{
  "abstract": "Qudits provide a larger local Hilbert space than qubits and have recently attracted interest as building blocks for efficient fault-tolerant quantum computation (FTQC). In this work, we extend many-hypercube (MHC) codes, high-rate concatenated quantum codes, from qubits to qudits of prime dimension $q$. We construct the level-2 and level-3 MHC codes with parameters $\\left[\\!\\left[6^2,4^2,2^2\\right]\\!\\right]_q$ and $\\left[\\!\\left[6^3,4^3,2^3\\right]\\!\\right]_q$, respectively, and generalize the level-by-level minimum-distance (LLMD) decoder originally proposed for the qubit MHC codes. In a qudit $X$-error model, we evaluate the code-capacity performance of the qudit MHC codes for dimensions up to $q=13$. We find that the error threshold increases monotonically with the local dimension $q$, reaching $10.0\\%$ for $q=13$, nearly double the value of $5.1\\%$ for qubits. Furthermore, for sufficiently large local dimensions, we observe a pronounced waterfall regime in which the logical error rate decreases substantially faster than expected from conventional distance-based estimates. To understand the origin of the observed qudit advantage, we analyze the decoding performance in terms of the entropy of the underlying $q$-ary noise channel. This analysis reveals a competition between the increased syndrome information available at larger $q$ and the simultaneous growth of the typical physical error weight at fixed entropy. These results demonstrate that higher-dimensional quantum systems can substantially improve the performance of high-rate concatenated quantum codes and motivate further development of qudit-based FTQC architectures.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.11225",
  "author_total": 2,
  "authors": [
    {
      "name": "Takanori Nishi"
    },
    {
      "name": "Hayato Goto"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0091zfqh8tf2d.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.11225",
  "fulltext_url": null,
  "id": "0091zfqh8tf2d",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.11225",
  "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": "W7221081032",
  "pdf_url": "https://arxiv.org/pdf/2610.11225",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0091zfqh8tf2d.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:54Z",
      "native_id": "2610.11225",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.11225"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "High-Rate Concatenated Quantum Error-Correcting Codes for Qudits",
  "title_text": "High-Rate Concatenated Quantum Error-Correcting Codes for Qudits",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:54Z",
  "url": "https://research.draconitic.com/paper/0091zfqh8tf2d",
  "venue": "arXiv",
  "versions": []
}