Related papers: Quantum automorphisms of matroids
In this paper we determine automorphism groups of cyclic algebraic curves defined over finite fields of any characteristic.
We introduce some equivalent notions of homomorphisms between quantum groups that behave well with respect to duality of quantum groups. Our equivalent definitions are based on bicharacters, coactions, and universal quantum groups,…
This paper defines the q-analogue of a matroid and establishes several properties like duality, restriction and contraction. We discuss possible ways to define a q-matroid, and why they are (not) cryptomorphic. Also, we explain the…
We show that the linear group of automorphism of Hermitian matrices which preserves the set of separable states is generated by \emph{natural} automorphisms: change of an orthonormal basis in each tensor factor, partial transpose in each…
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…
Obtaining the symmetries of a model is a critical step towards developing an understanding and ultimately analytically or numerically solving the model. However, finding symmetries is generally extremely complicated, often being the result…
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…
We introduce the coherent algebra of a compact metric measure space by analogy with the corresponding concept for a finite graph. As an application we show that upon topologizing the collection of isomorphism classes of compact metric…
Studying inequalities between subgraph- or homomorphism-densities is an important topic in graph theory. Sums of squares techniques have proven useful in dealing with such questions. Using an approach from real algebraic geometry, we…
We introduce quantum homomorphisms between quantum hypergraphs through the existence of perfect strategies for quantum non-local games, canonically associated with the quantum hypergraphs. We show that the relation of homomorphism of a…
Not necessarily self-adjoint quantum graphs -- differential operators on metric graphs -- are considered. Assume in addition that the underlying metric graph possesses an automorphism (symmetry) $ \mathcal P $. If the differential operator…
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 use a categorical topological semantics to examine the Deutsch-Jozsa, hidden subgroup and single-shot Grover algorithms. This reveals important structures hidden by conventional algebraic presentations, and allows novel proofs of…
In this expository article we present an overview of the current state-of-the-art in post-quantum group-based cryptography. We describe several families of groups that have been proposed as platforms, with special emphasis in polycyclic…
We compute the automorphism groups of some quantized algebras, including tensor products of quantum Weyl algebras and some skew polynomial rings.
For a strongly connected directed graph $\Lambda$, it is shown that the quantum automorphism group of $\Lambda$ acts isometrically in the sense of D. Goswami et al. on the spectral triple $(C^{\ast}(\Lambda), L^{2}(\Lambda^{\infty},M),D)$…
We propose a novel variational method for solving the sub-graph isomorphism problem on a gate-based quantum computer. The method relies (1) on a new representation of the adjacency matrices of the underlying graphs, which requires a number…
A discrete-time quantum walk on a graph is the repeated application of a unitary evolution operator to a Hilbert space corresponding to the graph. If this unitary evolution operator has an associated group of symmetries, then for certain…
This paper studies the properties of two kinds of matroids: (a) algebraic matroids and (b) finite and infinite matroids whose ground set have some canonical symmetry, for example row and column symmetry and transposition symmetry. For (a)…
A countable graph is ultrahomogeneous if every isomorphism between finite induced subgraphs can be extended to an automorphism. Woodrow and Lachlan showed that there are essentially four types of such countably infinite graphs: the random…