A New Perspective on the Average Mixing Matrix
Combinatorics
2017-09-13 v1 Quantum Physics
Abstract
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.
Cite
@article{arxiv.1709.03591,
title = {A New Perspective on the Average Mixing Matrix},
author = {Gabriel Coutinho and Chris Godsil and Krystal Guo and Hanmeng Zhan},
journal= {arXiv preprint arXiv:1709.03591},
year = {2017}
}
Comments
14 pages