Efficient Learning of Clifford-Scrambled Product States

Quantum Physics arXiv:2609.27128 (quant-ph) [Submitted on 22 Sep 2026] Title:Efficient Learning of Clifford-Scrambled Product States Authors:Tobias Haug View a PDF of the paper titled Efficient Learning of Clifford-Scrambled Product States, by Tobias Haug View PDF HTML (experimental) Abstract:Clifford circuits acting on product magic states provide a compact ansatz exhibiting extensive magic, volume-law entanglement, and even classically hard sampling under standard complexity assumptions. Here, we efficiently recover its hidden product subsystems from two-copy Bell sampling. Quadratic relations between Bell samples determine the irreducible blocks after removing Pauli stabilizers, and binary linear algebra constructs a Clifford disentangler. For logarithmic-size blocks, approximate learning of the full state is efficient whenever the state remains inverse-polynomially separated from acquiring additional Pauli stabilizers. We efficiently learn $n$-qubit states prepared by random $T$-doped Clifford circuits with $T$-gate density below one via $O(n^2)$ Bell samples, and disentangle hidden product blocks in Clifford-augmented matrix product states. For unitary learning, we exactly learn $T$-depth-one circuits using $O(n^2)$ queries. Finally, we rule out pseudorandom states and unitaries with a product bipartition hidden by Clifford circuits. Comments: Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2609.27128 [quant-ph] (or arXiv:2609.27128v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2609.27128 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Tobias Haug [view email] [v1] Tue, 22 Sep 2026 22:39:55 UTC (52 KB) Full-text links: Access Paper: View a PDF of the paper titled Efficient Learning of Clifford-Scrambled Product States, by Tobias HaugView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-09 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?)