Related papers: Mixed graph states
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…
It has been observed that the reduced density matrices of bipartite qudit pure states possess a Gram matrix structure. This observation has opened a possibility of analysing the entanglement in such systems from the purely geometrical point…
We consider the problem of classifying those graphs that arise as an undirected square of an oriented graph by generalising the notion of quasi-transitive directed graphs to mixed graphs. We fully classify those graphs of maximum degree…
We introduce a repeater scheme to efficiently distribute multipartite entangled states in a quantum network with optimal scaling. The scheme allows to generate graph states such as 2D and 3D cluster states of growing size or GHZ states over…
We study multi-qubit variational quantum states that can be considered as vertex- and edge-weighted graph. These states are constructed as single-layer variational circuits with $RX$ rotations and $RZZ$ entangling gates, corresponding to…
We consider quantum graph states that can be mapped to directed weighted graphs, also known as directed networks. The geometric measure of entanglement of the states is calculated for the quantum graph states corresponding to arbitrary…
Mixed graphs can be seen as digraphs with arcs and edges (or digons, that is, two opposite arcs). In this paper, we consider the case where such graphs are bipartite and in which the undirected and directed degrees are one. The best graphs,…
We proposed two classes of multiparticle entangled states, the multigraph states and multihypergraph states, defined by unique operations on the edges and hyperedges. A key discovery is the one-to-one correspondence between the proposed…
A graph theoretic perspective is taken for a range of phenomena in continuum physics in order to develop representations for analysis of large scale, high-fidelity solutions to these problems. Of interest are phenomena described by partial…
Quantum graph state is a special class of nonlocal state among multiple quantum particles, underpinning several nonclassical and promising applications such as quantum computing and quantum secret sharing. Recently, establishing quantum…
Measurement based (MB) quantum computation allows for universal quantum computing by measuring individual qubits prepared in entangled multipartite states, known as graph states. Unless corrected for, the randomness of the measurements…
We introduce the Graph Mixture Density Networks, a new family of machine learning models that can fit multimodal output distributions conditioned on graphs of arbitrary topology. By combining ideas from mixture models and graph…
We define cofinite graphs and cofinite groupoids in a unified way that extends the notion of cofinite groups introduced by Hartley. The common underlying structure of all these objects is that they are directed graphs endowed with a certain…
Graph states form a large family of quantum states that are in one-to-one correspondence with mathematical graphs. Graph states are used in many applications, such as measurement-based quantum computation, as multipartite entangled…
Let $G=(V,E)$ be a connected graph. A vertex $w\in V$ distinguishes two elements (vertices or edges) $x,y\in E\cup V$ if $d_G(w,x)\ne d_G(w,y)$. A set $S$ of vertices in a connected graph $G$ is a mixed metric generator for $G$ if every two…
In this article we apply the methods outlined in the previous paper of this series to the particular set of states obtained by choosing the complexifier to be a Laplace operator for each edge of a graph. The corresponding coherent state…
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…
For a set of quantum states generated by the action of a group, we consider the graph obtained by considering two group elements adjacent whenever the corresponding states are non-orthogonal. We analyze the structure of the connected…
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…
Measurement-based quantum computing offers a promising route towards scalable, universal photonic quantum computation. This approach relies on the deterministic and efficient generation of photonic graph states in which many photons are…