{
  "abstract": "Quantum error correction enables scalable fault-tolerant quantum computation by suppressing logical errors exponentially with code distance once physical error rates fall below a critical threshold. Here we demonstrate below-threshold operation of triangular color codes with distances $d=3,5,$ and $7$ on Quantinuum's Helios trapped-ion quantum processor. Leveraging both circuit- and hardware- level leakage reduction schemes, we achieve logical error rates as low as $5_{-2}^{+4}\\times 10^{-6}$, and demonstrate error suppression by over an order of magnitude, $Λ=12_{-2}^{+3}$, with each successive increase in code distance. Moreover, we demonstrate below threshold scaling of error rates for Clifford two-qubit randomized benchmarking circuits when encoded in $d=3,5$ color codes, achieving logical error rate of $7^{+3}_{-3}\\times 10^{-5}$ per logical two-qubit Clifford at distance $5$ with a suppression factor of $Λ=9_{-3}^{+8}$. We compare logical performance for existing near-optimal algorithmic decoders, and both convolutional neural network and transformer-based neural network decoders capable of real-time decoding an order of magnitude faster than the syndrome extraction rate. These results approach the logical error rates required for megaquop-scale quantum computation and indicate that scaled trapped-ion processors could reach application-relevant performance with substantially smaller code blocks than indicated by previous results in other qubit modalities.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.24077",
  "author_total": 23,
  "authors": [
    {
      "name": "Ali Lavasani"
    },
    {
      "name": "Adam P. Reed"
    },
    {
      "name": "Joan M. Dreiling"
    },
    {
      "name": "Annie J. Park"
    },
    {
      "name": "Michael Mills"
    },
    {
      "name": "Matteo Puviani"
    },
    {
      "name": "Gabriel Matos"
    },
    {
      "name": "M. S. Allman"
    },
    {
      "name": "Noah Berthusen"
    },
    {
      "name": "Natalie C. Brown"
    },
    {
      "name": "Victor E. Colussi"
    },
    {
      "name": "Brian Estey"
    },
    {
      "name": "Cameron Foltz"
    },
    {
      "name": "Daniel Gresh"
    },
    {
      "name": "Reza Haghshenas"
    },
    {
      "name": "Akhil Isanaka"
    },
    {
      "name": "Nikhil Kotibhaskar"
    },
    {
      "name": "Anthony Ransford"
    },
    {
      "name": "Ciarán Ryan-Anderson"
    },
    {
      "name": "Brian Neyenhuis"
    },
    {
      "name": "David Hayes"
    },
    {
      "name": "Tzvetan S. Metodi"
    },
    {
      "name": "Andrew C. Potter"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/00gbq5p9h1zp0.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.24077",
  "fulltext_url": null,
  "id": "00gbq5p9h1zp0",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.24077",
  "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": "W7223060522",
  "pdf_url": "https://arxiv.org/pdf/2610.24077",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/00gbq5p9h1zp0.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:52Z",
      "native_id": "2610.24077",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.24077"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Quantum error correction well below the color code threshold",
  "title_text": "Quantum error correction well below the color code threshold",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:41Z",
  "url": "https://research.draconitic.com/paper/00gbq5p9h1zp0",
  "venue": "arXiv",
  "versions": []
}