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A New Perspective on the Average Mixing Matrix

We consider the continuous-time quantum walk defined on the adjacency matrix of a graph. At each instant, the walk defines a mixing matrix which is doubly-stochastic. The average of the mixing matrices contains relevant information about the quantum walk and about the graph. We show that it is the m...

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Bibliographic Details
Published in:The Electronic journal of combinatorics 2018-10, Vol.25 (4)
Main Authors: Coutinho, Gabriel, Godsil, Chris, Guo, Krystal, Zhan, Hanmeng
Format: Article
Language:English
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Summary:We consider the continuous-time quantum walk defined on the adjacency matrix of a graph. At each instant, the walk defines a mixing matrix which is doubly-stochastic. The average of the mixing matrices contains relevant information about the quantum walk and about the graph. We show that it is the matrix of transformation of the orthogonal projection onto the commutant algebra of the adjacency matrix, restricted to diagonal matrices. Using this formulation of the average mixing matrix, we find connections between its rank and automorphisms of the graph.
ISSN:1077-8926
1077-8926
DOI:10.37236/7867