A New Perspective on the Average Mixing Matrix

Autor(es)

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

Afiliação do(s) autor(es)

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

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

^[3] Univ Libre Bruxelles, Brussels - Belgium

• Tipo de documento: Artigo Científico
• Fonte: ELECTRONIC JOURNAL OF COMBINATORICS; v. 25, n. 4 OCT 19 2018.
• Citações Web of Science: 1

Resumo

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)

• Processo FAPESP: 15/16339-2 - Aplicações de teoria algébrica de grafos à teoria quântica da informação e à combinatória extremal, e relações com programação semidefinida
• Beneficiário: Gabriel de Morais Coutinho
• Modalidade de apoio: Bolsas no Brasil - Pós-Doutorado