Quantum walks defined by digraphs and generalized Hermitian adjacency matrices

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. Furthermor...

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Bibliographic Details
Published in:Quantum information processing 2021-03, Vol.20 (3), Article 95
Main Authors: Kubota, Sho, Segawa, Etsuo, Taniguchi, Tetsuji
Format: Article
Language:English
Subjects:
Data Structures and Information Theory
Eigenvalues
Graph theory
Mathematical Physics
Physics
Physics and Astronomy
Quantum Computing
Quantum Information Technology
Quantum Physics
Spintronics
Transfer matrices
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Summary: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 exhibit explicit formulas of supports of their square. Also, we provide tables on the identification of digraphs by their eigenvalues.
ISSN:1570-0755
1573-1332
DOI:10.1007/s11128-021-03033-z