Related papers: On resonant spectral gap opening in quantum graph …
This work shows that minimizing the depth of a quantum circuit composed of commuting operations reduces to a vertex coloring problem on an appropriately constructed graph, where gates correspond to vertices and edges encode…
Graph neural networks (GNNs) have attracted considerable attention from the research community. It is well established that GNNs are usually roughly divided into spatial and spectral methods. Despite that spectral GNNs play an important…
A general treatment of the spectral problem of quantum graphs and tight-binding models in finite Hilbert spaces is given. The direct spectral problem and the inverse spectral problem are written in terms of simple algebraic equations…
The development of Graph Neural Networks (GNNs) has led to great progress in machine learning on graph-structured data. These networks operate via diffusing information across the graph nodes while capturing the structure of the graph.…
Graph neural networks (GNNs) are commonly divided into message-passing neural networks (MPNNs) and spectral graph neural networks, reflecting two largely separate research traditions in machine learning and signal processing. This paper…
Quantum dots embedded in photonic nanostructures have in recent years proven to be a very powerful solid-state platform for quantum optics experiments. The combination of near-unity radiative coupling of a single quantum dot to a photonic…
This review presents an account of the major works done on spectra of adjacency matrices drawn on networks and the basic understanding attained so far. We have divided the review under three sections: (a) extremal eigenvalues, (b) bulk part…
We present an algorithm for reliably and systematically proving the existence of spectral gaps in Hamiltonians with quasicrystalline order, based on numerical calculations on finite domains. We apply this algorithm to prove that the…
In analogy with the spectral theory of geometrically finite hyperbolic manifolds, we initiate the study of resonances on geometrically finite (q+1)-regular graphs of groups. We prove the meromorphic continuation of the resolvent of the…
Quantum networks with bipartite resources and shared randomness present the simplest infrastructure for implementing a future quantum internet. Here, we shall investigate which kinds of entanglement can or cannot be generated from this kind…
This paper is concerned with the analysis of linear quantum optical networks. It provides a systematic approach to the construction a model for a given quantum network in terms of a system of quantum stochastic differential equations. This…
The open problem of calculating the limiting spectrum (or its Shannon transform) of increasingly large random Hermitian finite-band matrices is described. In general, these matrices include a finite number of non-zero diagonals around their…
Entanglement is a fundamental resource for many applications in quantum information processing. Here, we investigate how quantum transport in simple quantum graphs, modeled as controlled two-level quantum systems, can be utilized to…
Using von Neumann algebras, we extend the theory of quantum computation on a graph to a theory of computation on an arbitrary topological space.
Due to the recent groundbreaking developmentsof nanotechnologies,it became possible to create intrinsically quantum systems able to serve as high-directional antennas in THz, infrared and optical ranges. Actually, the quantum antennas,as…
Quantum algorithms require a universal set of gates that can be implemented in a physical system. For these, an optimal decomposition into a sequence of available operations is desired. Here, we present a method to find such sequences for a…
We study gaps in the spectra of the adjacency matrices of large finite cubic graphs. It is known that the gap intervals $(2 \sqrt{2},3)$ and $[-3,-2)$ achieved in cubic Ramanujan graphs and line graphs are maximal. We give constraints on…
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…
We study relevant features of the spectrum of the quantum open baker map. The opening consists of a cut along the momentum $p$ direction of the 2-torus phase space, modelling an open chaotic cavity. We study briefly the classical forward…
Since the turn of the century, metamaterials have gained a large amount of attention due to their potential for possessing highly nontrivial and exotic properties such as cloaking or perfect lensing. There has been a great push to create…