{
  "abstract": "Quantum low-density parity-check codes now reach encoding rates up to 50% at useful distances. Their checks however are long-range group actions, not local neighbourhoods, and that connectivity has so far been supplied by neutral atoms. Silicon spin qubits offer the same primitive --- coherent transport of qubit blocks --- through electron shuttling, and on microsecond rather than millisecond timescales. They however travel along fabricated tracks rather than free space: permutations an atom array obtains by moving tweezers must here become collision-free motions on a physical lattice. We here present the first code and spin-qubit hardware co-design. We build an architecture whose geometry mimics that of a family of non-abelian groups, broad enough to host codes of excellent parameters: a hierarchy of nested conveyor-belt loops on a plain square lattice of shuttling tracks, in which every group multiplication becomes a rigid, globally controlled motion of whole qubit trains. We call it NeST, for Nested Shuttling Tracks. A code search over the family returns rate-20% mitten codes up to $[[1400,280,\\leq 28]]$, and circuit-level simulations including shuttling dephasing give thresholds above $10^{-3}$ with sub-$50μ$s stabiliser cycles, two to three orders of magnitude faster than neutral-atom implementations. Via extrapolations, we estimate that this largest code may reach a logical error probability per qubit per round of $10^{-14}$, assuming a ten-fold improvement on early shuttling demonstrations, with other physical errors at p=0.1%. Logic is compatible with NeST too: for the [[150,30,10]] code we build a code-surgery gadget in which every qubit again moves only by rigid belt motions, at no qubit cost and a 29% increase in gate layers. This demonstrates that ultra-low-overhead fault tolerance and a fast clock speed are not competing goals, and that silicon spin qubits can supply both.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.28538",
  "author_total": 1,
  "authors": [
    {
      "name": "Adam Siegel"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8c094z64vskw4.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.28538",
  "fulltext_url": null,
  "id": "8c094z64vskw4",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.28538",
  "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": "W7223114326",
  "pdf_url": "https://arxiv.org/pdf/2610.28538",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8c094z64vskw4.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:04Z",
      "native_id": "2610.28538",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.28538"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "NeST: ultra-high-rate qLDPC codes with sub-$50μ$s stabiliser cycles via spin shuttling",
  "title_text": "NeST: ultra-high-rate qLDPC codes with sub-50μs stabiliser cycles via spin shuttling",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:04Z",
  "url": "https://research.draconitic.com/paper/8c094z64vskw4",
  "venue": "arXiv",
  "versions": []
}