{
  "id": "oai:papers.qnfo.org:the-exponential-arena-a-reconciled-quantitative-account-of-hilbert-space-growth-",
  "slug": "the-exponential-arena-a-reconciled-quantitative-account-of-hilbert-space-growth-",
  "title": "The Exponential Arena: A Reconciled Quantitative Account of Hilbert-Space Growth with Qubit Number",
  "authors": [
    "Rowan Brad Quni-Gudzinas"
  ],
  "abstract": "A recurring question in quantum information is what \"space\" the state of a quantum computer inhabits, and how that space grows as the number of qubits n increases. This paper treats the question quantitatively, formalizing the arena of an n-qubit register as the complex projective Hilbert space CP^d-1 with d = 2^n, and deriving the scaling of its real dimension, the classical memory required to store one state vector, the per-gate cost of exact state-vector simulation, the entanglement entropy available across bipartitions, and the sparsity of classically simulable structured subsets. All headline numbers are computed explicitly from stated inputs: a general $n = 50$ register requires 2⁵4 ≈ 1.80 × 10¹6 bytes ($16$ PiB) per stored state vector; a single gate touches 2⁵0 ≈ 1.13 × 10¹5 amplitudes; the central cut of a $100$-qubit maximally entangled state carries $50$ bits of entropy, and reproducing it with a matrix-product state requires bond dimension 2⁵0 and ≈ 2.5 × 10³2 parameters — worse than the raw state vector. [...]",
  "abstract_markdown": "A recurring question in quantum information is what \"space\" the state of a quantum computer inhabits, and how that space grows as the number of qubits $n$ increases. This paper treats the question quantitatively, formalizing the arena of an $n$-qubit register as the complex projective Hilbert space $\\mathbb{CP}^{d-1}$ with $d = 2^n$, and deriving the scaling of its real dimension, the classical memory required to store one state vector, the per-gate cost of exact state-vector simulation, the entanglement entropy available across bipartitions, and the sparsity of classically simulable structured subsets. All headline numbers are computed explicitly from stated inputs: a general $n = 50$ register requires $2^{54} \\approx 1.80 \\times 10^{16}$ bytes ($16$ PiB) per stored state vector; a single gate touches $2^{50} \\approx 1.13 \\times 10^{15}$ amplitudes; the central cut of a $100$-qubit maximally entangled state carries $50$ bits of entropy, and reproducing it with a matrix-product state requires bond dimension $2^{50}$ and $\\approx 2.5 \\times 10^{32}$ parameters — worse than the raw state vector. [...]",
  "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/the-exponential-arena-a-reconciled-quantitative-account-of-hilbert-space-growth-",
  "license_url": "https://legal.qnfo.org/",
  "license_spdx": null,
  "sha256": "863b070266fb5bca34359be2d38ee8b5f8136b9c939fcfd24a2de8f06181aa45",
  "version_url": "https://papers.qnfo.org/papers/the-exponential-arena-a-reconciled-quantitative-account-of-hilbert-space-growth-/v/1.0.0",
  "datacite": {
    "schemaVersion": "http://datacite.org/schema/kernel-4",
    "identifiers": [
      {
        "identifier": "https://papers.qnfo.org/papers/the-exponential-arena-a-reconciled-quantitative-account-of-hilbert-space-growth-",
        "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": "The Exponential Arena: A Reconciled Quantitative Account of Hilbert-Space Growth with Qubit Number"
      }
    ],
    "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": "A recurring question in quantum information is what \"space\" the state of a quantum computer inhabits, and how that space grows as the number of qubits n increases. This paper treats the question quantitatively, formalizing the arena of an n-qubit register as the complex projective Hilbert space CP^d-1 with d = 2^n, and deriving the scaling of its real dimension, the classical memory required to store one state vector, the per-gate cost of exact state-vector simulation, the entanglement entropy available across bipartitions, and the sparsity of classically simulable structured subsets. All headline numbers are computed explicitly from stated inputs: a general $n = 50$ register requires 2⁵4 ≈ 1.80 × 10¹6 bytes ($16$ PiB) per stored state vector; a single gate touches 2⁵0 ≈ 1.13 × 10¹5 amplitudes; the central cut of a $100$-qubit maximally entangled state carries $50$ bits of entropy, and reproducing it with a matrix-product state requires bond dimension 2⁵0 and ≈ 2.5 × 10³2 parameters — worse than the raw state vector. [...]",
        "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"
    ]
  }
}