{
  "id": "oai:papers.qnfo.org:shor-assumptions-audit",
  "slug": "shor-assumptions-audit",
  "title": "Shor's Algorithm and the Unproven Premise: An Assumption Audit of the Quantum Factoring Narrative",
  "authors": [
    "Rowan Brad Quni-Gudzinas"
  ],
  "abstract": "Shor's 1994 algorithm proves FACTORING ∈ BQP, but the claim that this constitutes a quantum advantage requires the additional unproven premise FACTORING ∉ BPP. This paper decomposes Shor's claim architecture into nine assumptions spanning number theory, computational complexity, and quantum physics. Key findings: RSA-2048 requires 2.1–7.9M physical qubits at 99.9–99.999% fidelity with crossover ~2040; ≥80% of exponential quantum speedups reduce to abelian HSP; Shor's algorithm is better understood as detection of abelian algebraic periodicity via quantum interference rather than a general proof of quantum computational supremacy.",
  "abstract_markdown": "Shor's 1994 algorithm proves FACTORING ∈ BQP, but the claim that this constitutes a quantum advantage requires the additional unproven premise FACTORING ∉ BPP. This paper decomposes Shor's claim architecture into nine assumptions spanning number theory, computational complexity, and quantum physics. Key findings: RSA-2048 requires 2.1–7.9M physical qubits at 99.9–99.999% fidelity with crossover ~2040; ≥80% of exponential quantum speedups reduce to abelian HSP; Shor's algorithm is better understood as detection of abelian algebraic periodicity via quantum interference rather than a general proof of quantum computational supremacy.",
  "date": "2026-07-19",
  "first_published": "2026-07-19",
  "last_revised": "2026-07-19T00:00:00Z",
  "modified": "2026-07-19T00:00:00Z",
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  "language": "en",
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  "quality_label": "High-quality scholarly research",
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  "url": "https://papers.qnfo.org/papers/shor-assumptions-audit",
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      {
        "name": "Rowan Brad Quni-Gudzinas",
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    "titles": [
      {
        "title": "Shor's Algorithm and the Unproven Premise: An Assumption Audit of the Quantum Factoring Narrative"
      }
    ],
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    "publicationYear": "2026",
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    "dates": [
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        "description": "Shor's 1994 algorithm proves FACTORING ∈ BQP, but the claim that this constitutes a quantum advantage requires the additional unproven premise FACTORING ∉ BPP. This paper decomposes Shor's claim architecture into nine assumptions spanning number theory, computational complexity, and quantum physics. Key findings: RSA-2048 requires 2.1–7.9M physical qubits at 99.9–99.999% fidelity with crossover ~2040; ≥80% of exponential quantum speedups reduce to abelian HSP; Shor's algorithm is better understood as detection of abelian algebraic periodicity via quantum interference rather than a general proof of quantum computational supremacy.",
        "descriptionType": "Abstract"
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