Graph-State Circuit Blocks control Entanglement and Scrambling Velocities
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Quantum Physics arXiv:2605.11076 (quant-ph) [Submitted on 11 May 2026] Title:Graph-State Circuit Blocks control Entanglement and Scrambling Velocities Authors:Chandana Rao, Himanshu Sahu, Aranya Bhattacharya, Suhail Ahmad Rather, Mario Flory, Zahra Raissi View a PDF of the paper titled Graph-State Circuit Blocks control Entanglement and Scrambling Velocities, by Chandana Rao and 4 other authors View PDF HTML (experimental) Abstract:Random circuit models often describe local dynamics using generic two-qubit gates, which have proven successful in capturing entanglement growth and operator spreading in many contexts. This approach naturally leads to the expectation that detailed gate structure plays only a limited role in coarse-grained entanglement and scrambling diagnostics. We show that the internal structure of multipartite circuit primitives can significantly influence these dynamical rates, even within a fixed random-circuit architecture. To investigate this, we study an exactly simulable family of Clifford quantum circuits built from fixed $n$-qubit graph-state preparation unitaries, which we treat as elementary building blocks. Specifically, we consider a one-dimensional chain of $N$ qubits initialized in a product state and evolved by layers in which nonoverlapping length-$n$ blocks are placed at uniformly random positions with sparsity $\alpha$. We find that different choices of graph-state building blocks lead to strongly varying dynamical rates. Graph states that are inequivalent under local Clifford (LC) transformations generate sharply different entanglement velocities $v_E$ and butterfly velocities $v_B$, even though the circuits are drawn from the same ensemble with identical architecture and randomness parameters. We further show that this hierarchy is captured by two complementary block-level characteristics: the distribution of entanglement across internal bipartitions of the graph state, which correlates with $v_E$, and a graph-theoretic connectivity profile across bipartitions, which correlates with $v_B$. Neither descriptor alone fully determines the dynamics; rather, entanglement growth and operator spreading are controlled by distinct structural features of the local circuit blocks. Notably, AME states appear among the fastest scrambling building blocks within the ensembles studied here. Comments: Subjects: Quantum Physics (quant-ph); High Energy Physics - Theory (hep-th) Cite as: arXiv:2605.11076 [quant-ph] (or arXiv:2605.11076v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2605.11076 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Zahra Raissi [view email] [v1] Mon, 11 May 2026 18:00:03 UTC (415 KB) Full-text links: Access Paper: View a PDF of the paper titled Graph-State Circuit Blocks control Entanglement and Scrambling Velocities, by Chandana Rao and 4 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-05 Change to browse by: hep-th 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?)