Related papers: Quantum graphs and spin models
We show that any two Hadamard graphs on the same number of vertices are quantum isomorphic. This follows from a more general recipe for showing quantum isomorphism of graphs arising from certain association schemes. The main result is built…
The article surveys quantization schemes for metric graphs with spin. Typically quantum graphs are defined with the Laplace or Schrodinger operator which describe particles whose intrinsic angular momentum (spin) is zero. However, in many…
Quantum symmetry of a graph $C^{*}$-algebra $C^{*}(\Gamma)$ corresponding to a finite graph $\Gamma$ has been explored by several mathematicians within different categories in the past few years. In this article, we establish that there are…
Many computational problems are unchanged under some symmetry operation. In classical machine learning, this can be reflected with the layer structure of the neural network. In quantum machine learning, the ansatz can be tuned to correspond…
In supersymmetric quantum mechanics the emergence of a singularity may lead to the breakdown of isospectrality between partner potentials. One of the regularization recipes is based on a topologically nontrivial, multisheeted complex…
We classify instances of quantum pseudo-telepathy in the graph isomorphism game, exploiting the recently discovered connection between quantum information and the theory of quantum automorphism groups. Specifically, we show that graphs…
In this paper, we classify all spin models for singly-generated Yang-Baxter planar algebras in terms of certain highly regular graphs. Using Liu's classification of singly generated Yang-Baxter planar algebras, this classifies all spin…
An automorphism of a graph is called quasi-semiregular if it fixes a unique vertex of the graph and its remaining cycles have the same length. This kind of symmetry of graphs was first investigated by Kutnar, Malni\v{c}, Mart\'{i}nez and…
We give a general construction leading to different non-isomorphic families $\Gamma_{n,q}(\K)$ of connected $q$-regular semisymmetric graphs of order $2q^{n+1}$ embedded in $\PG(n+1,q)$, for a prime power $q=p^h$, using the linear…
This is a presentation of recent work on quantum permutation groups. Contains: a short introduction to operator algebras and Hopf algebras; quantum permutation groups, and their basic properties; diagrams, integration formulae, asymptotic…
Manin associated to a quadratic algebra (quantum space) the quantum matrix group of its automorphisms. This Talk aims to demonstrate that Manin's construction can be extended for quantum spaces which are non-quadratic homogeneous algebras.…
We consider orbit partitions of groups of automorphisms for the symplectic graph and apply Godsil-McKay switching. As a result, we find four families of strongly regular graphs with the same parameters as the symplectic graphs, including…
Algebro-geometric methods have proven to be very successful in the study of graphical models in statistics. In this paper we introduce the foundations to carry out a similar study of their quantum counterparts. These quantum graphical…
Quantum graphs have recently been introduced as model systems to study the spectral statistics of linear wave problems with chaotic classical limits. It is proposed here to generalise this approach by considering arbitrary, directed graphs…
In this article, we consider a spin-spin interaction network governed by $XX + YY$ Hamiltonian. The vertices and edges of the network represent the spin objects and their interactions, respectively. We take a privilege to switch on or off…
The intention of the paper is to move a step towards a classification of network topologies that exhibit periodic quantum dynamics. We show that the evolution of a quantum system, whose hamiltonian is identical to the adjacency matrix of a…
The study of graph C*-algebras has a long history in operator algebras. Surprisingly, their quantum symmetries have never been computed so far. We close this gap by proving that the quantum automorphism group of a finite, directed graph…
We demonstrate that a large class of one-dimensional quantum and classical exchange models can be described by the same type of graphs, namely Cayley graphs of the permutation group. Their well-studied spectral properties allow us to derive…
We prove a number of results to the effect that generic quantum graphs (defined via operator systems as in the work of Duan-Severini-Winter / Weaver) have few symmetries: for a Zariski-dense open set of tuples $(X_1,\cdots,X_d)$ of…
We define and study quantum permutations of infinite sets. This leads to discrete quantum groups which can be viewed as infinite variants of the quantum permutation groups introduced by Wang. More precisely, the resulting quantum groups…