Parameter-optimal unitary synthesis with flag decompositions

Quantum Physics [Submitted on 20 Mar 2026] Parameter-optimal unitary synthesis with flag decompositions Korbinian Kottmann, David Wierichs, Guillermo Alonso-Linaje, Nathan Killoran We introduce the flag decomposition as a central tool for unitary synthesis. It lets us carve out a diagonal unitary with 2^n degrees of freedom in such a way that the remaining flag circuit is parametrized by the optimal number of 4^n-2^n rotations. This enables us to produce parameter-optimal quantum circuits for generic unitaries and matrix product state preparation. Our approach improves upon the state of the art, both when compiling down to the {Clifford + Rot} gate set with what we call selective de-multiplexing, and when using phase gradient resource states together with quantum arithmetic to implement multiplexed rotations. All of our synthesis methods are efficiently implementable in terms of recursive Cartan decompositions realized by standard linear algebra routines, making them applicable to all practically relevant system sizes. Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2603.20376 [quant-ph]   (or arXiv:2603.20376v1 [quant-ph] for this version)   https://doi.org/10.48550/arXiv.2603.20376 Focus to learn more Submission history From: Korbinian Kottmann [view email] [v1] Fri, 20 Mar 2026 18:00:06 UTC (5,525 KB) Access Paper: 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?)