Anticoncentration and State Design of Doped Real Clifford Circuits and Tensor Networks

Quantum Physics arXiv:2512.15880 (quant-ph) [Submitted on 17 Dec 2025] Title:Anticoncentration and State Design of Doped Real Clifford Circuits and Tensor Networks Authors:Beatrice Magni, Markus Heinrich, Lorenzo Leone, Xhek Turkeshi View a PDF of the paper titled Anticoncentration and State Design of Doped Real Clifford Circuits and Tensor Networks, by Beatrice Magni and Markus Heinrich and Lorenzo Leone and Xhek Turkeshi View PDF Abstract:We investigate the statistical properties of orthogonal, or real, Clifford circuits doped with magic and imaginary resources. By developing the Weingarten calculus for the real Clifford group, we derive the exact overlap distribution of real stabilizer states, identifying a new universality class: the orthogonal Clifford Porter-Thomas distribution. We prove that local real architectures recover this global statistic in logarithmic depth. Furthermore, we uncover a sharp hierarchy in resource requirements: while retrieving Haar statistics necessitates a polylogarithmic amount of magic states, recovering the full unitary Clifford statistics requires only a single phase gate. Comments: Subjects: Quantum Physics (quant-ph); Statistical Mechanics (cond-mat.stat-mech) Cite as: arXiv:2512.15880 [quant-ph] (or arXiv:2512.15880v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2512.15880 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Beatrice Magni [view email] [v1] Wed, 17 Dec 2025 19:00:33 UTC (290 KB) Full-text links: Access Paper: View a PDF of the paper titled Anticoncentration and State Design of Doped Real Clifford Circuits and Tensor Networks, by Beatrice Magni and Markus Heinrich and Lorenzo Leone and Xhek TurkeshiView PDFTeX Source view license Current browse context: quant-ph new | recent | 2025-12 Change to browse by: cond-mat cond-mat.stat-mech 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?)