{
  "abstract": "Fermionic Gaussian states are the workhorse reference states for qubit-based quantum simulation of fermionic systems, yet existing certification protocols either proceed via fidelity estimation, leading to suboptimal sample complexity in the target precision $ε$, only apply to Haar-typical states, or require adaptive measurements on a large fraction of qubits. We give an adaptive protocol that certifies any $d$-mode pure fermionic Gaussian state using $O(d^2ε^{-1})$ copies, single-qubit measurements with only one qubit measured adaptively per copy, and $O(d^3)$ classical processing time per copy. The $ε^{-1}$ dependence is optimal for the certification problem, even among strategies using entangled measurements. The sample complexity is controlled by the spectral gap of a $d\\leftrightarrow d-2$ down-up walk---a Markov chain studied in the theory of high-dimensional expanders, equivalent to a two-site Glauber dynamics in statistical physics---relating certification efficiency to relaxation time to equilibrium. The worst-case bound is tight for this protocol and is attained by physically relevant states, including ground states of the fully dimerized Su-Schrieffer-Heeger (SSH) chain and BCS pair states. In contrast, numerics up to $d=14$ suggest that $O(d ε^{-1})$ copies suffice to certify Haar-typical Gaussian states, a factor of $d$ improvement over the worst-case bound. Finally, because the bound depends only on the target's computational-basis distribution, the protocol extends to efficiently phase-dressed states---states obtained by injecting an efficiently computable diagonal phase to Gaussian states---with the same sample complexity. The class includes a continuous family of four-mode non-Gaussian magic states for matchgate computation.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.28233",
  "author_total": 4,
  "authors": [
    {
      "name": "Ninnat Dangniam"
    },
    {
      "name": "Laphas Premcharoen"
    },
    {
      "name": "Metrasit Sripech"
    },
    {
      "name": "Thiparat Chotibut"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/b34eyd3r5kx8m.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.28233",
  "fulltext_url": null,
  "id": "b34eyd3r5kx8m",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.28233",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cond-mat.stat-mech"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "1702|Quantum Computing Algorithms and Architecture"
    ]
  ],
  "openalex": "W7214212453",
  "pdf_url": "https://arxiv.org/pdf/2609.28233",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/b34eyd3r5kx8m.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:56Z",
      "native_id": "2609.28233",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.28233"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.stat-mech",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Certifying fermionic Gaussian states (and a little more) with optimal precision dependence",
  "title_text": "Certifying fermionic Gaussian states (and a little more) with optimal precision dependence",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:56Z",
  "url": "https://research.draconitic.com/paper/b34eyd3r5kx8m",
  "venue": "arXiv",
  "versions": []
}