Related papers: Quantum association schemes
We clarify the correspondence between the two approaches to quantum graphs: via quantum adjacency matrices and via quantum relations. We show how the choice of a (possibly non-tracial) weight manifests itself on the quantum relation side…
Starting from an association scheme induced by a finite group and the corresponding Bose-Mesner algebra we construct quantum Markov chains (QMC), their entangled versions, and interacting Fock spaces (IFS) using the quantum probabilistic…
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,…
We introduce the notion of q-analogs of strongly regular graphs and give several examples of such structures. We prove a necessary condition on the parameters, show the connection to designs over finite fields, and present a classification.
We formulate a notion of the quantum automorphism group of a $2$-graph. After some preliminary computations, we define quantum isomorphism between a pair of $2$-graphs. We produce a `non-trivial' example of a pair of $2$-graphs that are not…
We develop a general approach to setting up and studying classes of quantum dynamical systems close to and structurally similar to systems having specified properties, in particular detailed balance. This is done in terms of transport plans…
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…
We introduce the concept of regular quantum graphs and construct connected quantum graphs with discrete symmetries. The method is based on a decomposition of the quantum propagator in terms of permutation matrices which control the way…
We give a short overview over recent developments on quantum graphs and outline the connection between general quantum graphs and so-called quantum random walks.
A fundamental problem in quantum information is to describe efficiently multipartite quantum states. An efficient representation in terms of graphs exists for several families of quantum states (graph, cluster, stabilizer states),…
We clarify the relations between the mathematical structures that enable fashioning quantum walks on regular graphs and their realizations in anyonic systems. Our protagonist is association schemes that may be synthesized from type-II…
In this paper, we study quantum walks on the extension of association schemes. Various state transfers can be achieved on these graphs, such as multiple state transfer among extreme points of a simplex, fractional revival on subsimplexes.…
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…
These notes are an introduction to the theory of quantum symmetries of finite and infinite sets, graphs, and locally compact spaces.
We introduce Quantum Graph Neural Networks (QGNN), a new class of quantum neural network ansatze which are tailored to represent quantum processes which have a graph structure, and are particularly suitable to be executed on distributed…
We study the transmission of a quantum particle along a straight input--output line to which a graph $\Gamma$ is attached at a point. In the point of contact we impose a singularity represented by a certain properly chosen scale-invariant…
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,…
In this paper, a new measurement to compare two large-scale graphs based on the theory of quantum probability is proposed. An explicit form for the spectral distribution of the corresponding adjacency matrix of a graph is established. Our…
Some very elementary ideas about quantum groups and quantum algebras are introduced and a few examples of their physical applications are mentioned.
We present quantum complexity lower and upper bounds for independent set problems in graphs. In particular, we give quantum algorithms for computing a maximal and a maximum independent set in a graph. We present applications of these…