{"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/optimal-quantum-circuits-for-general-two","title":"Optimal Quantum Circuits for General Two-Qubit Gates","arxiv_id":"quant-ph/0308006","date":"2003-08-01","proceeding":null,"authors":["Farrokh Vatan","Colin Williams"],"abstract":"In order to demonstrate non-trivial quantum computations experimentally, such as the synthesis of arbitrary entangled states, it will be useful to understand how to decompose a desired quantum computation into the shortest possible sequence of one-qubit and two-qubit gates. We contribute to this effort by providing a method to construct an optimal quantum circuit for a general two-qubit gate that requires at most 3 CNOT gates and 15 elementary one-qubit gates. Moreover, if the desired two-qubit gate corresponds to a purely real unitary transformation, we provide a construction that requires at most 2 CNOTs and 12 one-qubit gates. We then prove that these constructions are optimal with respect to the family of CNOT, y-rotation, z-rotation, and phase gates.","url_abs":"https://arxiv.org/abs/quant-ph/0308006v3","url_pdf":"https://arxiv.org/pdf/quant-ph/0308006v3.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":"optimal-quantum-circuits-for-general-two","repo_url":"https://github.com/iQuHACK/2021_Pauli-Wanna-Cracker","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null},{"paper_slug":"optimal-quantum-circuits-for-general-two","repo_url":"https://github.com/tson1111/quantum-gate-decomp","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}