10 citations · 32 across the 19 of their papers we have counts for
21 papers
Quantum walks and graph operations
Joy Cooper, Homer De Vera, Hermie Monterde +3
Let be the transition matrix of a quantum walk on a graph relative to its adjacency matrix or the Laplacian matrix . This paper investigates the behavior of qua…
Near-factorizations in association schemes
Allen Herman, Alice Lacaze-Masmonteil, Karen Meagher +1
We formally initiate the study of -fold near-factorizations in association schemes. Namely, given an association , we consider the existence of a facto…
Perfect -state transfer
Stephen Kirkland, Hermie Monterde, Sarah Plosker
Much work has been done in the last two decades on the topic of quantum state transfer in a quantum spin network. One can model such a system of interacting qubits using an undirec…
Maximum spectral sum of graphs
Hitesh Kumar, Lele Liu, Hermie Monterde +2
For a graph of order , the spectral sum of is defined to be the sum , where (resp. ) is the largest (resp. second largest) adjacency ei…
Laplacian state transfer in graphs with involutions
Swornalata Ojha, Hermie Monterde, Hiranmoy Pal
For , the generalized Laplacian of a graph is the matrix , where is the degree matrix and is the adjacency matrix of $X…
Local -uniform mixing in continuous quantum walks
Hermie Monterde
Let be a weighted graph and be its adjacency, Laplacian or signless Laplacian matrix. In a continuous quantum walk on , local -uniform mixing occurs at vertex if…
Sedentary quantum walks on bipartite and planar graphs
Karen Meagher, Hermie Monterde
If a quantum walk starting on a vertex tends to stay at home, then that vertex is said to be sedentary. We prove that almost all planar graphs and almost all trees contain at least…
Structured eigenbases and pair state transfer on threshold graphs
Leonardo de Lima, Renata Del-Vecchio, Hermie Monterde +1
Recently, Macharete, Del-Vecchio, Teixeira and de Lima showed that a star and any threshold graph on the same number of vertices share the same eigenbasis relative to the Laplacian…
Quantum walks on finite and bounded infinite graphs
Chris Godsil, Steve Kirkland, Sarojini Mohapatra +2
A weighted graph with countable vertex set is bounded if there is an upper bound on the maximum of the sum of absolute values of all edge weights incident to a vertex in . I…
More graphs with pair state transfer
Hermie Monterde, Hiranmoy Pal
This paper has two main goals. First, we characterize perfect state transfer between -pair states in strongly regular graphs, as well as graphs in association schemes admitting…
Laplacian quantum walks on blow-up graphs
Hermie Monterde, Hiranmoy Pal, Steve Kirkland
This paper is a sequel to the work of Bhattacharjya et al.\ (J. Phys. A-Math. 57.33: 335303, https://doi.org/10.1088/1751-8121/ad6653) on quantum state transfer on blow-up graphs,…
Perfect state transfer between real pure states
Chris Godsil, Stephen Kirkland, Hermie Monterde
Pure states correspond to one-dimensional subspaces of represented by unit vectors. In this paper, we develop the theory of perfect state transfer (PST) between real…
A generalization of quantum pair state transfer
Sooyeong Kim, Hermie Monterde, Bahman Ahmadi +3
An -pair state in a graph is a quantum state of the form , where and are vertices in the graph and is a non-zero complex number. If $s=-1…
New results in vertex sedentariness
Hermie Monterde
A vertex in a graph is said to be sedentary if a quantum state assigned on that vertex tends to stay on that vertex. Under mild conditions, we show that the direct product and join…
Quantum walks on join graphs
Steve Kirkland, Hermie Monterde
The join of two graphs and is the graph obtained by joining each vertex of to each vertex of . We explore the behaviour of a continuous quantum walk on a w…
Quantum walks on blow-up graphs
Bikash Bhattacharjya, Hermie Monterde, Hiranmoy Pal
A blow-up of copies of a graph is the graph obtained by replacing every vertex of by an independent set of size , where the copies of vertices…
Weakly Hadamard diagonalizable graphs and Quantum State Transfer
Darian McLaren, Hermie Monterde, Sarah Plosker
Hadamard diagonalizable graphs are undirected graphs for which the corresponding Laplacian is diagonalizable by a Hadamard matrix. Such graphs have been studied in the context of q…
Fractional revival between twin vertices
Hermie Monterde
In this paper, we provide a characterization of fractional revival between twin vertices in a weighted graph with respect to its adjacency, Laplacian and signless Laplacian matrice…
Sedentariness in quantum walks
Hermie Monterde
We formalize the notion of a sedentary vertex and present a relaxation of the concept of a sedentary family of graphs introduced by Godsil [Linear Algebra Appl. 614:356-375, 2021].…
Quantum state transfer between twins in weighted graphs
Stephen Kirkland, Hermie Monterde, Sarah Plosker
Twin vertices in simple unweighted graphs are vertices that have the same neighbours and, in the case of weighted graphs with possible loops, the corresponding incident edges have…
Strong Cospectrality and Twin Vertices in Weighted Graphs
Hermie Monterde
We explore algebraic and spectral properties of weighted graphs containing twin vertices that are useful in quantum state transfer. We extend the notion of adjacency strong cospect…