Related papers: Quantum Expander Mixing Lemma and its Structural C…
The purpose of this text is to set up a few basic notions concerning quantum graphs, to indicate some areas addressed in the quantum graph research, and to provide some pointers to the literature. The pointers in many cases are secondary,…
The advent of hybrid computing platforms consisting of quantum processing units integrated with conventional high-performance computing brings new opportunities for algorithm design. By strategically offloading select portions of the…
A central result in the foundations of quantum mechanics is the Kochen-Specker theorem. In short, it states that quantum mechanics is in conflict with classical models in which the result of a measurement does not depend on which other…
We introduce a new graphical framework for designing quantum error correction codes based on classical principles. A key feature of this graphical language, over previous approaches, is that it is closely related to that of factor graphs or…
We study the classical limit of quantum mechanics on graphs by introducing a Wigner function for graphs. The classical dynamics is compared to the quantum dynamics obtained from the propagator. In particular we consider extended open graphs…
We consider quantum graphs with transparent branching points. To design such networks, the concept of transparent boundary conditions is applied to the derivation of the vertex boundary conditions for the linear Schrodinger equation on…
Families of expander graphs were first constructed by Margulis from discrete groups with property (T). Within the framework of quantum information theory, several authors have generalised the notion of an expander graph to the setting of…
In this survey we aim to give a comprehensive overview of results using sublinear expanders. The term sublinear expanders refers to a variety of definitions of expanders, which typically are defined to be graphs $G$ such that every…
Quantum Graph Neural Networks (QGNNs) represent a novel fusion of quantum computing and Graph Neural Networks (GNNs), aimed at overcoming the computational and scalability challenges inherent in classical GNNs that are powerful tools for…
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…
This chapter provides an introduction to the use of diagrammatic language, or perhaps more accurately, diagrammatic calculus, in quantum information and quantum foundations. We illustrate the use of diagrammatic calculus in one particular…
Hybrid quantum-classical neural networks represent a promising frontier in the search for improved machine learning models. This thesis explores the integration of quantum layers within classical convolutional neural network architectures,…
Quantum graphs are commonly used as models of complex quantum systems, for example molecules, networks of wires, and states of condensed matter. We consider quantum statistics for indistinguishable spinless particles on a graph,…
Graphs are ubiquitous data structures for representing interactions between entities. With an emphasis on the use of graphs to represent chemical molecules, we explore the task of learning to generate graphs that conform to a distribution…
The Atomic Cluster Expansion provides local, complete basis functions that enable efficient parametrization of many-atom interactions. We extend the Atomic Cluster Expansion to incorporate graph basis functions. This naturally leads to…
Classical game theory is a powerful tool focusing on optimized resource distribution, allocation and sharing in classical wired and wireless networks. As quantum networks are emerging as a means of providing true connectivity between…
The Cheeger constant of a graph, or equivalently its coboundary expansion, quantifies the expansion of the graph. This notion assumes an implicit choice of a coefficient group, namely, $\mathbb{F}_2$. In this paper, we study Cheeger-type…
Graphs are a fundamental representation of complex, nonlinear structured data across various domains, including social networks and quantum systems. Quantum Graph Recurrent Neural Networks (QGRNNs) have been proposed to model quantum…
We present a general scheme for sharing quantum secrets, and an extension to sharing classical secrets, which contain all known quantum secret sharing schemes. In this framework we show the equivalence of existence of both schemes, that is,…
Quantum expanders are a natural generalization of classical expanders. These objects were introduced and studied by Ben-Aroya and Ta-Shma and by Hastings. In this note we show how to construct explicit, constant-degree quantum expanders.…