Emergence of Generic Entanglement Structure in Doped Matchgate Circuits

• URL: http://arxiv.org/abs/2507.12526v1
• Date: Wed, 16 Jul 2025 18:00:02 GMT
• Title: Emergence of Generic Entanglement Structure in Doped Matchgate Circuits
• Authors: Alessio Paviglianiti, Luca Lumia, Emanuele Tirrito, Alessandro Silva, Mario Collura, Xhek Turkeshi, Guglielmo Lami,
• Abstract summary: We show how doping random circuits with non-Gaussian resources restores entanglement structures of typical dynamics.<n>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.
• Score: 37.742691394718086
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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