相关论文: Perfect state transfer in NEPS of complete graphs
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…
The transition matrix of a graph $G$ corresponding to the adjacency matrix $A$ is defined by $H(t):=\exp{\left(-itA\right)},$ where $t\in\mathbb{R}$. The graph is said to exhibit pretty good state transfer between a pair of vertices $u$ and…
Suppose $C$ is a subset of non-zero vectors from the vector space $\mathbb{Z}_2^d$. The cubelike graph $X(C)$ has $\mathbb{Z}_2^d$ as its vertex set, and two elements of $\mathbb{Z}_2^d$ are adjacent if their difference is in $C$. If $M$ is…
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…
Pure states correspond to one-dimensional subspaces of $\mathbb{C}^n$ represented by unit vectors. In this paper, we develop the theory of perfect state transfer (PST) between real pure states with emphasis on the adjacency and Laplacian…
We prove new results on perfect state transfer of quantum walks on quotient graphs. Since a graph $G$ has perfect state transfer if and only if its quotient $G/\pi$, under any equitable partition $\pi$, has perfect state transfer, we…
A continuous-time quantum random walk describes the motion of a quantum mechanical particle on an underlying graph. The graph itself is associated with a Hilbert space of dimension equal to the number of vertices. The dynamics of the walk…
The total graph of a graph $G$, denoted $\mathcal{T}(G)$, is defined as the graph whose vertex set is the union of the vertex set of $G$ and the edge set of $G$, such that two vertices of $\mathcal{T}(G)$ are adjacent if the corresponding…
This paper focuses on periodicity and perfect state transfer of Grover walks on two well-known families of Cayley graphs, namely, the unitary Cayley graphs and the quadratic unitary Cayley graphs. Let $R$ be a finite commutative ring. The…
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…
The quadratic unitary Cayley graph $\mathcal{G}_{\mathbb{Z}_n}$ has vertex set $\mathbb{Z}_n: =\{0,1, \ldots ,n-1\}$, where two vertices $u$ and $v$ are adjacent if and only if $u - v$ or $v-u$ is a square of some units in $\mathbb{Z}_n$.…
We consider the representation of a continuous-time quantum walk in a graph $X$ by the matrix $\exp(itA(X))$. We provide necessary and sufficient criteria for distance-regular graphs and, more generally, for graphs in association schemes to…
We consider a quantum walk with two marked vertices, sender and receiver, and analyze its application to perfect state transfer on complete bipartite graphs. First, the situation with both the sender and the receiver vertex in the same part…
We characterize perfect state transfer on real-weighted graphs of the Johnson scheme $\mathcal{J}(n,k)$. Given $\mathcal{J}(n,k)=\{A_1, A_2, \cdots, A_k\}$ and $A(X) = w_0A_0 + \cdots + w_m A_m$, we show, using classical number theory…
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…
We study perfect state transfer on quantum networks represented by weighted graphs. Our focus is on graphs constructed from the join and related graph operators. Some specific results we prove include: (1) The join of a weighted two-vertex…
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…
Quantum walks on undirected graphs have been studied using symmetric matrices, such as the adjacency or Laplacian matrix, and many results about perfect state transfer are known. We extend some of those results to oriented graphs. We also…
A continuous-time quantum walk on a graph is a matrix-valued function $\exp(-\mathtt{i} At)$ over the reals, where $A$ is the adjacency matrix of the graph. Such a quantum walk has universal perfect state transfer if for all vertices $u,v$,…
The neighborhood corona $G \star H$ is the graph obtained by taking one copy $G$ and $|G|$ copies of $H$, and joining each vertex of the $j$th copy of $H$ to all neighbors of $v_{j}$ in $G$. In this paper, we study the state transfer of…