{
  "abstract": "Sample-based quantum diagonalization (SQD/QSCI) diagonalizes the Hamiltonian classically in determinant subspaces selected from quantum-circuit samples. Its iron–sulfur demonstrations underpin claims of utility-scale quantum chemistry, and a recent critique disputes them at matched subspace dimension. Both sides compare energies; neither reports which spin state was computed. Our spin audit uses the exact determinant-space ⟨S²⟩, the invariant spectrum of the S² block over quasi-degenerate manifolds, and higher moments (⟨S⁴⟩ to ⟨S⁸⟩) bounding the spin-sector weights. We apply it to the public [2Fe-2S] and [4Fe-4S] benchmarks, IBM's released qiskit-addon-sqd pipeline and published hardware data. No audited execution returned the named singlet at competitive energy; for published states unavailable to direct audit, the energy-only records do not establish singlet identity. Under the audited HCI protocols, selected-CI growth approaches a spin-contaminated state (⟨S²⟩ ≈ 4.7 on [2Fe-2S]) whose samples keep the contamination. Spin-inversion completion leaves the energy and ⟨S²⟩ of these states unchanged. The released [2Fe-2S] hardware samples give no energy advantage over the released uniform-random control. A scalar mean does not identify these states: two audited arms share ⟨S²⟩ ≈ 2.00, but one is a triplet eigenstate (Var(S²) = 3×10⁻⁶) and the other a 2:1 singlet–quintet mixture whose third moment bounds its triplet weight below 10⁻⁴. At the largest published dimension (5.625×10⁷ determinants, reconstructed here from the released support), the lowest root, 170 mHa below the published energy, has ⟨S²⟩ = 1.3711, unchanged under an 18.6-fold residual tightening to 1.1% of the 0.285 mHa gap. Its first two moments, with Var(S²) = 6.9, exclude any decomposition confined to S ≤ 2. Near-singlet character appears only as a non-stationary superposition, because determinant selection does not commute with S². Energy-only benchmarks therefore do not establish convergence to the named state. We recommend reporting spin moments with every energy and controlling spin during selection.",
  "abstract_shown": true,
  "affiliations": [
    "Pure State Labs"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Tyler Vitale",
      "orcid": "0009-0003-6156-0212"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1ksdpfcxpj0fv.bib",
  "cited_by": 0,
  "doi": "10.26434/chemrxiv.15006382/v2",
  "fulltext_url": null,
  "id": "1ksdpfcxpj0fv",
  "issns": [],
  "landing_url": "https://chemrxiv.org/doi/full/10.26434/chemrxiv.15006382/v2",
  "language": null,
  "licence": "CC-BY",
  "licence_label": "CC BY",
  "licence_source": "journal",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "openalex",
      "1702|Quantum Computing Algorithms and Architecture"
    ]
  ],
  "openalex": "W7213333254",
  "pdf_url": "https://chemrxiv.org/doi/pdf/10.26434/chemrxiv.15006382/v2",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-15",
  "publisher": "American Chemical Society (ACS)",
  "ris": "https://research.draconitic.com/paper/1ksdpfcxpj0fv.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:19Z",
      "native_id": "10.26434/chemrxiv.15006382",
      "source": "chemrxiv",
      "url": "https://chemrxiv.org/doi/full/10.26434/chemrxiv.15006382/v2"
    }
  ],
  "subjects": [
    {
      "field": "chemistry",
      "origin": "source:chemrxiv",
      "subfield": "general"
    }
  ],
  "title": "Which state are you converging? A spin audit of sample-based quantum diagonalization benchmarks on iron–sulfur clusters",
  "title_text": "Which state are you converging? A spin audit of sample-based quantum diagonalization benchmarks on iron–sulfur clusters",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:19Z",
  "url": "https://research.draconitic.com/paper/1ksdpfcxpj0fv",
  "venue": "ChemRxiv",
  "versions": []
}