Explicit States with Two-sided Long-Range Magic
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Quantum Physics arXiv:2603.25023 (quant-ph) [Submitted on 26 Mar 2026] Title:Explicit States with Two-sided Long-Range Magic Authors:Zhi Li View a PDF of the paper titled Explicit States with Two-sided Long-Range Magic, by Zhi Li View PDF HTML (experimental) Abstract:Nonstabilizerness, or magic, is a necessary resource for quantum advantage beyond the classically simulatable Clifford framework. Recent works have begun to chart the structure of magic in many-body states, introducing the concepts of long-range magic -- nonstabilizerness that cannot be removed by finite-depth local unitary (FDU) circuits -- and the magic hierarchy, which classifies quantum circuits by alternating layers of Clifford and FDUs. In this work, we construct explicit states that provably possess two-sided long-range magic, a stronger form of magic meaning that they cannot be prepared by a Clifford circuit and a FDU in either order, thus placing them provably outside the first level of the magic hierarchy. Our examples include the ``magical cat" state, $|\psi\rangle \propto |0^n\rangle + |+^n\rangle$, and ground states of certain nonabelian topological orders. These results provide new examples and proof techniques for circuit complexity, and in doing so, reveal the connection between long-range magic, the structure of many-body phases, and the principles of quantum error correction. Subjects: Quantum Physics (quant-ph); Other Condensed Matter (cond-mat.other) Cite as: arXiv:2603.25023 [quant-ph] (or arXiv:2603.25023v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2603.25023 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Zhi Li [view email] [v1] Thu, 26 Mar 2026 04:40:08 UTC (44 KB) Full-text links: Access Paper: View a PDF of the paper titled Explicit States with Two-sided Long-Range Magic, by Zhi LiView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-03 Change to browse by: cond-mat cond-mat.other 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?)