Operator dynamics in k-Markov random circuits

Quantum Physics [Submitted on 18 Mar 2026] Operator dynamics in k-Markov random circuits Unnati Akhouri, Pei-Jun Huang, Elliott Rose, Sarah Shandera 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: 5 pages 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 Submission history From: Sarah Shandera [view email] [v1] Wed, 18 Mar 2026 19:02:46 UTC (2,103 KB) Access Paper: HTML (experimental) view license Current browse context: quant-ph < prev   |   next > new | recent | 2026-03 References & Citations INSPIRE HEP NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation 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 Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)