{"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/synthesizing-toffoli-optimal-quantum-circuits","title":"Synthesizing Toffoli-optimal quantum circuits for arbitrary multi-qubit unitaries","arxiv_id":"2401.08950","date":"2024-01-17","proceeding":null,"authors":["Priyanka Mukhopadhyay"],"abstract":"In this paper we study the Clifford+Toffoli universal fault-tolerant gate set. We introduce a generating set in order to represent any unitary implementable by this gate set and with this we derive a bound on the Toffoli-count of arbitrary multi-qubit unitaries. We analyse the channel representation of the generating set elements, with the help of which we infer $|\\mathcal{J}_n^{Tof}|<|\\mathcal{J}_n^T|$, where $\\mathcal{J}_n^{Tof}$ and $\\mathcal{J}_n^T$ are the set of unitaries exactly implementable by the Clifford+Toffoli and Clifford+T gate set, respectively. We develop Toffoli-count optimal synthesis algorithms for both approximately and exactly implementable multi-qubit unitaries. With the help of these we prove $|\\mathcal{J}_n^{Tof}|=|\\mathcal{J}_n^{CS}|$, where $\\mathcal{J}_n^{CS}$ is the set of unitaries exactly implementable by the Clifford+CS gate set.","url_abs":"https://arxiv.org/abs/2401.08950v1","url_pdf":"https://arxiv.org/pdf/2401.08950v1.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":"synthesizing-toffoli-optimal-quantum-circuits","repo_url":"https://github.com/priyankamukhopadhyay/Toffoli-opt","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"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}