Related papers: Perfect state transfer in graphs related to linear…
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 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…
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…
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…
We describe new constructions of graphs which exhibit perfect state transfer on continuous-time quantum walks. Our constructions are based on variants of the double cones [BCMS09,ANOPRT10,ANOPRT09] and the Cartesian graph products (which…
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…
Perfect state transfer between qubits on a uniformly coupled network, with interactions specified by a graph, has advantages over an engineered chain, such as much faster transfer times (independent of the distance between the input and…
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…
Cubelike graphs are the Cayley graphs of the elementary abelian group (Z_2)^n (e.g., the hypercube is a cubelike graph). We give conditions for perfect state transfer between two particles in quantum networks modeled by a large class of…
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…
Perfect (quantum) state transfer has been proved to be an effective model for quantum information processing. In this paper, we give a characterization of cubelike graphs having perfect edge state transfer. By using a lifting technique, we…
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…
In 2018, Chen and Godsil proposed the concept of Laplacian perfect pair state transfer which is a brilliant generalization of Laplacian perfect state transfer. In this paper, we study the existence of Laplacian perfect pair state transfer…
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…
Regular families of coupled quantum networks are described such the unknown state of a qubit can be perfectly routed from any node to any other node in a time linear in the distance. Unlike previous constructions, the transfer can be…
We study perfect state transfer and multiple state transfer in oriented normal Cayley graphs. We construct examples in a variety of groups, ranging from abelian to nonsolvable, and establish some general restrictions and nonexistence…
For any graph $X$ with the adjacency matrix $A$, the transition matrix of the continuous-time quantum walk at time $t$ is given by the matrix-valued function $\mathcal{H}_X(t)=\mathrm{e}^{itA}$. We say that there is perfect state transfer…
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…
We study scattering for continuous-time quantum walks on finite graphs with two attached leads. We derive explicit formulae for the two-terminal scattering matrix in terms of characteristic polynomials of the finite graph and its…
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…