Quantum walks defined by digraphs and generalized Hermitian adjacency matrices
arXiv:1910.12536 · doi:10.1007/s11128-021-03033-z
Abstract
We propose a quantum walk defined by digraphs (mixed graphs). This is like Grover walk that is perturbed by a certain complex-valued function defined by digraphs. The discriminant of this quantum walk is a matrix that is a certain normalization of generalized Hermitian adjacency matrices. Furthermore, we give definitions of the positive and negative supports of the transfer matrix, and clarify explicit formulas of their supports of the square. In addition, we give tables by computer on the identification of digraphs by their eigenvalues.
arXiv comment28 pages
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- State transfer in Grover walks on unitary and quadratic unitary Cayley graphs over finite commutative rings