-Gaussian gates, which also restores Kardar-Parisi-Zhang fluctuations. When the evolution is perturbed with measurements, we uncover a measurement-induced phase transition between an area-law and a power-law entangled phase, S∼N^{α}, with α controlled by the doping. A genuine volume-law entangled phase is recovered only when non-Gaussian gates are injected at an extensive rate. Our findings bridge the dynamics of free and interacting fermionic systems, identifying non-Gaussianity as a key resource driving the emergence of nonintegrable behavior.

Source: Physical Review Letters

DOI: 10.1103/w97w-7zny