相关论文: Scaling and universality in nonlinear optical quan…

The geometry of quantum states can be an indicator of criticality, yet it remains less explored under non-Hermitian topological conditions. In this work, we unveil diverse scalings of the quantum geometry over the ground state manifold…

Nonlinear spectral gaps with respect to uniformly convex normed spaces are shown to satisfy a spectral calculus inequality that establishes their decay along Cesaro averages. Nonlinear spectral gaps of graphs are also shown to behave…

We present an exact analytical solution of the spectral problem of quasi one-dimensional scaling quantum graphs. Strongly stochastic in the classical limit, these systems are frequently employed as models of quantum chaos. We show that…

Topology has emerged as a fundamental property of many systems, manifesting in cosmology, condensed matter, high-energy physics and waves. Despite the rich textures, the topology has largely been limited to low dimensional systems that can…

Nonequilibrium states of quantum materials can exhibit exotic properties and enable unprecedented functionality and applications. These transient states are inherently inhomogeneous, characterized by the formation of topologically protected…

The past few years have seen a revived interest in quantum geometrical characterizations of band structures due to the rapid development of topological insulators and semi-metals. Although the metric tensor has been connected to many…

Transformers are increasingly employed for graph data, demonstrating competitive performance in diverse tasks. To incorporate graph information into these models, it is essential to enhance node and edge features with positional encodings.…

A compact review is given, and a few new numerical results are added to the recent studies of the q-pointed one-dimensional star-shaped quantum graphs. These graphs are assumed endowed with certain specific, manifestly non-Hermitian point…

Quantum graphs have attracted attention from mathematicians for some time. A quantum graph is defined by having a Laplacian on each edge of a metric graph and imposing boundary conditions at the vertices to get an eigenvalue problem. A…

To observe synchronization in a large network of classical or quantum systems demands both excellent control of the interactions between the nodes and very accurate preparation of the initial conditions due to the involved nonlinearities…

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…

We apply scaling and the theory of the fundamental limits of the second-order molecular susceptibility to identify material classes with ultralarge nonlinear-optical response. Size effects are removed by normalizing all nonlinearities to…

Quantum computing (QC) is a new computational paradigm whose foundations relate to quantum physics. Notable progress has been made, driving the birth of a series of quantum-based algorithms that take advantage of quantum computational…

We consider quantum graphs with transparent branching points. To design such networks, the concept of transparent boundary conditions is applied to the derivation of the vertex boundary conditions for the linear Schrodinger equation on…

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…

Quantum walks on graphs can model physical processes and serve as efficient tools in quantum information theory. Once we admit random variations in the connectivity of the underlying graph, we arrive at the problem of percolation, where the…

The paper is concerned with the number of open gaps in spectra of periodic quantum graphs. The well-known conjecture by Bethe and Sommerfeld (1933) says that the number of open spectral gaps for a system periodic in more than one direction…

Graph structures are ubiquitous throughout the natural sciences. Here we consider graph-structured quantum data and describe how to carry out its quantum machine learning via quantum neural networks. In particular, we consider training data…

In this paper we present an efficiently scaling quantum algorithm which finds the size of the maximum common edge subgraph for a pair of arbitrary graphs and thus provides a meaningful measure of graph similarity. The algorithm makes use of…

We propose a nanophotonic platform for topological quantum optics. Our system is composed of a two-dimensional lattice of non-linear quantum emitters with optical transitions embedded in a photonic crystal slab. The emitters interact…