{
  "abstract": "A programmable quantum processor implements a target unitary using information stored in a classical or quantum program register. For arbitrary unitaries in $\\mathrm{SU}(d)$, quantum programs attain the optimal leading-order memory cost, whereas deterministic classical rounding requires twice as much memory for the same diamond-distance error. We show that this gap disappears when classical randomization is allowed. We introduce barycentric programming, which stores the label of a unitary randomly selected from a finite set, with probabilities chosen so that first-order approximation errors cancel in the averaged unitary channel. Consequently, the diamond-distance error scales quadratically with the discretization spacing. For any $ν$-parameter family of unitaries forming a compact, smooth manifold without boundary, this method achieves error $\\varepsilon$ using only $(ν/2)\\log_2(1/\\varepsilon)+O(1)$ classical bits. We also prove a matching lower bound for arbitrary quantum programs, determining the optimal leading-order program size for general unitary families. Thus, classical randomization achieves the optimal scaling $(ν/2+o(1))\\log_2(1/\\varepsilon)$ without requiring coherent quantum memory.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.02441",
  "author_total": 3,
  "authors": [
    {
      "name": "Yutaka Hashimoto"
    },
    {
      "name": "Satoshi Yoshida"
    },
    {
      "name": "Mio Murao"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bmhvxs7kkfd32.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.02441",
  "fulltext_url": null,
  "id": "bmhvxs7kkfd32",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.02441",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2611.02441",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bmhvxs7kkfd32.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:20:59Z",
      "native_id": "2611.02441",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.02441"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Barycentric programming: Classical realization of programs for universal quantum processors",
  "title_text": "Barycentric programming: Classical realization of programs for universal quantum processors",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:18Z",
  "url": "https://research.draconitic.com/paper/bmhvxs7kkfd32",
  "venue": "arXiv",
  "versions": []
}