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.

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BibTeX RIS

BibTeX

@misc{lakkaraju2026fermionic,
  title = {{Fermionic non-Gaussianity via computable measures and experimentally accessible bounds}},
  author = {Leela Ganesh Chandra Lakkaraju and Naga Dileep Varikuti and Philipp Hauke},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.17219},
  eprint = {2610.17219},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.17219},
}

RIS

TY  - UNPB
TI  - Fermionic non-Gaussianity via computable measures and experimentally accessible bounds
AU  - Leela Ganesh Chandra Lakkaraju
AU  - Naga Dileep Varikuti
AU  - Philipp Hauke
PY  - 2026
DA  - 2026/10/12
PB  - arXiv
DO  - 10.48550/arxiv.2610.17219
UR  - https://arxiv.org/abs/2610.17219
AB  - 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.
ER  -

Abstract

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