Clifford synthesis via generalized S and CZ gates

Quantum Physics [Submitted on 25 Mar 2026] Clifford synthesis via generalized S and CZ gates Vadym Kliuchnikov, Marcus P. da Silva We show that any n-qubit Clifford unitary can be implemented using at most 2n multi-qubit joint measurements. All the multi-qubit joint measurements used for implementing the Clifford unitary can be chosen to form at most two sets of independent mutually-commuting measurements. Each of these sets is of size at most n. This enables very flexible space-time trade-offs when implementing Clifford unitaries. We also discuss a version of the result that relies on multi-target CNOTs and is more relevant for targeting fault-tolerant hardware based on Quantum LDPC codes. Comments: 8 pages, 4 figures Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2603.24731 [quant-ph]   (or arXiv:2603.24731v1 [quant-ph] for this version)   https://doi.org/10.48550/arXiv.2603.24731 Focus to learn more Submission history From: Marcus Silva [view email] [v1] Wed, 25 Mar 2026 18:54:46 UTC (110 KB) Access Paper: HTML (experimental) view license Current browse context: quant-ph < prev   |   next > new | recent | 2026-03 References & Citations INSPIRE HEP NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)