Parameter-optimal unitary synthesis with flag decompositions
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Quantum Physics arXiv:2603.20376 (quant-ph) [Submitted on 20 Mar 2026] Title:Parameter-optimal unitary synthesis with flag decompositions Authors:Korbinian Kottmann, David Wierichs, Guillermo Alonso-Linaje, Nathan Killoran View a PDF of the paper titled Parameter-optimal unitary synthesis with flag decompositions, by Korbinian Kottmann and 3 other authors View PDF Abstract: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 arXiv-issued DOI via DataCite (pending registration) Submission history From: Korbinian Kottmann [view email] [v1] Fri, 20 Mar 2026 18:00:06 UTC (5,525 KB) Full-text links: Access Paper: View a PDF of the paper titled Parameter-optimal unitary synthesis with flag decompositions, by Korbinian Kottmann and 3 other authorsView PDFTeX Source view license Current browse context: quant-ph new | recent | 2026-03 References & Citations INSPIRE HEP NASA ADSGoogle Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: 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 Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv (What is alphaXiv?) Links to Code Toggle CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub Toggle DagsHub (What is DagsHub?) GotitPub Toggle Gotit.pub (What is GotitPub?) Huggingface Toggle Hugging Face (What is Huggingface?) Links to Code Toggle Papers with Code (What is Papers with Code?) ScienceCast Toggle ScienceCast (What is ScienceCast?) Demos Demos Replicate Toggle Replicate (What is Replicate?) Spaces Toggle Hugging Face Spaces (What is Spaces?) Spaces Toggle TXYZ.AI (What is TXYZ.AI?) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower (What are Influence Flowers?) Core recommender toggle CORE Recommender (What is CORE?) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs. Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)