72 citations · 248 across the 29 of their papers we have counts for
32 papers
Compact graphs and quantum automorphisms
Pedro Baptista, Gabriel Coutinho, Chris Godsil +1
Compact graphs are graphs for which the fractional automorphism polytope has no genuinely fractional vertices. This paper proposes a quantum analogue of this idea by evaluating the…
Total Conformal Rigidity in Graphs
Henrique Assumpção, Gabriel Coutinho, Chris Godsil
We introduce and study a generalization of conformal rigidity for graphs. A graph is -conformally rigid if the uniform edge weights simultaneously maximize the sum of the sm…
Unexpected Averages of Mixing Matrices
Pedro Baptista, Gabriel Coutinho, Vitor Marques
The (standard) average mixing matrix of a continuous-time quantum walk is computed by taking the expected value of the mixing matrices of the walk under the uniform sampling distri…
Sums of squares of eigenvalues and the vector chromatic number
Gabriel Coutinho, Thomás Jung Spier
In this short paper we prove that the sum of the squares of negative (or positive) eigenvalues of the adjacency matrix of a graph is lower bounded by the sum of the degrees divided…
No perfect state transfer in trees with more than 3 vertices
Gabriel Coutinho, Emanuel Juliano, Thomás Jung Spier
We prove that the only trees that admit perfect state transfer according to the adjacency matrix model are and . This answers a question first asked by Godsil in 2012 an…
The spectrum of symmetric decorated paths
Gabriel Coutinho, Emanuel Juliano, Thomás Jung Spier
The main result of this paper states that in a rooted product of a path with rooted graphs which are disposed in a somewhat mirror-symmetric fashion, there are distinct eigenvalues…
Quantum Walks in the Normalized Laplacian
Gabriel Coutinho, Pedro Ferreira Baptista
We provide a characterization of perfect state transfer in a quantum walk whose Hamiltonian is given by the normalized Laplacian. We discuss a connection between classical random w…
Irrational quantum walks
Gabriel Coutinho, Pedro Ferreira Baptista, Chris Godsil +2
The adjacency matrix of a graph G is the Hamiltonian for a continuous-time quantum walk on the vertices of G. Although the entries of the adjacency matrix are integers, its eigenva…
A novel reconstruction attack on foreign-trade official statistics, with a Brazilian case study
Danilo Fabrino Favato, Gabriel Coutinho, Mário S. Alvim +1
In this paper we describe, formalize, implement, and experimentally evaluate a novel transaction re-identification attack against official foreign-trade statistics releases in Braz…
Strong cospectrality in trees
Gabriel Coutinho, Emanuel Juliano, Thomás Jung Spier
We prove that no tree contains a set of three vertices which are pairwise strongly cospectral. This answers a question raised by Godsil and Smith in 2017.
Why and how to add direction to a quantum walk
Rodrigo Chaves, Bruno Oliveira Chagas, Gabriel Coutinho
We formalize the treatment of directed (or chiral) quantum walks using Hermitian adjacency matrices, bridging two developing fields of research in quantum information and spectral…
Quantum walks do not like bridges
Gabriel Coutinho, Chris Godsil, Emanuel Juliano +1
We consider graphs with two cut vertices joined by a path with one or two edges, and prove that there can be no quantum perfect state transfer between these vertices, unless the gr…
An eigenvalue bound for the fractional chromatic number
Marcel K. de Carli Silva, Gabriel Coutinho, Rafael Grandsire
We show that Hoffman's sum of eigenvalues bound for the chromatic number is at least as good as the Lovász theta number, but no better than the ceiling of the fractional chromatic…
Fundamentals of fractional revival in graphs
Ada Chan, Gabriel Coutinho, Whitney Drazen +6
We develop a general spectral framework to analyze quantum fractional revival in quantum spin networks. In particular, we introduce generalizations of the notions of cospectral and…
Colouring the normalized Laplacian
Gabriel Coutinho, Rafael Grandsire, Célio Passos
We apply Cauchy's interlacing theorem to derive some eigenvalue bounds to the chromatic number using the normalized Laplacian matrix, including a combinatorial characterization of…
Algebras, graphs and thetas
Marcel K. de Carli Silva, Gabriel Coutinho, Chris Godsil +1
We extend the clique-coclique inequality, previously known to hold for graphs in association schemes and vertex-transitive graphs, to graphs in homogeneous coherent configurations…
Dual Hoffman Bounds for the Stability and Chromatic Numbers Based on SDP
Nathan Benedetto Proença, Marcel K. de Carli Silva, Gabriel Coutinho
The notion of duality is a key element in understanding the interplay between the stability and chromatic numbers of a graph. This notion is a central aspect in the celebrated theo…
Fractional Revival and Association Schemes
Ada Chan, Gabriel Coutinho, Christino Tamon +2
Fractional revival occurs between two vertices in a graph if a continuous-time quantum walk unitarily maps the characteristic vector of one vertex to a superposition of the charact…
Perfect State Transfer in a Spin Chain without Mirror Symmetry
Gabriel Coutinho, Luc Vinet, Hanmeng Zhan +1
We introduce an analytical spin chain with asymmetrical transport properties. It has an even number of sites labeled by . It does not exhibit perfect state…
On the -independence number of graphs
A. Abiad, G. Coutinho, M. A. Fiol
This paper generalizes and unifies the existing spectral bounds on the -independence number of a graph, which is the maximum size of a set of vertices at pairwise distance great…
Quantum walks and the size of the graph
Gabriel Coutinho
A continuous-time quantum walk is modelled using a graph. In this short paper, we provide lower bounds on the size of a graph that would allow for some quantum phenomena to occur.…
Quantum Fractional Revival on Graphs
Ada Chan, Gabriel Coutinho, Christino Tamon +2
Fractional revival is a quantum transport phenomenon important for entanglement generation in spin networks. This takes place whenever a continuous-time quantum walk maps the chara…
A New Perspective on the Average Mixing Matrix
Gabriel Coutinho, Chris Godsil, Krystal Guo +1
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 o…
Discretization of continuous-time quantum walks via the staggered model with Hamiltonians
Gabriel Coutinho, Renato Portugal
We characterize a close connection between the continuous-time quantum-walk model and a discrete-time quantum-walk version, based on the staggered model with Hamiltonians in a clas…