{
  "abstract": "Small high-rate non-CSS stabilizer codes provide compact platforms for encoded quantum computation, but mixed-Pauli checks and limited native transversal logical gates complicate fault-tolerant dynamics. Block-level constructions offer an alternative by mapping an entire logical block to a physical circuit rather than compiling separately protected logical gates. We investigate this approach using the high-rate [[8,3,3]] non-CSS code and logical Trotter circuits as a testbed. We construct flagged syndrome-extraction circuits and establish a circuit-level memory pseudo-threshold near \\(1.5\\times10^{-3}\\). We then apply our symplectic-transvection construction, which maps a logical Trotter circuit to a physical circuit with the same block pattern for any stabilizer code. Although this mapping preserves the intended unitary algebraically, encoded Trotter circuits exhibit asymmetry between logical-\\(X\\) and logical-\\(Z\\) failure channels. Single-fault analysis identifies the mechanism: a fault on the shared parity ancilla can propagate through the uncomputation network into an undetectable logical operator, reducing the effective circuit distance in the affected sector. We evaluate flag-conditioned recovery, biased-noise decoding, CliNR resource verification, flag postselection, and asymmetric gate-noise models. These methods suppress propagated faults but do not simultaneously suppress both logical sectors in the realistic configurations studied. A diagnostic protected limit removing the identified malignant first-order locations restores pseudo-threshold behavior in both sectors, approaching memory performance. These results demonstrate the potential of block-level logical constructions for non-CSS codes without rich native transversal gate sets and the joint protection of the parity network, analog rotation, and recovery required to preserve fault-tolerant distance.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.16159",
  "author_total": 2,
  "authors": [
    {
      "name": "Zhuangzhuang Chen"
    },
    {
      "name": "Narayanan Rengaswamy"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/98yw8eyw3e24a.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.16159",
  "fulltext_url": null,
  "id": "98yw8eyw3e24a",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.16159",
  "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",
      "cs.IT"
    ],
    [
      "arxiv",
      "math.IT"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "1702|Quantum Computing Algorithms and Architecture"
    ]
  ],
  "openalex": "W7213395605",
  "pdf_url": "https://arxiv.org/pdf/2609.16159",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/98yw8eyw3e24a.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:41Z",
      "native_id": "2609.16159",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.16159"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.IT",
      "subfield": "general"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Towards Block-Level Fault-Tolerant Quantum Simulation on Small High-Rate Non-CSS Codes",
  "title_text": "Towards Block-Level Fault-Tolerant Quantum Simulation on Small High-Rate Non-CSS Codes",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:45Z",
  "url": "https://research.draconitic.com/paper/98yw8eyw3e24a",
  "venue": "arXiv",
  "versions": []
}