This book gives an elementary treatment of the basic material about graph spectra, both for
ordinary, and Laplace and Seidel spectra. The text progresses systematically, by covering …

We review the subject of perfect state transfer—how one designs the (fixed) interactions of a
chain of spins so that a quantum state, initially inserted on one end of the chain, is perfectly …

If X is a graph with adjacency matrix A, then we define H (t) to be the operator exp (itA). We
say that we have perfect state transfer in X from the vertex u to the vertex v at time τ if the uv …

The last decade has witnessed substantial interest in protocols for transferring information
on networks of quantum mechanical objects. A variety of control methods and network …

In this paper, we shall give a survey of applications of the theory of graph spectra to
Computer Science. Eigenvalues and eigenvectors of several graph matrices appear in …

We provide a brief survey of perfect state transfer in quantum walks on finite graphs. The
ability to transfer a quantum state from one part of a quantum computer to another is a key …

arxiv:1809.09829v3 [math.CO] 22 Apr 2022 Eigenvalues of Cayley graphs Page 1 arxiv:1809.09829v3
[math.CO] 22 Apr 2022 Eigenvalues of Cayley graphs **aogang Liu∗ School of Mathematics …

Let $ X $ be a graph on $ n $ vertices with with adjacency matrix $ A $ and let $ H (t) $
denote the matrix-valued function $\exp (iAt) $. If $ u $ and $ v $ are distinct vertices in $ X …

Motivated by the need for quantum computers to communicate between multiple, well
separated qubits, we introduce the task of quantum routing for distributing quantum states …

A graph G of order n is called hyperenergetic if E (G)> 2n-2, where E (G) denotes the energy
of G. The unitary Cayley graph Xn has vertex set Zn={0, 1, 2,…, n-1} and vertices a and b are …