{"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/factoring-integers-with-sublinear-resources","title":"Factoring integers with sublinear resources on a superconducting quantum processor","arxiv_id":"2212.12372","date":"2022-12-23","proceeding":null,"authors":["Bao Yan","Ziqi Tan","Shijie Wei","Haocong Jiang","Weilong Wang","Hong Wang","Lan Luo","Qianheng Duan","Yiting Liu","Wenhao Shi","Yangyang Fei","Xiangdong Meng","Yu Han","Zheng Shan","Jiachen Chen","Xuhao Zhu","Chuanyu Zhang","Feitong Jin","Hekang Li","Chao Song","Zhen Wang","Zhi Ma","H. Wang","Gui-Lu Long"],"abstract":"Shor's algorithm has seriously challenged information security based on public key cryptosystems. However, to break the widely used RSA-2048 scheme, one needs millions of physical qubits, which is far beyond current technical capabilities. Here, we report a universal quantum algorithm for integer factorization by combining the classical lattice reduction with a quantum approximate optimization algorithm (QAOA). The number of qubits required is O(logN/loglog N), which is sublinear in the bit length of the integer $N$, making it the most qubit-saving factorization algorithm to date. We demonstrate the algorithm experimentally by factoring integers up to 48 bits with 10 superconducting qubits, the largest integer factored on a quantum device. We estimate that a quantum circuit with 372 physical qubits and a depth of thousands is necessary to challenge RSA-2048 using our algorithm. Our study shows great promise in expediting the application of current noisy quantum computers, and paves the way to factor large integers of realistic cryptographic significance.","url_abs":"https://arxiv.org/abs/2212.12372v1","url_pdf":"https://arxiv.org/pdf/2212.12372v1.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":"factoring-integers-with-sublinear-resources","repo_url":"https://github.com/BenPrie/qaoa-for-cvp","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null},{"paper_slug":"factoring-integers-with-sublinear-resources","repo_url":"https://github.com/2024-MindSpore-1/Code3/tree/main/MindQuantum-2","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"mindspore","reach":null},{"paper_slug":"factoring-integers-with-sublinear-resources","repo_url":"https://github.com/google-research/google-research/tree/master/factoring_sqif","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"jax","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}