Emergence of Generic Entanglement Structure in Doped Matchgate Circuits

TL;DR

This paper shows how adding non-Gaussian gates to matchgate circuits restores typical entanglement growth and phase transition behaviors, bridging free and interacting fermionic system dynamics.

Contribution

It demonstrates that doping matchgate circuits with extensive non-Gaussian resources recovers ballistic entanglement growth and volume-law phases, revealing non-Gaussianity as a key to non-integrable dynamics.

Findings

Doping matchgate circuits with non-Gaussian gates restores ballistic entanglement growth.

Measurement-induced phase transition between area-law and power-law entangled phases.

Extensive non-Gaussian gates are necessary for genuine volume-law entanglement.

Abstract

Free fermionic Gaussian, a.k.a. matchgate, random circuits exhibit atypical behavior compared to generic interacting systems. They produce anomalously slow entanglement growth, characterized by diffusive scaling $S(t) \sim \sqrt{t}$, and evolve into volume-law entangled states at late times, $S \sim N$, which are highly unstable to 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 $S(t) \sim t$ is recovered after injecting an extensive total amount of non-Gaussian gates, also restoring 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, $S \sim N^\alpha$, with $\alpha$ 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 non-integrable behavior.