A new quantum walk model that depends on surface embeddings yields a face-decomposed scattering matrix and a comfortability formula ranking embeddings by genus.
and Segawa, E., Dynamical system induced by quantum walks, Journal of Physics A: Mathematical and Theoretical 52 (2019) 39520
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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.