Structure, Optimality, and Symmetry in Shadow Unitary Inversion

Quantum Physics arXiv:2510.24880 (quant-ph) [Submitted on 28 Oct 2025] Title:Structure, Optimality, and Symmetry in Shadow Unitary Inversion Authors:Guocheng Zhen, Yu-Ao Chen, Mingrui Jing, Jingu Xie, Ranyiliu Chen, Xin Wang View a PDF of the paper titled Structure, Optimality, and Symmetry in Shadow Unitary Inversion, by Guocheng Zhen and Yu-Ao Chen and Mingrui Jing and Jingu Xie and Ranyiliu Chen and Xin Wang View PDF HTML (experimental) Abstract:The ability to reverse any unknown unitary operation plays a fundamental role in quantum computing. While existing studies mostly focus on realizing the inversion map of the unknown unitary, how to reverse a unitary with respect to a given observable, which we call shadow unitary inversion, has remained a natural basic question that is less developed. In this work, we systematically investigate shadow unitary inversion by providing explicit protocols and optimization problem simplification. First, we present a deterministic protocol for shadow inversion of qubit-unitaries. Such construction sequentially queries the unitary 3 times, which is suggested to be optimal by our numerical experiments. Second, we provide a complete characterization of feasible quantum operations for qubit shadow inversion under any fixed qubit observable. Third, for the qudit case, we give a framework of semidefinite programming for optimizing the shadow unitary inversion sequential protocol for tackling high-dimensional cases, utilizing tools from representation theory. Comments: Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2510.24880 [quant-ph] (or arXiv:2510.24880v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2510.24880 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Ranyiliu Chen [view email] [v1] Tue, 28 Oct 2025 18:28:07 UTC (975 KB) Full-text links: Access Paper: View a PDF of the paper titled Structure, Optimality, and Symmetry in Shadow Unitary Inversion, by Guocheng Zhen and Yu-Ao Chen and Mingrui Jing and Jingu Xie and Ranyiliu Chen and Xin WangView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2025-10 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?)