Related papers: Quantum networks modelled by graphs
We examine transmission through a quantum graph vertex to which auxiliary edges with constant potentials are attached. We find a characterization of vertex couplings for which the transmission probability from a given "input" line to a…
The quantum graph plays the role of a solvable model for a two-dimensional network. Here fitting parameters of the quantum graph for modelling the junction is discussed, using previous results of the second author.
A finite dimensional operator that commutes with some symmetry group admits quotient operators, which are determined by the choice of associated representation. Taking the quotient isolates the part of the spectrum supporting the chosen…
In this work we present a general mathematical framework to deal with Quantum Networks, i.e. networks resulting from the interconnection of elementary quantum circuits. The cornerstone of our approach is a generalization of the Choi…
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 determine the optimum topology of quasi-one dimensional nonlinear optical structures using generalized quantum graph models. Quantum graphs are relational graphs endowed with a metric and a multiparticle Hamiltonian acting on the edges,…
We present a quantum algorithm that additively approximates the value of a tensor network to a certain scale. When combined with existing results, this provides a complete problem for quantum computation. The result is a simple new way of…
Topological metrics of graphs provide a natural way to describe the prominent features of various types of networks. Graph metrics describe the structure and interplay of graph edges and have found applications in many scientific fields. In…
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…
This paper introduces a novel architecture for Quantum Graph Neural Networks, which is significantly different from previous approaches found in the literature. The proposed approach produces similar outcomes with respect to previous models…
We study Schr\"odinger operators on compact finite metric graphs subject to $\delta$-coupling and standard boundary conditions. We compare the $n$-th eigenvalues of those self-adjoint realizations and derive an asymptotic result for the…
We study the statistical properties of the scattering matrix associated with generic quantum graphs. The scattering matrix is the quantum analogue of the classical evolution operator on the graph. For the energy-averaged spectral form…
Quantum network is an emerging type of network structure that leverages the principles of quantum mechanics to transmit and process information. Compared with classical data reconstruction algorithms, quantum networks make image…
The Fast Fourier Transform is extended to functions on finite graphs whose edges are identified with intervals of finite length. Spectral and pseudospectral methods are developed to solve a wide variety of time dependent partial…
The paper deals with some spectral properties of (mostly infinite) quantum and combinatorial graphs. Quantum graphs have been intensively studied lately due to their numerous applications to mesoscopic physics, nanotechnology, optics, and…
In loop quantum gravity we now have a clear picture of the quantum geometry of space, thanks in part to the theory of spin networks. The concept of `spin foam' is intended to serve as a similar picture for the quantum geometry of spacetime.…
This paper initiates the study of quantum computing within the constraints of using a polylogarithmic ($O(\log^k n), k\geq 1$) number of qubits and a polylogarithmic number of computation steps. The current research in the literature has…
Quantum network is fragile to disturbances when qubits are transmitted through quantum channel. Reliability is an essential requirement for a quantum network and even the future quantum internet. A metric is needed to describe the…
Quantum communication is a growing area of research, with quantum internet being one of the most promising applications. Studying the statistical properties of this network is essential to understanding its connectivity and the efficiency…
We study a set of scattering matrices of quantum graphs containing minimal number of passbands, i.e., maximal number of zero elements. The cases of even and odd vertex degree are considered. Using a solution of inverse scattering problem,…