Unitary designs from perturbed time evolutions of a chaotic Hamiltonian

Quantum Physics arXiv:2607.24851 (quant-ph) [Submitted on 25 Jul 2026] Title:Unitary designs from perturbed time evolutions of a chaotic Hamiltonian Authors:Zhongyi Yang, Biao Wu View a PDF of the paper titled Unitary designs from perturbed time evolutions of a chaotic Hamiltonian, by Zhongyi Yang and Biao Wu View PDF HTML (experimental) Abstract:Unitary designs provide efficient substitutes for Haar-random unitaries in quantum information processing, randomized measurements, and many-body quantum dynamics. We propose a protocol based on time evolutions of a single chaotic Hamiltonian with intermediate unitary perturbations to generate unitary designs. We derive the frame potential of the resulting ensemble which relies on the frame potentials of the intermediate ensemble. The intermediate ensemble need not itself be Haar random or a unitary design even approximately; it is sufficient that its frame-potential growth remains well suppressed relative to the maximal possible scaling. The nontrivial Pauli set and the Clifford ensemble are simple examples satisfying this criterion, while fixed-size ensembles generally fail. We further show that, at the level of frame potentials, multi-Hamiltonian temporal protocols can be recursively replaced by one-Hamiltonian protocols interleaved with fixed trace-suppressed perturbations. Comments: Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2607.24851 [quant-ph] (or arXiv:2607.24851v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2607.24851 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Zhongyi Yang [view email] [v1] Sat, 25 Jul 2026 08:44:01 UTC (676 KB) Full-text links: Access Paper: View a PDF of the paper titled Unitary designs from perturbed time evolutions of a chaotic Hamiltonian, by Zhongyi Yang and Biao WuView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-07 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?) 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?)