Related papers: Laplacian state transfer in graphs with involution…
We provide a characterization of perfect state transfer in a quantum walk whose Hamiltonian is given by the normalized Laplacian. We discuss a connection between classical random walks and quantum walks only present in this model, and we…
Graph neural networks (GNNs) extends the functionality of traditional neural networks to graph-structured data. Similar to CNNs, an optimized design of graph convolution and pooling is key to success. Borrowing ideas from physics, we…
A continuous quantum walk on a graph $X$ with adjacency matrix $A$ is specified by the 1-parameter family of unitary matrices $U(t)=\exp(itA)$. These matrices act on the state space of a quantum system, the states of which we may represent…
It is shown how to systematically construct the $XX$ quantum spin chains with nearest-neighbor interactions that allow perfect state transfer (PST). Sets of orthogonal polynomials (OPs) are in correspondence with such systems. The key…
Perfect state transfer (PST) is discussed in the context of passive quantum networks with logical bus topology, where many logical nodes communicate using the same shared media, without any external control. The conditions under which, a…
In this paper, we prove a variant of the Burger-Brooks transfer principle which, combined with recent eigenvalue bounds for surfaces, allows to obtain upper bounds on the eigenvalues of graphs as a function of their genus. More precisely,…
The Laplacian matrix of a simple graph is the difference of the diagonal matrix of vertex degree and the (0,1) adjacency matrix. In the past decades, the Laplacian spectrum has received much more and more attention, since it has been…
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…
The evolution of spin network states in loop quantum gravity can be described by introducing a time variable, defined by the surfaces of constant value of an auxiliary scalar field. We regulate the Hamiltonian, generating such an evolution,…
The Laplacian matrix and its pseudo-inverse for a strongly connected directed graph is fundamental in computing many properties of a directed graph. Examples include random-walk centrality and betweenness measures, average hitting and…
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…
Using the signed laplacian matrix, and weighted and hybrid graphs, we present additional ways to interpret graphs as grid states. Hybrid graphs offer the most general interpretation. Existing graphical methods that characterize entanglement…
The intention of the paper is to move a step towards a classification of network topologies that exhibit periodic quantum dynamics. We show that the evolution of a quantum system, whose hamiltonian is identical to the adjacency matrix of a…
In a paper by Nishikawa and Motter, a quantity called the normalized spread of the Laplacian eigenvalues is used to measure the synchronizability of certain network dynamics. Through simulations, and without theoretical validation, it is…
Connections between the 1-excitation dynamics of spin lattices and quantum walks on graphs will be surveyed. Attention will be paid to perfect state transfer (PST) and fractional revival (FR) as well as to the role played by orthogonal…
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…
Consider any random graph model where potential edges appear independently, with possibly different probabilities, and assume that the minimum expected degree is omega(ln n). We prove that the adjacency matrix and the Laplacian of that…
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…
We generalize triadic closure, along with previous generalizations of triadic closure, under an intuitive umbrella generalization: the Subgraph-to-Subgraph Transition (SST). We present algorithms and code to model graph evolution in terms…
We prove that the empirical density of states of quantum spin glasses on arbitrary graphs converges to a normal distribution as long as the maximal degree is negligible compared with the total number of edges. This extends the recent…