Work

A New Perspective on the Average Mixing Matrix

Year: 2017

Type: preprint

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.

Source: LA Referencia (Red Federada de Repositorios Institucionales de Publicaciones Científicas)

DOI: 10.48550/arxiv.1709.03591

Authors: Coutinho, Gabriel, Godsil, Chris, Guo, Krystal, Zhan, Hanmeng

Institutions: Universidade Federal de Minas Gerais, University of Waterloo, Université Libre de Bruxelles

Language: English

Topic: Graph theory and applications

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W2755734061

Cites: 8

Cited by: 1

Related to: 10