{
  "abstract": "We construct an exact $n$-bit quantum adder with $O(n)$ gates and $O(\\log n)$ depth that requires no ancillary qubits. The circuit uses only $X$, CNOT, and Toffoli gates under all-to-all connectivity and is classically reversible. Our construction accelerates the controlled ladder underlying addition. Grouping the data into blocks and use existing control qubits as conditional workspace gives a recursive construction with $O(n\\log\\log n)$ gates and $O(\\log n)$ depth. We then coordinate inter-block propagation via two short-path forest operations to cut the per-block workspace requirement, yielding a nonrecursive implementation with $O(n)$ gates. Both the gate count and circuit depth are asymptotically optimal.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.34446",
  "author_total": 4,
  "authors": [
    {
      "name": "Junhong Nie"
    },
    {
      "name": "Jialiang Tang"
    },
    {
      "name": "Xiaoming Sun"
    },
    {
      "name": "Wei Zi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6mt83n9m98mwf.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.34446",
  "fulltext_url": null,
  "id": "6mt83n9m98mwf",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.34446",
  "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": "W7223805656",
  "pdf_url": "https://arxiv.org/pdf/2610.34446",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-25",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6mt83n9m98mwf.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:35Z",
      "native_id": "2610.34446",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.34446"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Ancilla-free optimal quantum adder",
  "title_text": "Ancilla-free optimal quantum adder",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:35Z",
  "url": "https://research.draconitic.com/paper/6mt83n9m98mwf",
  "venue": "arXiv",
  "versions": []
}