{"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/synthesis-of-unitaries-with-clifford-t","title":"Synthesis of unitaries with Clifford+T circuits","arxiv_id":"1306.3200","date":"2013-06-13","proceeding":null,"authors":["Vadym Kliuchnikov"],"abstract":"We describe a new method for approximating an arbitrary $n$ qubit unitary with precision $\\varepsilon$ using a Clifford and T circuit with $O(4^{n}n(\\log(1/\\varepsilon)+n))$ gates. The method is based on rounding off a unitary to a unitary over the ring $\\mathbb{Z}[i,1/\\sqrt{2}]$ and employing exact synthesis. We also show that any $n$ qubit unitary over the ring $\\mathbb{Z}[i,1/\\sqrt{2}]$ with entries of the form $(a+b\\sqrt{2}+ic+id\\sqrt{2})/2^{k}$ can be exactly synthesized using $O(4^{n}nk)$ Clifford and T gates using two ancillary qubits. This new exact synthesis algorithm is an improvement over the best known exact synthesis method by B. Giles and P. Selinger requiring $O(3^{2^{n}}nk)$ elementary gates.","url_abs":"https://arxiv.org/abs/1306.3200v1","url_pdf":"https://arxiv.org/pdf/1306.3200v1.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":"synthesis-of-unitaries-with-clifford-t","repo_url":"https://github.com/wmkirby1/schur-transform","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","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}