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Comment on "Evolution Operator Can Always Be Separated into the Product of Holonomy and Dynamic Operators"

arXiv Quantum Physics
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⚡ Quantum Brief
Physicists Adam Fredriksson and Erik Sjöqvist published a rebuttal in Physical Review Letters (February 2026) disproving a 2023 claim that quantum evolution operators can universally decompose into holonomy and dynamic components. The original assertion, published in PRL 131, relied on circular logic by implicitly using the time evolution operator itself to derive the separation, rendering the proof invalid. Their analysis demonstrates that the proposed factorization fails mathematically, as it presupposes the structure it aims to prove, undermining the generality of the decomposition. The critique targets foundational assumptions in quantum control theory, particularly holonomic quantum computing, where such separations are often assumed for gate design. This correction clarifies limits in quantum operator theory, impacting research on geometric phases and non-adiabatic quantum dynamics.
Comment on "Evolution Operator Can Always Be Separated into the Product of Holonomy and Dynamic Operators"

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Quantum Physics arXiv:2602.13648 (quant-ph) [Submitted on 14 Feb 2026] Title:Comment on "Evolution Operator Can Always Be Separated into the Product of Holonomy and Dynamic Operators" Authors:Adam Fredriksson, Erik Sjöqvist View a PDF of the paper titled Comment on "Evolution Operator Can Always Be Separated into the Product of Holonomy and Dynamic Operators", by Adam Fredriksson and 1 other authors View PDF HTML (experimental) Abstract:We show that the claim in Ref. [PRL 131, 200202 (2023)], that the quantum time evolution always can be written as a product of a holonomy operator and a dynamic operator, is false, as it is based on a circular use of the time evolution operator. Comments: Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2602.13648 [quant-ph] (or arXiv:2602.13648v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2602.13648 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Journal reference: Phys. Rev. Lett. 136, 068901 (2026) Related DOI: https://doi.org/10.1103/d5rt-jpjk Focus to learn more DOI(s) linking to related resources Submission history From: Erik Sjoqvist [view email] [v1] Sat, 14 Feb 2026 07:41:37 UTC (2 KB) Full-text links: Access Paper: View a PDF of the paper titled Comment on "Evolution Operator Can Always Be Separated into the Product of Holonomy and Dynamic Operators", by Adam Fredriksson and 1 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-02 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?)

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Source: arXiv Quantum Physics