{
  "abstract": "Ordered search is the problem of locating a target element in a sorted list of size $n$ using comparison queries. Classically, binary search requires $\\lceil \\log_2 n\\rceil$ queries, which is optimal. Quantum algorithms offer a constant-factor speedup, but the precise constant has been a longstanding open question. We close this gap by exhibiting two new quantum algorithms for ordered search, each using the optimal $\\frac{1}π\\ln n+o(\\log n)$ queries. The first, discovered by Claude Fable 5, is a simple zero-error algorithm derived from a continuum relaxation of the problem. The second, discovered by GPT-5.6-Sol (informed by Claude's zero-error algorithm), is an exact algorithm based on an analytic solution of the polynomial program of Farhi, Goldstone, Gutmann, and Sipser.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.34293",
  "author_total": 2,
  "authors": [
    {
      "name": "Joseph Carolan"
    },
    {
      "name": "Andrew M. Childs"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bb8azq7bbwd9t.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.34293",
  "fulltext_url": null,
  "id": "bb8azq7bbwd9t",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.34293",
  "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": "W7214760044",
  "pdf_url": "https://arxiv.org/pdf/2609.34293",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bb8azq7bbwd9t.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:12Z",
      "native_id": "2609.34293",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.34293"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Optimal Quantum Algorithms for Ordered Search",
  "title_text": "Optimal Quantum Algorithms for Ordered Search",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:12Z",
  "url": "https://research.draconitic.com/paper/bb8azq7bbwd9t",
  "venue": "arXiv",
  "versions": []
}