5 papers
Sedentary quantum walks on bipartite 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…
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…