The discrete-time quaternionic quantum walk on a graph

The discrete-time quaternionic quantum walk on a graph Recently, the quaternionic quantum walk was formulated by the first author as a generalization of discrete-time quantum walks. We deal with the right eigenvalue problem of quaternionic matrices in order to study spectra of the transition matrix of a quaternionic quantum walk. The way to obtain all the right eigenvalues of a quaternionic matrix is given. From the unitary condition on the transition matrix of a quaternionic quantum walk, we deduce some remarkable properties of it. Our main results determine all the right eigenvalues of the quaternionic quantum walk by using those of the corresponding weighted matrix. In addition, we give some examples of quaternionic quantum walks and their right eigenvalues. Quantum Information Processing Springer Journals

The discrete-time quaternionic quantum walk on a graph

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Springer US
Copyright © 2015 by Springer Science+Business Media New York
Physics; Quantum Information Technology, Spintronics; Quantum Computing; Data Structures, Cryptology and Information Theory; Quantum Physics; Mathematical Physics
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