Information scrambling in quantum walks: Discrete-time formulation of Krylov complexity
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866929578355720192 |
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| author | Sahu, Himanshu |
| author_facet | Sahu, Himanshu |
| contents | We study information scrambling -- a spread of initially localized quantum information into the system's many degree of freedom -- in discrete-time quantum walks. We consider out-of-time-ordered correlators (OTOC) and K-complexity as a probe of information scrambling. The OTOC for local spin operators in all directions has a light-cone structure which is ``shell-like''. As the wavefront passes, the OTOC approaches to zero in the long-time limit, showing no signature of scrambling. The introduction of spatial or temporal disorder changes the shape of the light-cone akin to localization of wavefunction. We formulate the K-complexity in system with discrete-time evolution, and show that it grows linearly in discrete-time quantum walk. The presence of disorder modifies this growth to sub-linear. Our study present interesting case to explore many-body phenomenon in a discrete-time quantum walk using scrambling. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_05865 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Information scrambling in quantum walks: Discrete-time formulation of Krylov complexity Sahu, Himanshu Quantum Physics Disordered Systems and Neural Networks We study information scrambling -- a spread of initially localized quantum information into the system's many degree of freedom -- in discrete-time quantum walks. We consider out-of-time-ordered correlators (OTOC) and K-complexity as a probe of information scrambling. The OTOC for local spin operators in all directions has a light-cone structure which is ``shell-like''. As the wavefront passes, the OTOC approaches to zero in the long-time limit, showing no signature of scrambling. The introduction of spatial or temporal disorder changes the shape of the light-cone akin to localization of wavefunction. We formulate the K-complexity in system with discrete-time evolution, and show that it grows linearly in discrete-time quantum walk. The presence of disorder modifies this growth to sub-linear. Our study present interesting case to explore many-body phenomenon in a discrete-time quantum walk using scrambling. |
| title | Information scrambling in quantum walks: Discrete-time formulation of Krylov complexity |
| topic | Quantum Physics Disordered Systems and Neural Networks |
| url | https://arxiv.org/abs/2406.05865 |