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 Sarlette, A., Quantum fast-forwarding; Markov chains and graph property testing, Quantum Information and Computation 19 (2019) 181–213
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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.