Quantum walks on graphs embedded in orientable surfaces

• URL: http://arxiv.org/abs/2402.00360v1
• Date: Thu, 1 Feb 2024 05:59:44 GMT
• Title: Quantum walks on graphs embedded in orientable surfaces
• Authors: Yusuke Higuchi, Etsuo Segawa
• Abstract summary: We show that the scattering matrix is obtained by finding the faces on the underlying surface which have the overlap to the boundary. We show that the stationary state is obtained by counting two classes of the rooted spanning subgraphs of the dual graph on the underlying embedding.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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