Related papers: Quantum Networks on Cubelike Graphs
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…
Quantum networks are often modelled using Schroedinger operators on metric graphs. To give meaning to such models one has to know how to interpret the boundary conditions which match the wave functions at the graph vertices. In this article…
We study perfect state transfer in Grover walks on two important classes of graphs: strongly regular graphs and strongly walk-regular graphs. The latter class is a generalization of the former. We first give a complete classification of…
A graph is called normal if its vertex set can be covered by cliques and also by stable sets, such that every such clique and stable set have non-empty intersection. This notion is due to Korner, who introduced the class of normal graphs as…
This work studies how a suitably-designed classical system generates with a quantum-like (QL) state space mediated by a graph. The graph plays a special dual role by directing the topology of the classical network and defining a state space…
The $(n,k)$-star graphs are an important class of interconnection networks that generalize star graphs, which are superior to hypercubes. In this paper, we continue the work begun by Cheng et al.~(Graphs and Combinatorics 2017) and complete…
We introduce a scheme for perfect routing of quantum states and entanglement in regular cavity QED networks. The couplings between the cavities are quasi-uniform and each cavity is doped with a two-level atom. Quasi-uniform couplings leads…
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…
Graph structures are ubiquitous throughout the natural sciences. Here we consider graph-structured quantum data and describe how to carry out its quantum machine learning via quantum neural networks. In particular, we consider training data…
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 $\mathbb{Z}_n$.…
Networks constitute efficient tools for assessing universal features of complex systems. In physical contexts, classical as well as quantum, networks are used to describe a wide range of phenomena, such as phase transitions, intricate…
A graph is said to be a bi-Cayley graph over a group H if it admits H as a group of automorphisms acting semiregularly on its vertices with two orbits. A non-abelian group is called an inner-abelian group if all of its proper subgroups are…
The evolution of certain pair state in a quantum network with isomorphic branches, governed by the Heisenberg $XY$ Hamiltonian, depends solely on the local structure, and it remains unaffected even if the global structure is altered. All…
Quantum networks are important for quantum communication, enabling tasks such as quantum teleportation, quantum key distribution, quantum sensing, and quantum error correction, often utilizing graph states, a specific class of multipartite…
We demonstrate that a large class of one-dimensional quantum and classical exchange models can be described by the same type of graphs, namely Cayley graphs of the permutation group. Their well-studied spectral properties allow us to derive…
Quantum networks are distributed quantum many-body systems with tailored topology and controlled information exchange. They are the backbone of distributed quantum computing architectures and quantum communication. Here we present a…
Motivated by a recent application of quantum graphs to model the anomalous Hall effect we discuss quantum graphs the vertices of which exhibit a preferred orientation. We describe an example of such a vertex coupling and analyze the…
We generalise the standard constructions of a Cayley graph in terms of a group presentation by allowing some vertices to obey different relators than others. The resulting notion of presentation allows us to represent every vertex…
We classify the finite quasisimple groups whose commuting graph is perfect and we give a general structure theorem for finite groups whose commuting graph is perfect.
Pretty good state transfer in networks of qubits occurs when a continuous-time quantum walk allows the transmission of a qubit state from one node of the network to another, with fidelity arbitrarily close to 1. We prove that in a…