Related papers: Perfect state transfer on graphs with clusters
Graph states are an important class of multipartite entangled quantum states. We propose a new approach for distributing graph states across a quantum network. We consider a quantum network consisting of nodes-quantum computers within which…
A mixed circulant graph is called integral if all eigenvalues of its Hermitian adjacency matrix are integers. The main purpose of this paper is to investigate the existence of perfect state transfer (PST for short) and multiple state…
We study the synchronization properties of a generic networked dynamical system, and show that, under a suitable approximation, the transition to synchronization can be predicted with the only help of eigenvalues and eigenvectors of the…
Graphs defined over a finite ring are well-studied in the literature. Due to their nature, these types of graphs connect several branches of mathematics, including algebra, number theory, matrix theory, and representation theory. In recent…
Previously it was shown that (almost) perfect state transfer can be achieved on the complete bipartite graph by a discrete-time coined quantum walk based algorithm when both the sender and receiver vertices are in the same partition of the…
A common approach for analyzing hypergraphs is to consider the projected adjacency or Laplacian matrices for each order of interactions (e.g., dyadic, triadic, etc.). However, this method can lose information about the hypergraph structure…
This paper characterizes the graphical properties of an optimal topology with minimal Laplacian energy under the constraint of fixed numbers of vertices and edges, and devises an algorithm to construct such connected optimal graphs. These…
This paper discusses continuous-time quantum walks and asymptotic state transfer in graphs with an involution. By providing quantitative bounds on the eigenvectors of the Hamiltonian, it provides an approach to achieving high-fidelity state…
In this paper, we consider the problem on the existence of perfect state transfer(PST for short) on semi-Cayley graphs over abelian groups (which are not necessarily regular), i.e on the graphs having semiregular and abelian subgroups of…
Typically, graph structures are represented by one of three different matrices: the adjacency matrix, the unnormalised and the normalised graph Laplacian matrices. The spectral (eigenvalue) properties of these different matrices are…
In this note, we study Laplacians on graphs for which connectivity within certain subgraphs tends to infinity. Our main focus are graphs sharing a common node set on which edge weights within certain clusters grow to infinity. As…
We consider three broad classes of quantum secret sharing with and without eavesdropping and show how a graph state formalism unifies otherwise disparate quantum secret sharing models. In addition to the elegant unification provided by…
We suggest a scheme that allows arbitrarily perfect state transfer even in the presence of random fluctuations in the couplings of a quantum chain. The scheme performs well for both spatially correlated and uncorrelated fluctuations if they…
We study deterministic constructions of graphs for which the unique completion of low rank matrices is generically possible regardless of the values of the entries. We relate the completability to the presence of some patterns (particular…
We introduce the concept of a $k$-token signed graph and study some of its combinatorial and algebraic properties. We prove that two switching isomorphic signed graphs have switching isomorphic token graphs. Moreover, we show that the…
We consider the model of random interlacements on transient graphs, which was first introduced by Sznitman [Ann. of Math. (2) (2010) 171 2039-2087] for the special case of ${\mathbb{Z}}^d$ (with $d\geq3$). In Sznitman [Ann. of Math. (2)…
In order to maintain stable grid operations, system monitoring and control processes require the computation of grid states (e.g. voltage magnitude and angles) at high granularity. It is necessary to infer these grid states from…
Full synchronization of dynamical elements coupled via hypergraphs can be analyzed with the hypergraph projection onto dyadic matrices, but this is not sufficient for analyzing cluster synchronization. Here we develop the necessary…
We discuss Laplacian spectrum on a finite metric graph with vertex couplings violating the time-reversal invariance. For the class of star graphs we determine, under the condition of a fixed total edge length, the configurations for which…
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…