Related papers: Perfect State Transfer on Abelian Cayley Graphs

This paper investigates perfect state transfer in Grover walks, a model of discrete-time quantum walks. We establish a necessary and sufficient condition for the occurrence of perfect state transfer on graphs belonging to an association…

We study the existence of state transfer with respect to the $q$-Laplacian matrix of a graph equipped with a non-trivial involution. We show that the occurrence of perfect state transfer between certain pair (or plus) states in such a graph…

Perfect state transfer in graphs is a concept arising from quantum physics and quantum computing. Given a graph $G$ with adjacency matrix $A_G$, the transition matrix of $G$ with respect to $A_G$ is defined as $H_{A_{G}}(t) =…

We introduce the concept of group state transfer on graphs, summarize its relationship to other concepts in the theory of quantum walks, set up a basic theory, and discuss examples. Let $X$ be a graph with adjacency matrix $A$ and consider…

Let $L$ denote the Laplacian matrix of a graph $G$. We study continuous quantum walks on $G$ defined by the transition matrix $U(t)=\exp\left(itL\right)$. The initial state is of the pair state form, $e_a-e_b$ with $a,b$ being any two…

Quantum state transfer within a quantum computer can be achieved by using a network of qubits, and such a network can be modelled mathematically by a graph. Here, we focus on the corresponding Laplacian matrix, and those graphs for which…

The $\mathcal{Q}$-graph of a graph $G$, denoted by $\mathcal{Q}(G)$, is the graph derived from $G$ by plugging a new vertex to each edge of $G$ and adding a new edge between two new vertices which lie on adjacent edges of $G$. In this…

Perfect state transfer between two marked vertices of a graph by means of discrete-time quantum walk is analyzed. We consider the quantum walk search algorithm with two marked vertices, sender and receiver. It is shown by explicit…

Let $G$ be a finite abelian group. Bridges and Mena characterized the Cayley graphs of $G$ that have only integer eigenvalues. Here we consider the $(0,1,-1)$ adjacency matrix of an oriented Cayley graph or of a signed Cayley graph $X$ on…

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, where instead of the adjacency matrix, we take the Laplacian…

In this paper we study the spectral features, on fractal-like graphs, of Hamiltonians which exhibit the special property of perfect quantum state transfer: the transmission of quantum states without dissipation. The essential goal is to…

We study continuous-time quantum walks on normal Cayley graphs of certain non-abelian groups, called extraspecial groups. By applying general results for graphs in association schemes we determine the precise conditions for perfect state…

Using graphs with clusters, we provide a unified approach for constructing graphs with pair state transfer-relative to the adjacency, Laplacian, and signless Laplacian matrix-between the same pair of states at the same time, despite being…

Let $G$ be a graph with adjacency matrix $A$. The transition matrix of $G$ relative to $A$ is defined by $H(t):=\exp{\left(-itA\right)},\;t\in\Rl$. The graph $G$ is said to admit pretty good state transfer between a pair of vertices $u$ and…

We construct infinite families of graphs in which pretty good state transfer can be induced by adding a potential to the nodes of the graph (i.e. adding a number to a diagonal entry of the adjacency matrix). Indeed, we show that given any…

We study perfect state transfer in Grover walks, which are typical discrete-time quantum walk models. In particular, we focus on states associated to vertices of a graph. We call such states vertex type states. Perfect state transfer…

By using some techniques such as spectral distribution and stratification associated with the graphs, employed in [1,2] for the purpose of Perfect state transfer (PST) of a single qubit over antipodes of distance-regular spin networks and…

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 transferred to the opposite end in a fixed time.…

In this paper we study quantum state transfer (also called quantum tunneling) on graphs when there is a potential function on the vertex set. We present two main results. First, we show that for paths of length greater than three, there is…

We consider quantum state transfer relative to the Laplacian matrix of a graph. Let $N(u)$ denote the set of all neighbors of a vertex $u$ in a graph $G$. A pair of vertices $u$ and $v$ are called twin vertices of $G$ provided…