{"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/clifford-gates-with-logical-transversality","title":"Clifford gates with logical transversality for self-dual CSS codes","arxiv_id":"2503.19790","date":"2025-03-25","proceeding":null,"authors":["Theerapat Tansuwannont","Yugo Takada","Keisuke Fujii"],"abstract":"Quantum error-correcting codes with high encoding rate are good candidates for large-scale quantum computers as they use physical qubits more efficiently than codes of the same distance that encode only a few logical qubits. Some logical gate of a high-rate code can be fault-tolerantly implemented using transversal physical gates, but its logical operation may depend on the choice of a symplectic basis that defines logical Pauli operators of the code. In this work, we focus on $[\\![n,k,d]\\!]$ self-dual Calderbank-Shor-Steane (CSS) codes with $k \\geq 1$ and prove necessary and sufficient conditions for the code to have a symplectic basis such that (1) transversal logical Hadamard gates $\\bigotimes_{j=1}^{k} \\bar{H}_j$ can be implemented by transversal physical Hadamard gates $\\bigotimes_{i=1}^{n} H_i$, and (2) for any $(a_1,\\dots,a_k)\\in\\{-1,1\\}^k$, transversal logical phase gates $\\bigotimes_{j=1}^{k} \\bar{S}_j^{a_j}$ can be implemented by transversal physical phase gates $\\bigotimes_{i=1}^{n} S_i^{b_i}$ for some $(b_1,\\dots,b_n)\\in\\{-1,1\\}^n$. Self-dual CSS codes satisfying the conditions include any codes with odd $n$. We also generalize the idea to concatenated self-dual CSS codes and show that certain logical Clifford gates have multiple transversal implementations, each by logical gates at a different level of concatenation. Several applications of our results for fault-tolerant quantum computation with low overhead are also provided.","url_abs":"https://arxiv.org/abs/2503.19790v1","url_pdf":"https://arxiv.org/pdf/2503.19790v1.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":"clifford-gates-with-logical-transversality","repo_url":"https://github.com/yugotakada/mlvtrans","is_official":1,"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}