{
  "abstract": "Algorithms which prepare states via the variational principle assume that closeness in energy implies closeness in state; we formalise how this assumption can fail by showing that a ground-state energy estimate converged to within $ε$ of the true value is compatible with observable expectation values in error by up to $\\sqrt{2εχ_O}$ at leading order, where $χ_O$ is the static susceptibility of the observable. As a result, the observable error can be orders of magnitude larger than the energy error, a mechanism we call non-linear error amplification, and because a variational algorithm cannot guarantee the correctness of these properties from energy alone, energy does not necessarily certify an observable. In light of our findings, we examine three algorithms: the variational quantum eigensolver on the transverse-field Ising chain, the density-matrix renormalisation group on a pair of weakly coupled hydrogen chains, and Krylov quantum diagonalisation on lithium fluoride. In each case we demonstrate that a well-converged energy can leave observables uncertified.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.03989",
  "author_total": 1,
  "authors": [
    {
      "name": "Ganga Singh Manchanda"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/acn8hr1p9qwgp.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.03989",
  "fulltext_url": null,
  "id": "acn8hr1p9qwgp",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.03989",
  "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",
      "quant-ph"
    ],
    [
      "openalex",
      "1702|Quantum Computing Algorithms and Architecture"
    ]
  ],
  "openalex": "W7220694241",
  "pdf_url": "https://arxiv.org/pdf/2610.03989",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/acn8hr1p9qwgp.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:01Z",
      "native_id": "2610.03989",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.03989"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Certification failure in variational-principle observables",
  "title_text": "Certification failure in variational-principle observables",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:01Z",
  "url": "https://research.draconitic.com/paper/acn8hr1p9qwgp",
  "venue": "arXiv",
  "versions": []
}