Fermionic non-Gaussianity via computable measures and experimentally accessible bounds

Abstract:Interacting fermions owe both their non-trivial correlations and their computational power to their departure from Gaussianity. Yet, quantifying that departure geometrically faces two challenges: the Gaussian manifold is non-convex, and perturbative treatments are confined to weak interactions. Here, we introduce a geometric measure of fermionic non-Gaussianity, the fidelity distance of a target state to the manifold of fermionic Gaussian states. We construct an iteration formalism to numerically access it, applicable also at strong coupling. Further, we prove a sharpened operator Jensen inequality, of interest in its own right. We use it to derive a witness that involves only two- and four-point fermionic correlators. Numerical benchmarks on the one-dimensional Fermi--Hubbard model show that the quality of the witness improves with system size and, for strong coupling, is tighter than antiflatness. Our results open a scalable route to charting non-Gaussianity of strongly-interacting fermionic quantum simulators.

Quantum Physics (quant-ph); Strongly Correlated Electrons (cond-mat.str-el)

arXiv:2610.17219 [quant-ph]

(or arXiv:2610.17219v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2610.17219 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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