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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2603.18217 |
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| _version_ | 1866918396950478848 |
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| author | Akhouri, Unnati Huang, Pei-Jun Rose, Elliott Shandera, Sarah |
| author_facet | Akhouri, Unnati Huang, Pei-Jun Rose, Elliott Shandera, Sarah |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_18217 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Operator dynamics in k-Markov random circuits Akhouri, Unnati Huang, Pei-Jun Rose, Elliott Shandera, Sarah Quantum Physics 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. |
| title | Operator dynamics in k-Markov random circuits |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2603.18217 |