相关论文: Solution of scaling quantum networks

In his survey "Beyond graph energy: Norms of graphs and matrices" (2016), Nikiforov proposed two problems concerning characterizing the graphs that attain equality in a lower bound and in a upper bound for the energy of a graph,…

A method for estimating the spectral gap along with higher eigenvalues of nonequilateral quantum graphs has been introduced by Amini and Cohen-Steiner recently: it is based on a new transference principle between discrete and continuous…

We present a possible candidate of construction of a scalable, uniform and universal quantum network, which is built from quantum gates to elements of quantum circuit, again to quantum subnetworks and finally to an entire quantum network.…

We define a class of quantum systems called regular quantum graphs. Although their dynamics is chaotic in the classical limit with positive topological entropy, the spectrum of regular quantum graphs is explicitly computable analytically…

The unitary evolution maps in closed chaotic quantum graphs are known to have universal spectral correlations, as predicted by random matrix theory. In chaotic graphs with absorption the quantum maps become non-unitary. We show that their…

We consider some examples of quantum super-integrable systems and the associated nonlinear extensions of Lie algebras. The intimate relationship between super-integrability and exact solvability is illustrated. Eigenfunctions are…

Any directed graph G with N vertices and J edges has an associated line-graph L(G) where the J edges form the vertices of L(G). We show that the non-zero eigenvalues of the adjacency matrices are the same for all graphs of such a family…

Quantum graphs have recently emerged as models of nonlinear optical, quantum confined systems with exquisite topological sensitivity and the potential for predicting structures with an intrinsic, off-resonance response approaching the…

Consider a sequence of finite regular graphs (GN) converging, in the sense of Benjamini-Schramm, to the infinite regular tree. We study the induced quantum graphs with equilateral edge lengths, Kirchhoff conditions (possibly with a non-zero…

Random graph models have played a dominant role in the theoretical study of networked systems. The Poisson random graph of Erdos and Renyi, in particular, as well as the so-called configuration model, have served as the starting point for…

A new family of analytically solvable quantum geometric models is proposed. The structure of the energy spectra as well as the form of the corresponding eigenfunctions are presented pointing out their main specific properties.

We derive an optimal eigenvalue ratio estimate for finite weighted graphs satisfying the curvature-dimension inequality $CD(0,\infty)$. This estimate is independent of the size of the graph and provides a general method to obtain higher…

We prove that the spectrum of an individual chaotic quantum graph shows universal spectral correlations, as predicted by random--matrix theory. The stability of these correlations with regard to non--universal corrections is analyzed in…

Arrangement graphs were introduced for their connection to computational networks and have since generated considerable interest in the literature. In a pair of recent articles by Chen, Ghorbani and Wong, the eigenvalues for the adjacency…

Many standard linear algebra problems can be solved on a quantum computer by using recently developed quantum linear algebra algorithms that make use of block encodings and quantum eigenvalue/singular value transformations. A block encoding…

We investigate the equidistribution of the eigenfunctions on quantum graphs in the high-energy limit. Our main result is an estimate of the deviations from equidistribution for large well-connected graphs. We use an exact field-theoretic…

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…

We introduce a mapping between graphs and pure quantum bipartite states and show that the associated entanglement entropy conveys non-trivial information about the structure of the graph. Our primary goal is to investigate the family of…

This paper addresses the challenge of spectral analysis and structural investigation for graphs that are not distance-regular, where computing the spectrum using standard methods based on equitable and orbit partitions can be complex. Our…

We study numerically the spectrum and eigenfunctions of the quantum Neumann model, illustrating some general properties of a non trivial integrable model.