Operator dynamics in k-Markov random circuits
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Quantum Physics arXiv:2603.18217 (quant-ph) [Submitted on 18 Mar 2026] Title:Operator dynamics in k-Markov random circuits Authors:Unnati Akhouri, Pei-Jun Huang, Elliott Rose, Sarah Shandera View a PDF of the paper titled Operator dynamics in k-Markov random circuits, by Unnati Akhouri and 3 other authors View PDF HTML (experimental) Abstract:We demonstrate that $k$-Markov sequences of unitary gates provide low-cost handles to manipulate the rate and structure of information spreading compared to traditional random, 0-Markov, circuits. For SWAP gates and brickwork circuits, we use graph cover time to demonstrate how $k$-Markov processes can be used to control operator transport. With SWAP gates and the set of Clifford gates that can change operator weight, we show how $k$-Markov sequences can be used to manipulate scrambling time and generate novel structures of spatial-temporal correlations across a qubit network. We show that $k$-Markov circuits constructed from PSWAP gates at fixed angle are equivalent to standard brickwork circuits with PSWAP angle drawn from non-uniform distributions generated by the $k$-Markov process. In those circuits, the time evolution of the average Hamming weight and the space-time correlation structure after equilibrium again vary significantly from the 0-Markov case, depending on the transition probabilities of the process. Comments: Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2603.18217 [quant-ph] (or arXiv:2603.18217v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2603.18217 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Sarah Shandera [view email] [v1] Wed, 18 Mar 2026 19:02:46 UTC (2,103 KB) Full-text links: Access Paper: View a PDF of the paper titled Operator dynamics in k-Markov random circuits, by Unnati Akhouri and 3 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-03 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?)