Quantum walks on graphs embedded in orientable surfaces
Fuente:
arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866913218841018368 |
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| author | Higuchi, Yusuke Segawa, Etsuo |
| author_facet | Higuchi, Yusuke Segawa, Etsuo |
| contents | A quantum walk model which reflects the $2$-cell embedding on the orientable closed surface of a graph in the dynamics is introduced. We show that the scattering matrix is obtained by finding the faces on the underlying surface which have the overlap to the boundary and the stationary state is obtained by counting two classes of the rooted spanning subgraphs of the dual graph on the underlying embedding. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_00360 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Quantum walks on graphs embedded in orientable surfaces Higuchi, Yusuke Segawa, Etsuo Quantum Physics Mathematical Physics Combinatorics A quantum walk model which reflects the $2$-cell embedding on the orientable closed surface of a graph in the dynamics is introduced. We show that the scattering matrix is obtained by finding the faces on the underlying surface which have the overlap to the boundary and the stationary state is obtained by counting two classes of the rooted spanning subgraphs of the dual graph on the underlying embedding. |
| title | Quantum walks on graphs embedded in orientable surfaces |
| topic | Quantum Physics Mathematical Physics Combinatorics |
| url | https://arxiv.org/abs/2402.00360 |