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Quantum walks on graphs embedded in orientable surfaces
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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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Cited by 1 Pith paper
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Comfortability of quantum walks on embedded graphs on surfaces
A new quantum walk model that depends on surface embeddings yields a face-decomposed scattering matrix and a comfortability formula ranking embeddings by genus.
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