{
  "id": "oai:papers.qnfo.org:passive-fault-tolerance-via-bruhat-tits-tree-codes-claim-encoding-quantum-inform",
  "slug": "passive-fault-tolerance-via-bruhat-tits-tree-codes-claim-encoding-quantum-inform",
  "title": "Passive Fault Tolerance via Bruhat-Tits Tree Codes. Claim: encoding quantum information on Bruhat-Tits trees (p-adic ultrametric geometry) y",
  "authors": [
    "Rowan Brad Quni-Gudzinas"
  ],
  "abstract": "Scalable quantum computation is presently limited by the need for active error‑correction cycles that require millikelvin refrigeration and extensive syndrome measurement overhead. A proposed alternative encodes logical information on the branches of a Bruhat‑Tits tree, exploiting the ultrametric geometry to confine local depolarizing errors to isolated sub‑trees. By mapping the logical error rate under independent depolarizing noise to the depth of the tree, we derive an analytical passive threshold of approximately 10 % physical error probability for a depth‑3 tree, far above the ∼1 % threshold of surface codes. The model predicts that a tree of depth 3 reduces the logical error probability to below 10^-3 for a physical error rate of 10 %. Moreover, the passive scheme eliminates syndrome extraction, allowing operation at 4 K on pulse‑tube cryocoolers and removing the ∼90‑fold cooling gap that constrains active codes. If validated, the result reframes scalability as a geometric and thermodynamic problem rather than an engineering one, enabling cheap, large‑scale quantum processors.",
  "abstract_markdown": "Scalable quantum computation is presently limited by the need for active error‑correction cycles that require millikelvin refrigeration and extensive syndrome measurement overhead. A proposed alternative encodes logical information on the branches of a Bruhat‑Tits tree, exploiting the ultrametric geometry to confine local depolarizing errors to isolated sub‑trees. By mapping the logical error rate under independent depolarizing noise to the depth of the tree, we derive an analytical passive threshold of approximately 10 % physical error probability for a depth‑3 tree, far above the ∼1 % threshold of surface codes. The model predicts that a tree of depth 3 reduces the logical error probability to below $10^{-3}$ for a physical error rate of 10 %. Moreover, the passive scheme eliminates syndrome extraction, allowing operation at 4 K on pulse‑tube cryocoolers and removing the ∼90‑fold cooling gap that constrains active codes. If validated, the result reframes scalability as a geometric and thermodynamic problem rather than an engineering one, enabling cheap, large‑scale quantum processors.",
  "date": "2026-10-26",
  "first_published": "2026-10-26",
  "last_revised": "2026-10-26T00:00:00Z",
  "modified": "2026-10-26T00:00:00Z",
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  "peer_review_status": "Not independently peer-reviewed",
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  "doi": null,
  "doi_url": null,
  "url": "https://papers.qnfo.org/papers/passive-fault-tolerance-via-bruhat-tits-tree-codes-claim-encoding-quantum-inform",
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        "name": "Rowan Brad Quni-Gudzinas",
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    "titles": [
      {
        "title": "Passive Fault Tolerance via Bruhat-Tits Tree Codes. Claim: encoding quantum information on Bruhat-Tits trees (p-adic ultrametric geometry) y"
      }
    ],
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    "publicationYear": "2026",
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    "dates": [
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        "date": "2026-10-26",
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        "description": "Scalable quantum computation is presently limited by the need for active error‑correction cycles that require millikelvin refrigeration and extensive syndrome measurement overhead. A proposed alternative encodes logical information on the branches of a Bruhat‑Tits tree, exploiting the ultrametric geometry to confine local depolarizing errors to isolated sub‑trees. By mapping the logical error rate under independent depolarizing noise to the depth of the tree, we derive an analytical passive threshold of approximately 10 % physical error probability for a depth‑3 tree, far above the ∼1 % threshold of surface codes. The model predicts that a tree of depth 3 reduces the logical error probability to below 10^-3 for a physical error rate of 10 %. Moreover, the passive scheme eliminates syndrome extraction, allowing operation at 4 K on pulse‑tube cryocoolers and removing the ∼90‑fold cooling gap that constrains active codes. If validated, the result reframes scalability as a geometric and thermodynamic problem rather than an engineering one, enabling cheap, large‑scale quantum processors.",
        "descriptionType": "Abstract"
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