This is a textbook about quantum walks and quantum search algorithms. The readers will
take advantage of the pedagogical aspects and learn the topics faster and make less effort …

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 …

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 …

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 …

Suppose C is a subset of non-zero vectors from the vector space Z 2 d. The cubelike graph X
(C) has Z 2 d as its vertex set, and two elements of Z 2 d are adjacent if their difference is in …

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 …

We consider the representation of a continuous-time quantum walk in a graph X by the
matrix exp⁡(− it A (X)). We provide necessary and sufficient criteria for distance-regular …

Perfect transfer of a quantum state through a one-dimensional chain is now well understood,
allowing one not only to decide whether a fixed Hamiltonian achieves perfect transfer but to …

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 …