Related papers: Quantum graphs with the Bethe-Sommerfeld property

Partial Boolean algebra underlies the quantum logic as an important tool for quantum contextuality. We propose the notion atom graphs to reveal the graph structure of partial Boolean algebra for finite dimensional quantum systems by proving…

We construct quantum models of two particles on a compact metric graph with singular two-particle interactions. The Hamiltonians are self-adjoint realisations of Laplacians acting on functions defined on pairs of edges in such a way that…

We prove that for every pair of quantum isomorphic graphs, their block trees and their block graphs are isomorphic, and that such an isomorphism can be chosen so that the corresponding blocks are quantum isomorphic -- in particular,…

In the broad range of studies related to quantum graphs, quantum graph spectra appear as a topic of special interest. They are important in the context of diffusion type problems posed on metric graphs. Theoretical findings suggest that…

We introduce n-particle quantum graphs with singular two-particle interactions in such a way that eigenfunctions can be given in the form of a Bethe ansatz. We show that this leads to a secular equation characterising eigenvalues of the…

We present an infinite sequence of finite graphs with trivial automorphism group and non-trivial quantum automorphism group. These are the first known examples of graphs with this property. Moreover, to the best of our knowledge, these are…

We connect quantum compact graphs with infinite leads, and turn them into scattering systems. We derive an exact expression for the scattering matrix, and explain how it is related to the spectrum of the corresponding closed graph. The…

We study the spectral statistics of quantum (metric) graphs whose vertices are equipped with preferred orientation vertex conditions. When comparing their spectral statistics to those predicted by suitable random matrix theory ensembles,…

The determination of the quantum chromatic number of graphs has attracted considerable attention recently. However, there are few families of graphs whose quantum chromatic numbers are determined. A notable exception is the family of…

We study a family of closed quantum graphs described by one singular vertex of order n=4. By suitable choice of the parameters specifying the singular vertex, we can construct a closed sequence of paths in the parameter space that…

We study multi-qubit variational quantum states that can be considered as vertex- and edge-weighted graph. These states are constructed as single-layer variational circuits with $RX$ rotations and $RZZ$ entangling gates, corresponding to…

Given an unbalanced open quantum graph, we derive a formula relating sums over its scattering resonances with integrals outside a strip. We deduce lower bounds on the number of resonances (in bounded regions of the complex plane),that 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…

A quantum particle on a circle in a quadratic potential exhibits a spectrum that is not harmonic, despite having all algebraic properties of the quantum harmonic oscillator. This raises the question where the usual algebraic argument --…

We prove upper and lower bounds for the number of zeroes of linear combinations of Schr\"odinger eigenfunctions on metric (quantum) graphs. These bounds are distinct from both the interval and manifolds. We complement these bounds by giving…

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…

For vertex and edge connectivity we construct infinitely many pairs of regular graphs with the same spectrum, but with different connectivity.

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…

In this paper we introduce the concept of characteristic number that are proven to be useful in the study of the combinatorics of graph cohomology. We claim that it is a good combinatorial counterpart for geometric Betti numbers. We then…

We consider the inverse scattering on the quantum graph associated with the hexagonal lattice. Assuming that the potentials on the edges are compactly supported and symmetric, we show that the S-matrix for all energies in any given open set…