{"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/quantum-addition-circuits-and-unbounded-fan","title":"Quantum Addition Circuits and Unbounded Fan-Out","arxiv_id":"0910.2530","date":"2009-10-14","proceeding":null,"authors":["Yasuhiro Takahashi","Seiichiro Tani","Noboru Kunihiro"],"abstract":"We first show how to construct an O(n)-depth O(n)-size quantum circuit for addition of two n-bit binary numbers with no ancillary qubits. The exact size is 7n-6, which is smaller than that of any other quantum circuit ever constructed for addition with no ancillary qubits. Using the circuit, we then propose a method for constructing an O(d(n))-depth O(n)-size quantum circuit for addition with O(n/d(n)) ancillary qubits for any d(n)=\\Omega(log n). If we are allowed to use unbounded fan-out gates with length O(n^c) for an arbitrary small positive constant c, we can modify the method and construct an O(e(n))-depth O(n)-size circuit with o(n) ancillary qubits for any e(n)=\\Omega(log* n). In particular, these methods yield efficient circuits with depth O(log n) and with depth O(log* n), respectively. We apply our circuits to constructing efficient quantum circuits for Shor's discrete logarithm algorithm.","url_abs":"https://arxiv.org/abs/0910.2530v1","url_pdf":"https://arxiv.org/pdf/0910.2530v1.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":"quantum-addition-circuits-and-unbounded-fan","repo_url":"https://github.com/shaunmillerc1010/QuantumCircuits","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}