{
  "id": "oai:papers.qnfo.org:fidelity-budgets-for-discrete-regularizations-of-gauge-theories-exact-single-lin",
  "slug": "fidelity-budgets-for-discrete-regularizations-of-gauge-theories-exact-single-lin",
  "title": "Fidelity Budgets for Discrete Regularizations of Gauge Theories: Exact Single-Link Computations, Scaling Laws, and the Limits of Heuristic Bounds",
  "authors": [
    "Rowan Brad Quni-Gudzinas"
  ],
  "abstract": "Discrete regularizations of gauge theories — finite-dimensional link Hilbert spaces in quantum link models, truncated electric bases on quantum registers, and tensor networks on Bruhat–Tits trees — all face the same structural question: when does the discrete object faithfully encode its continuum or infinite-dimensional target? We develop a unified fidelity-budget framework that decomposes a target accuracy ε = 10^-4 into per-component truncation errors with explicit scaling laws. As a fully worked case study, we compute exactly, with all arithmetic shown, the truncation infidelity and energy bias of a single thermal U(1) link at dimensionless inverse temperature β g² = 0.5: the infidelity falls from 1.150 × 10^-2 at n_max=3 to 7.242 × 10^-5 at n_max=5 and 6.44 × 10^-8 at n_max=7, while the register cost grows only from 3 to 4 qubits. We document, in an explicit divergence appendix, why a competing heuristic bound proposed in an independent draft fails algebraic scrutiny and was rejected.",
  "abstract_markdown": "Discrete regularizations of gauge theories — finite-dimensional link Hilbert spaces in quantum link models, truncated electric bases on quantum registers, and tensor networks on Bruhat–Tits trees — all face the same structural question: when does the discrete object faithfully encode its continuum or infinite-dimensional target? We develop a unified fidelity-budget framework that decomposes a target accuracy $\\epsilon = 10^{-4}$ into per-component truncation errors with explicit scaling laws. As a fully worked case study, we compute exactly, with all arithmetic shown, the truncation infidelity and energy bias of a single thermal $\\mathrm{U}(1)$ link at dimensionless inverse temperature $\\beta g^2 = 0.5$: the infidelity falls from $1.150 \\times 10^{-2}$ at $n_{\\max}=3$ to $7.242 \\times 10^{-5}$ at $n_{\\max}=5$ and $6.44 \\times 10^{-8}$ at $n_{\\max}=7$, while the register cost grows only from 3 to 4 qubits. We document, in an explicit divergence appendix, why a competing heuristic bound proposed in an independent draft fails algebraic scrutiny and was rejected.",
  "date": "2026-10-09",
  "first_published": "2026-10-09",
  "last_revised": "2026-10-09T00:00:00Z",
  "modified": "2026-10-09T00:00:00Z",
  "version": "1.0.0",
  "version_count": 1,
  "language": "en",
  "keywords": [],
  "quality_tags": [
    "High-quality scholarly research",
    "open-access scholarly work",
    "versioned research publication"
  ],
  "quality_label": "High-quality scholarly research",
  "quality_basis": "QNFO publisher classification for open-access, versioned research with a public revision history and reader correction channel; this is not a claim of independent peer review.",
  "quality_evidence_url": "https://qnfo.org/about",
  "peer_review_status": "Not independently peer-reviewed",
  "resource_type": "ScholarlyArticle",
  "doi": null,
  "doi_url": null,
  "url": "https://papers.qnfo.org/papers/fidelity-budgets-for-discrete-regularizations-of-gauge-theories-exact-single-lin",
  "license_url": "https://legal.qnfo.org/",
  "license_spdx": null,
  "sha256": "d61887e7179ed411cf38d29266d69494a912d1cbb8180295b06a5074f36cc8e3",
  "version_url": "https://papers.qnfo.org/papers/fidelity-budgets-for-discrete-regularizations-of-gauge-theories-exact-single-lin/v/1.0.0",
  "datacite": {
    "schemaVersion": "http://datacite.org/schema/kernel-4",
    "identifiers": [
      {
        "identifier": "https://papers.qnfo.org/papers/fidelity-budgets-for-discrete-regularizations-of-gauge-theories-exact-single-lin",
        "identifierType": "URL"
      }
    ],
    "creators": [
      {
        "name": "Rowan Brad Quni-Gudzinas",
        "nameType": "Personal",
        "nameIdentifiers": [
          {
            "nameIdentifier": "https://orcid.org/0009-0002-4317-5604",
            "nameIdentifierScheme": "ORCID",
            "schemeUri": "https://orcid.org"
          }
        ]
      }
    ],
    "titles": [
      {
        "title": "Fidelity Budgets for Discrete Regularizations of Gauge Theories: Exact Single-Link Computations, Scaling Laws, and the Limits of Heuristic Bounds"
      }
    ],
    "publisher": "QNFO",
    "publicationYear": "2026",
    "resourceType": {
      "resourceTypeGeneral": "Text",
      "resourceType": "ScholarlyArticle"
    },
    "subjects": [
      {
        "subject": "High-quality scholarly research",
        "subjectScheme": "QNFO publisher classification",
        "schemeUri": "https://qnfo.org/about"
      },
      {
        "subject": "open-access scholarly work",
        "subjectScheme": "QNFO publisher classification",
        "schemeUri": "https://qnfo.org/about"
      },
      {
        "subject": "versioned research publication",
        "subjectScheme": "QNFO publisher classification",
        "schemeUri": "https://qnfo.org/about"
      }
    ],
    "dates": [
      {
        "date": "2026-10-09",
        "dateType": "Issued"
      },
      {
        "date": "2026-10-09",
        "dateType": "Updated"
      }
    ],
    "language": "en",
    "version": "1.0.0",
    "rightsList": [
      {
        "rightsUri": "https://legal.qnfo.org/"
      }
    ],
    "descriptions": [
      {
        "description": "Discrete regularizations of gauge theories — finite-dimensional link Hilbert spaces in quantum link models, truncated electric bases on quantum registers, and tensor networks on Bruhat–Tits trees — all face the same structural question: when does the discrete object faithfully encode its continuum or infinite-dimensional target? We develop a unified fidelity-budget framework that decomposes a target accuracy ε = 10^-4 into per-component truncation errors with explicit scaling laws. As a fully worked case study, we compute exactly, with all arithmetic shown, the truncation infidelity and energy bias of a single thermal U(1) link at dimensionless inverse temperature β g² = 0.5: the infidelity falls from 1.150 × 10^-2 at n_max=3 to 7.242 × 10^-5 at n_max=5 and 6.44 × 10^-8 at n_max=7, while the register cost grows only from 3 to 4 qubits. We document, in an explicit divergence appendix, why a competing heuristic bound proposed in an independent draft fails algebraic scrutiny and was rejected.",
        "descriptionType": "Abstract"
      },
      {
        "description": "Publisher quality classification: High-quality scholarly research. QNFO publisher classification for open-access, versioned research with a public revision history and reader correction channel; this is not a claim of independent peer review.",
        "descriptionType": "Other"
      },
      {
        "description": "Peer review status: Not independently peer-reviewed",
        "descriptionType": "Other"
      }
    ],
    "formats": [
      "text/html"
    ]
  }
}