Direct U(2) approximation via repeat-until-success circuits

Quantum Physics [Submitted on 21 Apr 2026] Direct U(2) approximation via repeat-until-success circuits Vadym Kliuchnikov, Jendrik Brachter, Marcus P. da Silva We show how to directly and efficiently approximate arbitrary one-qubit unitaries, bypassing the Euler decomposition and the magnitude approximation problem, at the cost of one ancillary qubit. Our technique also applies to approximating unitaries with multi-qubit gate sets such as Clifford and CS, or Clifford and CCZ, as well as to approximating orthogonal matrices using multi-qubit gate sets such as Real Clifford and CCZ. The key tools are repeat-until-success circuits, lattice-based exact synthesis algorithms, integer point enumeration in convex sets, and relative norm equations. Comments: 9 pages, 1 figure, 1 table Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2604.20033 [quant-ph]   (or arXiv:2604.20033v1 [quant-ph] for this version)   https://doi.org/10.48550/arXiv.2604.20033 Focus to learn more Submission history From: Marcus Silva [view email] [v1] Tue, 21 Apr 2026 22:35:49 UTC (14 KB) Access Paper: view license Current browse context: quant-ph < prev   |   next > new | recent | 2026-04 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?)