{"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/circuit-for-shors-algorithm-using-2n3-qubits","title":"Circuit for Shor's algorithm using 2n+3 qubits","arxiv_id":"quant-ph/0205095","date":"2002-05-15","proceeding":null,"authors":["Stephane Beauregard"],"abstract":"We try to minimize the number of qubits needed to factor an integer of n bits using Shor's algorithm on a quantum computer. We introduce a circuit which uses 2n+3 qubits and O(n^3 lg(n)) elementary quantum gates in a depth of O(n^3) to implement the factorization algorithm. The circuit is computable in polynomial time on a classical computer and is completely general as it does not rely on any property of the number to be factored. Keywords: Factorization, quantum circuits, modular arithmetics","url_abs":"https://arxiv.org/abs/quant-ph/0205095v3","url_pdf":"https://arxiv.org/pdf/quant-ph/0205095v3.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":"circuit-for-shors-algorithm-using-2n3-qubits","repo_url":"https://github.com/Fagin-H/Google-Cirq","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null},{"paper_slug":"circuit-for-shors-algorithm-using-2n3-qubits","repo_url":"https://github.com/HK-ilohas/quantum_simulation","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null},{"paper_slug":"circuit-for-shors-algorithm-using-2n3-qubits","repo_url":"https://github.com/SamScherf/shors-algorithm","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null},{"paper_slug":"circuit-for-shors-algorithm-using-2n3-qubits","repo_url":"https://github.com/alfa871212/shor_paper","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"tf","reach":null},{"paper_slug":"circuit-for-shors-algorithm-using-2n3-qubits","repo_url":"https://github.com/bartek-bartlomiej/master-thesis","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok","spdx":"Apache-2.0"}},{"paper_slug":"circuit-for-shors-algorithm-using-2n3-qubits","repo_url":"https://github.com/gkotas/IBM","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}