相关论文: Optimization of Bottlenecks in Quantum Graphs Guid…

We introduce a novel harmonic analysis for functions defined on the vertices of a strongly connected directed graph of which the random walk operator is the cornerstone. As a first step, we consider the set of eigenvectors of the random…

Spectral graph theory is a branch of mathematics that studies the relationships between the eigenvectors and eigenvalues of Laplacian and adjacency matrices and their associated graphs. The Variational Quantum Eigensolver (VQE) algorithm…

Given a graph and one of its weighted Laplacian matrix, a Fiedler vector is an eigenvector with respect to the second smallest eigenvalue. The Fiedler vectors have been used widely for graph partitioning, graph drawing, spectral clustering,…

Quantum solutions to differential equations represent quantum data -- states that contain relevant information about the system's behavior, yet are difficult to analyze. We propose a toolbox for reading out information from such data, where…

The development of Graph Neural Networks (GNNs) has led to great progress in machine learning on graph-structured data. These networks operate via diffusing information across the graph nodes while capturing the structure of the graph.…

Bayesian networks represent relations between variables using a directed acyclic graph (DAG). Learning the DAG is an NP-hard problem and exact learning algorithms are feasible only for small sets of variables. We propose two scalable…

Learning directed acyclic graphs (DAGs) from data is a challenging task both in theory and in practice, because the number of possible DAGs scales superexponentially with the number of nodes. In this paper, we study the problem of learning…

Graph data, essential in fields like knowledge representation and social networks, often involves large networks with many nodes and edges. Transmitting these graphs can be highly inefficient due to their size and redundancy for specific…

Quantum networks are essential to quantum information distributed applications, and communicating over them is a key challenge. Complex networks have rich and intriguing properties, which are as yet unexplored in the quantum setting. Here,…

By using highly entangled states, quantum metrology guarantees precision impossible with classical measurements. Unfortunately such states can be very susceptible to noise, and it is a great challenge of the field to maintain quantum…

We propose a novel method using a quantum annealer -- an analog quantum computer based on the principles of quantum adiabatic evolution -- to solve the Graph Isomorphism problem, in which one has to determine whether two graphs are…

We investigate resource allocation for quantum entanglement distribution over an optical network. We characterize and model a network architecture that employs a single broadband quasi-deterministic time-frequency heralded…

Deep neural networks with discrete latent variables offer the promise of better symbolic reasoning, and learning abstractions that are more useful to new tasks. There has been a surge in interest in discrete latent variable models, however,…

Stochastic transport processes on networked domains (modelled on metric graphs) arise in a variety of applications where diffusion and drift mechanisms interact with an underlying graph structure. The Fokker--Planck equation provides a…

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…

Hypergraphs naturally arise when studying group relations and have been widely used in the field of machine learning. To the best of our knowledge, the recently proposed edge-dependent vertex weights (EDVW) modeling is one of the most…

The quadratic embedding constant (QE constant) of a graph is a new characteristic value of a graph defined through the distance matrix. We derive formulae for the QE constants of the join of two regular graphs, double graphs and certain…

Consider a quantum graph consisting of a ring with two attached edges, and assume Kirchhoff-Neumann conditions hold at the internal vertices. Associated to this graph is a Schr\"{o}dinger type operator $L=-\Delta +q(x)$ with Dirichlet…

We investigate the spectral properties of chaotic quantum graphs. We demonstrate that the `energy'--average over the spectrum of individual graphs can be traded for the functional average over a supersymmetric non--linear $\sigma$--model…

A challenge for scalability of demand-responsive, elastic optical Dense Wavelength Division Multiplexing (DWDM) and Flexgrid networks is the computational complexity of allocating many optical routes on large networks. We demonstrate that…