{
  "id": "oai:papers.qnfo.org:holographic-quantum-error-correction-as-ads-cft-renormalization-group-flow-on-br",
  "slug": "holographic-quantum-error-correction-as-ads-cft-renormalization-group-flow-on-br",
  "title": "Holographic Quantum Error Correction as AdS/CFT Renormalization‑Group Flow on Bruhat–Tits Trees: A Conditional Threshold Analysis at 10^-4",
  "authors": [
    "Rowan Brad Quni-Gudzinas"
  ],
  "abstract": "Quantum error‑correction (QEC) thresholds determine whether physical error rates can be suppressed to arbitrarily low logical error probabilities. A recent proposal encodes logical information as a renormalization‑group (RG) flow on a p‑adic Bruhat–Tits tree T_p, with a bosonic cat‑code inner layer and a p‑ary majority‑vote outer layer. We ask whether this architecture can sustain a threshold of at least 10^-4 per logical qubit per cycle. Using the Tianyan‑287 superconducting processor error rates (p₂q=4.4×10^-3, p₁q=1.0×10^-3, p_rm ro=1.3×10^-2) and a cat‑code mean photon number bar n=6, we derive an exact recursion f(p)=3p²-2p³ for a ternary tree, locate its non‑trivial fixed point p^ast=1/4, and propagate the hardware budget through the stack. The effective bit‑flip rate after bosonic suppression is p_rm eff=2.703×10^-8, giving a margin of 3.70×10³ over 10^-4. A depth‑2 concatenation yields a logical error 1.4×10^-29 under the independence assumption, while a conservative correlated‑error floor is 8.0×10^-8 per cycle. The tightest margin (readout‑dominated dephasing) is 19.2×, and the threshold holds provided correlated bursts satisfy p_rm corr≤7.7×10^-6 per subtree per cycle. These results are analytic, fully documented, and identify concrete falsifiable tests on superconducting and trapped‑ion platforms.",
  "abstract_markdown": "Quantum error‑correction (QEC) thresholds determine whether physical error rates can be suppressed to arbitrarily low logical error probabilities. A recent proposal encodes logical information as a renormalization‑group (RG) flow on a $p$‑adic Bruhat–Tits tree $\\mathcal{T}_p$, with a bosonic cat‑code inner layer and a $p$‑ary majority‑vote outer layer. We ask whether this architecture can sustain a threshold of at least $10^{-4}$ per logical qubit per cycle. Using the Tianyan‑287 superconducting processor error rates ($p_{2q}=4.4\\times10^{-3}$, $p_{1q}=1.0\\times10^{-3}$, $p_{\\rm ro}=1.3\\times10^{-2}$) and a cat‑code mean photon number $\\bar n=6$, we derive an exact recursion $f(p)=3p^{2}-2p^{3}$ for a ternary tree, locate its non‑trivial fixed point $p^{\\ast}=1/4$, and propagate the hardware budget through the stack. The effective bit‑flip rate after bosonic suppression is $p_{\\rm eff}=2.703\\times10^{-8}$, giving a margin of $3.70\\times10^{3}$ over $10^{-4}$. A depth‑2 concatenation yields a logical error $1.4\\times10^{-29}$ under the independence assumption, while a conservative correlated‑error floor is $8.0\\times10^{-8}$ per cycle. The tightest margin (readout‑dominated dephasing) is $19.2\\times$, and the threshold holds provided correlated bursts satisfy $p_{\\rm corr}\\le7.7\\times10^{-6}$ per subtree per cycle. These results are analytic, fully documented, and identify concrete falsifiable tests on superconducting and trapped‑ion platforms.",
  "date": "2026-10-02",
  "first_published": "2026-10-02",
  "last_revised": "2026-10-19T13:31:27Z",
  "modified": "2026-10-19T13:31:27Z",
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  "url": "https://papers.qnfo.org/papers/holographic-quantum-error-correction-as-ads-cft-renormalization-group-flow-on-br",
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  "version_url": "https://papers.qnfo.org/papers/holographic-quantum-error-correction-as-ads-cft-renormalization-group-flow-on-br/v/2.0.1",
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    "creators": [
      {
        "name": "Rowan Brad Quni-Gudzinas",
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    "titles": [
      {
        "title": "Holographic Quantum Error Correction as AdS/CFT Renormalization‑Group Flow on Bruhat–Tits Trees: A Conditional Threshold Analysis at 10^-4"
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    "publicationYear": "2026",
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        "date": "2026-10-02",
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        "description": "Quantum error‑correction (QEC) thresholds determine whether physical error rates can be suppressed to arbitrarily low logical error probabilities. A recent proposal encodes logical information as a renormalization‑group (RG) flow on a p‑adic Bruhat–Tits tree T_p, with a bosonic cat‑code inner layer and a p‑ary majority‑vote outer layer. We ask whether this architecture can sustain a threshold of at least 10^-4 per logical qubit per cycle. Using the Tianyan‑287 superconducting processor error rates (p₂q=4.4×10^-3, p₁q=1.0×10^-3, p_rm ro=1.3×10^-2) and a cat‑code mean photon number bar n=6, we derive an exact recursion f(p)=3p²-2p³ for a ternary tree, locate its non‑trivial fixed point p^ast=1/4, and propagate the hardware budget through the stack. The effective bit‑flip rate after bosonic suppression is p_rm eff=2.703×10^-8, giving a margin of 3.70×10³ over 10^-4. A depth‑2 concatenation yields a logical error 1.4×10^-29 under the independence assumption, while a conservative correlated‑error floor is 8.0×10^-8 per cycle. The tightest margin (readout‑dominated dephasing) is 19.2×, and the threshold holds provided correlated bursts satisfy p_rm corr≤7.7×10^-6 per subtree per cycle. These results are analytic, fully documented, and identify concrete falsifiable tests on superconducting and trapped‑ion platforms.",
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