{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/translation-invariant-quantum-algorithms-for","title":"Translation-Invariant Quantum Algorithms for Ordered Search are Optimal","arxiv_id":"2503.21090","date":"2025-03-27","proceeding":null,"authors":["Joseph Carolan","Andrew M. Childs","Matt Kovacs-Deak","Luke Schaeffer"],"abstract":"Ordered search is the task of finding an item in an ordered list using comparison queries. The best exact classical algorithm for this fundamental problem uses $\\lceil \\log_{2}{n}\\rceil$ queries for a list of length $n$. Quantum computers can achieve a constant-factor speedup, but the best possible coefficient of $\\log_{2}{n}$ for exact quantum algorithms is only known to lie between $(\\ln{2})/\\pi \\approx 0.221$ and $4/\\log_{2}{605} \\approx 0.433$. We consider a special class of translation-invariant algorithms with no workspace, introduced by Farhi, Goldstone, Gutmann, and Sipser, that has been used to find the best known upper bounds. First, we show that any bounded-error, $k$-query quantum algorithm for ordered search can be implemented by a $k$-query algorithm in this special class. Second, we use linear programming to show that the best exact $5$-query quantum algorithm can search a list of length $7265$, giving an ordered search algorithm that asymptotically uses $5 \\log_{7265}{n} \\approx 0.390 \\log_{2}{n}$ quantum queries.","url_abs":"https://arxiv.org/abs/2503.21090v1","url_pdf":"https://arxiv.org/pdf/2503.21090v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"translation-invariant-quantum-algorithms-for","repo_url":"https://github.com/jacarolan/ordered_search_public","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":"https://app.syntology.ai/?focus=2503.21090","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}