{
  "abstract": "Compilation of two-qubit Fibonacci anyon gates is complicated by leakage ($\\ell$) from the four-dimensional computational sector to the fifth state of the fusion space. We construct a GPU pipeline to find low-leakage representatives of the $[\\text{CNOT}]$ class on different subsets of the braid group. We exhaustively explore the full positive five-generator alphabet up to $L=21$ with minimal leakage $\\ell\\sim10^{-3}$ and error $d_{[\\text{CNOT}]}\\sim 10^{-8}$ on it. To reach larger lengths, the search space is successively narrowed to three-generator, boundary-$σ_3$, and palindromic braids, and by considering only the Garside left normal form. These optimizations allow us to reach $L=72$. For $L=69$, a braid with $\\ell\\sim10^{-10}$ and $d_{[\\text{CNOT}]}\\sim 10^{-10}$ is found. In addition to directly enumerating optimal braids, we proved that $\\ell\\in\\mathbb Z[φ]$, and any nonzero leakage obeys an exponential lower bound in the braid length, and obtained the limit laws $F_{3,\\infty}(\\ell)=\\ell^2$ and $F_{5,\\infty}(\\ell)=\\ell^4$ for our sets. Using asymptotics for the distribution function $F$, we showed that for sufficiently long braids, the asymptotics of exhaustive search are better than the asymptotics of random sampling for finding low-leakage braids.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.37552",
  "author_total": 2,
  "authors": [
    {
      "name": "Matvei Fedin"
    },
    {
      "name": "Andrey Morozov"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4qv6qcy0t7evn.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.37552",
  "fulltext_url": null,
  "id": "4qv6qcy0t7evn",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.37552",
  "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",
      "hep-th"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "1702|Quantum Computing Algorithms and Architecture"
    ]
  ],
  "openalex": "W7224130991",
  "pdf_url": "https://arxiv.org/pdf/2610.37552",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4qv6qcy0t7evn.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:50Z",
      "native_id": "2610.37552",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.37552"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:hep-th",
      "subfield": "high-energy"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Meet-in-the-Middle Compilation of the $[\\mathrm{CNOT}]$ Class with Fibonacci Anyons",
  "title_text": "Meet-in-the-Middle Compilation of the [CNOT] Class with Fibonacci Anyons",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:50Z",
  "url": "https://research.draconitic.com/paper/4qv6qcy0t7evn",
  "venue": "arXiv",
  "versions": []
}