{
  "id": "oai:papers.qnfo.org:local-hilbert-space-dimension-as-a-resolution-parameter-information-theoretic-bo",
  "slug": "local-hilbert-space-dimension-as-a-resolution-parameter-information-theoretic-bo",
  "title": "Local Hilbert-Space Dimension as a Resolution Parameter: Information-Theoretic Bounds for Qudit Quantum Cellular Automata as Substrates of Emergent Holographic Geometry",
  "authors": [
    "Rowan Brad Quni-Gudzinas"
  ],
  "abstract": "Discrete models of quantum gravity lack a computable criterion for when their emergent geometry becomes semiclassical, and the system sizes at which quantum cellular automata (QCA) show holographic entanglement structure remain out of reach of exact simulation. We ask whether enlarging the local Hilbert space from qubits to qudits lowers the system size N at which continuum-like behavior appears. We develop the analytical framework for qudit QCA with local dimension d: we derive the exact scaling of Hilbert-space dimension d^N, the maximum cut entanglement S_max=min(|A|,|B|)log₂d, the site-count equivalence N_d=N_q/log₂d between qudit and qubit chains at matched information capacity, and the per-gate simulation overhead d²/4 at matched Hilbert dimension. These bounds give concrete numbers: a d=3 chain of 16 sites carries the entropy capacity of a 26-site qubit chain (a 36.9% site saving) at 2.25× the per-gate simulation cost, and a d=4 chain of 12 sites matches a 24-site qubit chain at 4× cost. We propose a falsifiable protocol comparing Ryu–Takayanagi-style entropy curves across d at matched capacity. The central conjecture — that emergence thresholds scale as 1/log₂d — is stated as a projection with explicit assumptions, giving candidate thresholds N^ast≈ 20, $13$, $10$ for d=2,3,4, and the smallest simulation that would confirm or refute it is specified.",
  "abstract_markdown": "Discrete models of quantum gravity lack a computable criterion for when their emergent geometry becomes semiclassical, and the system sizes at which quantum cellular automata (QCA) show holographic entanglement structure remain out of reach of exact simulation. We ask whether enlarging the local Hilbert space from qubits to qudits lowers the system size $N$ at which continuum-like behavior appears. We develop the analytical framework for qudit QCA with local dimension $d$: we derive the exact scaling of Hilbert-space dimension $d^{N}$, the maximum cut entanglement $S_{\\max}=\\min(|A|,|B|)\\log_{2}d$, the site-count equivalence $N_{d}=N_{q}/\\log_{2}d$ between qudit and qubit chains at matched information capacity, and the per-gate simulation overhead $d^{2}/4$ at matched Hilbert dimension. These bounds give concrete numbers: a $d=3$ chain of 16 sites carries the entropy capacity of a 26-site qubit chain (a 36.9% site saving) at 2.25× the per-gate simulation cost, and a $d=4$ chain of 12 sites matches a 24-site qubit chain at 4× cost. We propose a falsifiable protocol comparing Ryu–Takayanagi-style entropy curves across $d$ at matched capacity. The central conjecture — that emergence thresholds scale as $1/\\log_{2}d$ — is stated as a projection with explicit assumptions, giving candidate thresholds $N^{\\ast}\\approx 20$, $13$, $10$ for $d=2,3,4$, and the smallest simulation that would confirm or refute it is specified.",
  "date": "2026-10-15",
  "first_published": "2026-10-15",
  "last_revised": "2026-10-15T00:00:00Z",
  "modified": "2026-10-15T00:00:00Z",
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  "url": "https://papers.qnfo.org/papers/local-hilbert-space-dimension-as-a-resolution-parameter-information-theoretic-bo",
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    "creators": [
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        "name": "Rowan Brad Quni-Gudzinas",
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    "titles": [
      {
        "title": "Local Hilbert-Space Dimension as a Resolution Parameter: Information-Theoretic Bounds for Qudit Quantum Cellular Automata as Substrates of Emergent Holographic Geometry"
      }
    ],
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    "publicationYear": "2026",
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        "description": "Discrete models of quantum gravity lack a computable criterion for when their emergent geometry becomes semiclassical, and the system sizes at which quantum cellular automata (QCA) show holographic entanglement structure remain out of reach of exact simulation. We ask whether enlarging the local Hilbert space from qubits to qudits lowers the system size N at which continuum-like behavior appears. We develop the analytical framework for qudit QCA with local dimension d: we derive the exact scaling of Hilbert-space dimension d^N, the maximum cut entanglement S_max=min(|A|,|B|)log₂d, the site-count equivalence N_d=N_q/log₂d between qudit and qubit chains at matched information capacity, and the per-gate simulation overhead d²/4 at matched Hilbert dimension. These bounds give concrete numbers: a d=3 chain of 16 sites carries the entropy capacity of a 26-site qubit chain (a 36.9% site saving) at 2.25× the per-gate simulation cost, and a d=4 chain of 12 sites matches a 24-site qubit chain at 4× cost. We propose a falsifiable protocol comparing Ryu–Takayanagi-style entropy curves across d at matched capacity. The central conjecture — that emergence thresholds scale as 1/log₂d — is stated as a projection with explicit assumptions, giving candidate thresholds N^ast≈ 20, $13$, $10$ for d=2,3,4, and the smallest simulation that would confirm or refute it is specified.",
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