If $ A $ is an $ n\times n $ Hermitian matrix with eigenvalues $\lambda _1 (A),\dots,
$$\lambda _n (A) $ and $ i, j= 1,\dots, n $, then the $ j $ th component $ v_ {i, j} $ of a unit …

Two emerging topics in graph theory are the study of cospectral vertices of a graph, and the
study of isospectral reductions of graphs. In this paper, we prove a fundamental relationship …

Quantum walks on graphs are fundamental to quantum computing and have led to many
interesting open problems in algebraic graph theory. This review article highlights three key …

In this paper, we present an abstract model of continuous-time quantum walk (CTQW) based
on Bernoulli functionals and show that the model has perfect state transfer (PST), among …

Search and state transfer between hubs, ie, fully connected vertices, on otherwise arbitrary
connected graph is investigated. Motivated by a recent result of Razzoli et al.[J. Phys. A …

A discrete-time quantum walk is the quantum analogue of a Markov chain on a graph. Zhan
[J. Algebraic Combin. 53 (4): 1187-1213, 2020] proposes a model of discrete-time quantum …

A discrete-time quantum walk is the quantum analogue of a Markov chain on a graph. We
show that the evolution of a general discrete-time quantum walk that consists of two …

The study of perfect state transfer on graphs has attracted a great deal of attention during the
past ten years because of its applications to quantum information processing and quantum …

A graph short-time Fourier transform is defined using the eigenvectors of the graph
Laplacian and a graph heat kernel as a window parametrized by a nonnegative time …

We examine conditions for a pair of strongly cospectral vertices to have pretty good quantum
state transfer in terms of minimal polynomials, and provide cases where pretty good state …