Related papers: Quantum graphs: an introduction and a brief survey
A broader definition of generalized truncations of graphs is introduced followed by an exploration of some standard concepts and parameters with regard to generalized truncations.
In this survey article we give basic introduction to the theory of quantum families of maps. We begin with a general look at non-commutative (or "quantum") topology. Then we formulate all our results in this language. Existence of quantum…
General Relativity describes gravity in geometrical terms. This suggests that quantizing such theory is the same as quantizing geometry. The subject can therefore be called quantum geometry and one may think that mathematicians are…
The vision of a quantum internet is to fundamentally enhance Internet technology by enabling quantum communication between any two points on Earth. While the first realisations of small scale quantum networks are expected in the near…
In this paper, we describe {\sc quantitative graph theory} and argue it is a new graph-theoretical branch in network science, however, with significant different features compared to classical graph theory. The main goal of quantitative…
Quantum gravity is the missing piece in our understanding of the fundamental interactions today. Given recent observational breakthroughs in gravity, providing a quantum theory for what lies beyond general relativity is more urgent than…
This paper is an introduction to diagrammatic methods for representing quantum processes and quantum computing. We review basic notions for quantum information and quantum computing. We discuss topological diagrams and some issues about…
This paper provides a thorough introduction to the causal set hypothesis aimed at students, and other interested persons, with some knowledge of general relativity and nonrelativistic quantum mechanics. I elucidate the arguments for why the…
In this brief paper we present some results on creating and manipulating spectral gaps for a (regular) quantum graph by inserting appropriate internal structures into its vertices. Complete proofs and extensions of the results are planned…
There are many falsely intuitive introductions to quantum theory and quantum computation in a handwave. There are also numerous documents which teach those subjects in a mathematically sound manner. To my knowledge this paper is the…
This is an introductory review on the basic principles of quantum computation. Various important quantum logic gates and algorithms based on them are introduced. Quantum teleportation and decoherence are discussed briefly. Some problems,…
The main goal of this paper is to give a pedagogical introduction to Quantum Information Theory-to do this in a new way, using network diagrams called Quantum Bayesian Nets. A lesser goal of the paper is to propose a few new ideas, such as…
We study how quantum walks can be used to find structural anomalies in graphs via several examples. Two of our examples are based on star graphs, graphs with a single central vertex to which the other vertices, which we call external…
We summarize different approaches to the theory of quantum graphs and provide several ways to construct concrete examples. First, we classify all undirected quantum graphs on the quantum space $M_2$. Secondly, we apply the theory of…
Quantum walks in general graphs, or more specifically scattering on graphs, encompass enough complexity to perform universal quantum computation. Any given quantum circuit can be broken down into single- and two-qubit gates, which can then…
This article provides a quick overview of quantum communication, bringing together several innovative aspects of quantum enabled transmission. We first take a neutral look at the role of quantum communication, presenting its importance for…
Two natural generalizations of knot theory are the study of spatial graphs and virtual knots. Our goal is to unify these two approaches into the study of virtual spatial graphs. This paper is a survey, and does not contain any new results.…
Some explanations and implications of the underlying theory approach for quantum theories (QM or QFT) are discussed and suggested. This simple idea seems to have significantly nontrivial effects for our understanding of the quantum…
In this expository paper we present a brief introduction to the geometrical modeling of some quantum computing problems. After a brief introduction to establish the terminology, we focus on quantum information geometry and ZX-calculus,…
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…