{"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/190407356","title":"Asymptotically Efficient Quantum Karatsuba Multiplication","arxiv_id":"1904.07356","date":"2019-04-15","proceeding":null,"authors":["Craig Gidney"],"abstract":"We improve the space complexity of Karatsuba multiplication on a quantum computer from $O(n^{1.427})$ to $O(n)$ while maintaining $O(n^{\\lg 3})$ gate complexity. We achieve this by ensuring recursive calls can add their outputs directly into subsections of the output register. This avoids the need to store, and uncompute, intermediate results. This optimization, which is analogous to classical tail-call optimization, should be applicable to a wide range of recursive quantum algorithms.","url_abs":"http://arxiv.org/abs/1904.07356v1","url_pdf":"http://arxiv.org/pdf/1904.07356v1.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":"190407356","repo_url":"https://github.com/Strilanc/quantum-karatsuba-2019","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok"}}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1904.07356","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}