2024/02/01 by Yusuke Higuchi, Etsuo Segawa, Higuchi, Yusuke +1
Computer Science · #Blockchain Technology in Education and Learning #Combinatorics (math.CO) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Physics (quant-ph)
paper · pdf · doi:10.48550/arxiv.2402.00360
openalex publication_date 2024/02/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.