A New Perspective on the Average Mixing Matrix

Author(s)

Coutinho, Gabriel ^[1] ; Godsil, Chris ^[2] ; Guo, Krystal ^{[3, 2]} ; Zhan, Hanmeng ^[2]

Affiliation

^[1] Univ Fed Minas Gerais, Belo Horizonte, MG - Brazil

^[2] Univ Waterloo, Waterloo, ON - Canada

^[3] Univ Libre Bruxelles, Brussels - Belgium

• Document type: Journal article
• Source: ELECTRONIC JOURNAL OF COMBINATORICS; v. 25, n. 4 OCT 19 2018.
• Web of Science Citations: 1

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. (AU)

• FAPESP's process: 15/16339-2 - Algebraic graph theory methods in quantum information theory and extremal combinatorics, and connections to semidefinite programming
• Grantee: Gabriel de Morais Coutinho
• Support Opportunities: Scholarships in Brazil - Post-Doctoral