{
  "abstract": "Code surgery measures a logical operator of a quantum LDPC code with $O(d)$ rounds of syndrome extraction. Lifted surgery amortises this cost on Abelian group-algebra codes by measuring an orbit of logical operators under a translation symmetry in one merged code. We extend it to two-block group-algebra codes over non-Abelian groups and ask whether non-commutativity lets one merged code measure more operators than any Abelian group of its symmetries. We classify the block-affine automorphisms of these codes and find that, measured against this full group, most apparent non-Abelian gains disappear. We prove that the gain is at most the index of a largest Abelian subgroup. We find codes with exact distance up to $13$ where the gain is two, including codes in which one merged code reads out every logical qubit, and codes over products of $A_4$, $S_4$ and SL(2,3) with gain three for a best logical, up to $[[336,26,12]]$. A merged-distance lemma gives a simple condition for the gadget to preserve the code distance. In circuit-level simulations with Relay-BP decoding, at the error rates we can resolve, the non-Abelian gadget is as reliable as, or more reliable than, the Abelian gadgets it replaces within statistical error, while using two to three times fewer rounds.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.05307",
  "author_total": 1,
  "authors": [
    {
      "name": "Tushar Pandey"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4hsfn7bfar10s.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.05307",
  "fulltext_url": null,
  "id": "4hsfn7bfar10s",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.05307",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "1702|Quantum Computing Algorithms and Architecture"
    ]
  ],
  "openalex": "W7220736163",
  "pdf_url": "https://arxiv.org/pdf/2610.05307",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4hsfn7bfar10s.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:01Z",
      "native_id": "2610.05307",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.05307"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Lifted surgery for non-Abelian two-block group-algebra codes",
  "title_text": "Lifted surgery for non-Abelian two-block group-algebra codes",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:01Z",
  "url": "https://research.draconitic.com/paper/4hsfn7bfar10s",
  "venue": "arXiv",
  "versions": []
}