{
  "abstract": "A finite-dimensional physical processor cannot exactly program a continuous family of distinct unitary channels. We show that this obstruction becomes quantitative when the target channel is stored in a normalized Choi state and its output observables are reconstructed by sampling physical channels and classically post-processing their measurement outcomes. For arbitrary $d$-dimensional channels, we construct a target-independent exact reconstruction protocol and prove the optimal one-copy sampling overhead, which grows quadratically with system dimension. We further prove the sharp fixed-$d$ law that the excess overhead vanishes inversely with the number of identical Choi programs. The upper bound combines deterministic port-based teleportation with a quasi-decomposition that corrects its depolarizing distortion. The converse maps any low-overhead reconstruction protocol to a physical learner of unknown unitaries and uses local quantum estimation to recover the same leading coefficient. These results recast the universal no-programming obstruction as a quantitative trade-off between quantum program memory and classical sampling, with a leading cost that reflects the locally learnable unitary degrees of freedom.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.01419",
  "author_total": 4,
  "authors": [
    {
      "name": "Mingrui Jing"
    },
    {
      "name": "Mengbo Guo"
    },
    {
      "name": "Hongshun Yao"
    },
    {
      "name": "Xin Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/aaqpv08rap9fr.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.01419",
  "fulltext_url": null,
  "id": "aaqpv08rap9fr",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.01419",
  "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": "W7206157485",
  "pdf_url": "https://arxiv.org/pdf/2609.01419",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/aaqpv08rap9fr.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:00Z",
      "native_id": "2609.01419",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.01419"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Exact Virtual Channel Programming with Vanishing Excess Overhead",
  "title_text": "Exact Virtual Channel Programming with Vanishing Excess Overhead",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:00Z",
  "url": "https://research.draconitic.com/paper/aaqpv08rap9fr",
  "venue": "arXiv",
  "versions": []
}