{
  "abstract": "We present an organizing framework for concatenated quantum error correction based on the observation that the syndrome projection of a stabilizer code reshapes the noise channel in a code-determined manner. For any stabilizer code, one level of QEC maps the physical noise to a block-diagonal logical channel whose diagonal Pauli weights are fixed by the code geometry. Coherences between different syndrome classes vanish, and no physical Pauli twirl is required to reach this block-diagonal form. Concatenation can then be viewed as the iteration of the same redistribution step: the dominant logical error after one level selects the code used at the next. We instantiate the framework with the two smallest stabilizer codes, the bit-flip and phase-flip codes, and apply it to amplitude damping. The redistribution rules give the concatenation protocol $C_2(\\hatσ_y) C_1(\\hatσ_x)$, whose ideal-recovery fidelity scales as $f_l=1-\\mathcal O(γ^2)$. Solving the crossover condition $F_l>F_{l-1}$ in the ideal-gate limit yields a critical damping parameter $γ_c\\approx0.30$; in terms of the initial channel fidelity, $f=1-1.72755γ^2$. Under the same ideal-recovery assumption, we compare the overall gate accuracy rate with that of the five-qubit code. The scope of the framework, in particular for coherent and correlated noise, is stated explicitly.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.31007",
  "author_total": 1,
  "authors": [
    {
      "name": "Long Huang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4yztcyre398d8.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.31007",
  "fulltext_url": null,
  "id": "4yztcyre398d8",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.31007",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "1702|Quantum Computing Algorithms and Architecture"
    ]
  ],
  "openalex": "W7223385670",
  "pdf_url": "https://arxiv.org/pdf/2610.31007",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4yztcyre398d8.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:34Z",
      "native_id": "2610.31007",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.31007"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Noise redistribution by stabilizer codes: an organizing view of concatenated three-qubit codes",
  "title_text": "Noise redistribution by stabilizer codes: an organizing view of concatenated three-qubit codes",
  "type": "preprint",
  "updated_at": "2026-11-04T15:20:50Z",
  "url": "https://research.draconitic.com/paper/4yztcyre398d8",
  "venue": "arXiv",
  "versions": []
}