Related papers: Perfect State Transfer on Abelian Cayley Graphs
The question of perfect state transfer existence in quantum spin networks based on weighted graphs has been recently presented by many authors. We give a simple condition for characterizing weighted circulant graphs allowing perfect state…
Perfect state transfer is significant in quantum communication networks. There are very few graphs having this property. So, it is useful to find some new graphs having perfect state transfer. A good way to construct new graphs is by…
For a graph $G$ and a related symmetric matrix $M$, the continuous-time quantum walk on $G$ relative to $M$ is defined as the unitary matrix $U(t) = \exp(-itM)$, where $t$ varies over the reals. Perfect state transfer occurs between…
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 $u,v$,…
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…
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…
A continuous-time quantum walk on a graph $G$ is given by the unitary matrix $U(t) = \exp(-itA)$, where $A$ is the Hermitian adjacency matrix of $G$. We say $G$ has pretty good state transfer between vertices $a$ and $b$ if for any…
We investigate quantum state transfer in XY spin chains and propose a recursive procedure to construct the nonuniform couplings of these chains with arbitrary length to achieve perfect state transfer(PST). We show that this method is…
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…
A blow-up of $n$ copies of a graph $G$ is the graph $\overset{n}\uplus~G$ obtained by replacing every vertex of $G$ by an independent set of size $n$, where the copies of vertices in $G$ are adjacent in the blow-up if and only if the…
A continuous-time quantum walk on a graph $X$ is represented by the complex matrix $\exp (-\mathrm{i} t A)$, where $A$ is the adjacency matrix of $X$ and $t$ is a non-negative time. If the graph models a network of interacting qubits,…
We study perfect state transfer in Kendon's model of discrete quantum walks. In particular, we give a characterization of perfect state transfer purely in terms of the graph spectra, and construct an infinite family of $4$-regular circulant…
We propose a quantum network consisting of optical waveguides in the linear regime for quantum state transfer. The circular topology of our network introduces novel functionalities that enable us to analytically identify the conditions…
It is shown how to perfectly transfer an arbitrary qudit state in interacting boson networks. By defining a family of Hamiltonians related to Bose-Hubbard model, we describe a possible method for state transfer through bosonic atoms trapped…
We study the existence of quantum state transfer in $\mathcal{Q}$-graphs in this paper. 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…
Let $G$ be a graph with adjacency matrix $A$. The transition matrix of $G$ relative to $A$ is defined by $H_{A}(t):=\exp{(-itA)},\;t\in\Rl$. We say that the graph $G$ admits perfect state transfer between the verteices $u$ and $v$ at…
We study perfect state transfer of quantum walks on signed graphs. Our aim is to show that negative edges are useful for perfect state transfer. Specific results we prove include: (1) The signed join of a negative 2-clique with any positive…
We consider quantum state transfer on finite graphs which are attached to infinite paths. The finite graph represents an operational quantum system for performing useful quantum information tasks. In contrast, the infinite paths represent…
Given a graph with Hermitian adjacency matrix $H$, perfect state transfer occurs from vertex $a$ to vertex $b$ if the $(b,a)$-entry of the unitary matrix $\exp(-iHt)$ has unit magnitude for some time $t$. This phenomenon is relevant for…
Quantum walks, an important tool in quantum computing, have been very successfully investigated using techniques in algebraic graph theory. We are motivated by the study of state transfer in continuous-time quantum walks, which is…