{
  "abstract": "On a chain of exchange-coupled quantum dots a Heisenberg exchange pulse of area pi is a SWAP, so the parallel bubble-sort SWAP network of superconducting chains is native to exchange-only (EO) spin qubits, and any other pulse area fuses routing with an entangling interaction. We build a variational \"bubble-sort exchange network\" (odd-even transposition, one parameter per pulse) and study it as a Born machine read out by Pauli spin blockade. Exchange conserves total spin, so the reachable readout distributions are fixed by the total-spin content of the initial product state. For the two-spin singlet-triplet encoding we derive a selection rule -- outcomes with k triplet pairs are bounded by the initial weight in sectors S <= k (S = 0 excluded for k = 1) -- and prove by a transportation argument that it is also sufficient: the reachable distributions form the polytope cut out by the rule, and its total-variation floor is attained. Products of singlets and T0's forbid whole outcome classes; the Neel state forbids none; the three-spin EO code has no floor. We then distil, in noise-free simulation, next-token distributions of GPT-2 over restricted vocabularies into the network, with matrix-product-state (MPS) Born machines as classical control. At six logical qubits the three-spin chain reaches KL = 0.011 nat at depth N and 0.004 at 2N, below the bond-dimension-4 MPS; the two-spin chain from the Neel state reaches 0.014 at 2N and 0.004 at 3N, against 0.28-1.5 from singlet/triplet products for the first teacher. Final states lie largely outside the code space: leakage is a resource, not an error. No arrangement of disjoint pulses meets every pair in fewer than N-1 rounds, and at depth 2N the chain distils as well as a 2D array or non-local couplings. Sector-restricted simulation extends this to 10-14 logical qubits (up to 30 dots).",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.22093",
  "author_total": 1,
  "authors": [
    {
      "name": "Yuichiro Minato"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4asbgz32ms7fj.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.22093",
  "fulltext_url": null,
  "id": "4asbgz32ms7fj",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.22093",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "1702|Quantum Computing Algorithms and Architecture"
    ]
  ],
  "openalex": "W7222567621",
  "pdf_url": "https://arxiv.org/pdf/2610.22093",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4asbgz32ms7fj.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:50Z",
      "native_id": "2610.22093",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.22093"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Bubble-Sort Exchange Networks: Symmetry Selection Rules and Language-Model Distillation on Exchange-Only Spin Chains",
  "title_text": "Bubble-Sort Exchange Networks: Symmetry Selection Rules and Language-Model Distillation on Exchange-Only Spin Chains",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:50Z",
  "url": "https://research.draconitic.com/paper/4asbgz32ms7fj",
  "venue": "arXiv",
  "versions": []
}