Quantum walks defined by digraphs and generalized Hermitian adjacency matrices

We propose a quantum walk defined by digraphs (mixed graphs). This is like Grover that perturbed certain complex-valued function digraphs. The discriminant of this matrix normalization generalized Hermitian adjacency matrices. Furthermore, we give definitions the positive and negative supports transfer matrix, clarify explicit formulas their square. In addition, tables computer on identification eigenvalues.