相关论文: On the level spacing distribution in quantum graph…
A discrete time quantum walk is known to be the single-particle sector of a quantum cellular automaton. Searching in this mathematical framework has interested the community since a long time. However, most results consider spatial search…
Building large-scale quantum computers, essential to demonstrating quantum advantage, is a key challenge. Quantum Networks (QNs) can help address this challenge by enabling the construction of large, robust, and more capable quantum…
This work deals with quantum graphs, focusing on the transmission properties they engender. We first select two simple diamond graphs, and two hexagonal graphs in which the vertices are all of degree 3, and investigate their transmission…
We propose a quantum multi-level estimation framework for a functional $\sum_{i=1}^n f(p_i)$ of a discrete distribution $(p_i)_{i=1}^n$. We partition the values $p_i$ into logarithmically many intervals whose length decays exponentially.…
Recently, the classical configuration model for random graphs with given degree distribution has been extensively used as a null model in contraposition to real networks with the same degree distribution. In this paper, we briefly review…
We present quantum graphs with remarkably regular spectral characteristics. We call them {\it regular quantum graphs}. Although regular quantum graphs are strongly chaotic in the classical limit, their quantum spectra are explicitly…
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…
This work will appear as a chapter in a forthcoming volume titled "Topics in Probabilistic Graph Theory". A theory of scaling limits for random graphs has been developed in recent years. This theory gives access to the large-scale geometric…
The form factor of a quantum graph is a function measuring correlations within the spectrum of the graph. It can be expressed as a double sum over the periodic orbits on the graph. We propose a scheme which allows one to evaluate the…
We solve an open problem by constructing quantum walks that not only detect but also find marked vertices in a graph. In the case when the marked set $M$ consists of a single vertex, the number of steps of the quantum walk is quadratically…
Random graphs are more and more used for modeling real world networks such as evolutionary networks of proteins. For this purpose we look at two different models and analyze how properties like connectedness and degree distributions are…
The distribution of the ratios of nearest neighbor level spacings has become a popular indicator of spectral fluctuations in complex quantum systems like interacting many-body localized and thermalization phases, quantum chaotic systems,…
Quantum walks are quantum counterparts of random walks and their probability distributions are different from each other. A quantum walker distributes on a Hilbert space and it is observed at a location with a probability. The finding…
Quantum random walks have been shown to be powerful quantum algorithms for certain tasks on graphs like database searching, quantum simulations etc. In this work we focus on its applications for the graph isomorphism problem. In particular…
This work presents an upper-bound to value that the Kullback-Leibler (KL) divergence can reach for a class of probability distributions called quantum distributions (QD). The aim is to find a distribution $U$ which maximizes the KL…
We investigate the bottom of the spectra of infinite quantum graphs, i.e., Laplace operators on metric graphs having infinitely many edges and vertices. We introduce a new definition of the isoperimetric constant for quantum graphs and then…
The paper investigates the approximation of the symmetric Total Variation functional on graphs. Such an approximation is given in terms of a discrete and symmetric finite difference model defined on point clouds obtained by randomly…
A continuous-time quantum walk on a dynamic graph evolves by Schr\"odinger's equation with a sequence of Hamiltonians encoding the edges of the graph. This process is universal for quantum computing, but in general, the dynamic graph that…
We provide an explicit solution of the problem of level-set percolation for multivariate Gaussians defined in terms of weighted graph Laplacians on complex networks. The solution requires an analysis of the heterogeneous micro-structure of…
We investigate the level spacing distribution for the quantum spectrum of the square billiard. Extending work of Connors--Keating, and Smilansky, we formulate an analog of the Hardy--Littlewood prime $k$-tuple conjecture for sums of two…