Related papers: Numerical Simulations on Nonlinear Quantum Graphs …
We present quantum simulation experiments of Ising-like spins on Platonic graphs, which are performed with two-dimensional arrays of Rydberg atoms and quantum-wire couplings. The quantum wires are used to couple otherwise uncoupled…
Quantum computing has been a prominent research area for decades, inspiring transformative fields such as quantum simulation, quantum teleportation, and quantum machine learning (QML), which are undergoing rapid development. Within QML,…
Many quantum statistical models are most conveniently formulated in terms of non-orthonormal bases. This is the case, for example, when mixtures and superpositions of coherent states are involved. In these instances, we show that the…
We present an efficient quantum algorithm for some independent set problems in graph theory, based on non-abelian adiabatic mixing. We illustrate the performance of our algorithm with analysis and numerical calculations for two different…
We consider a wide class of nonlinear canonical quantum systems described by a one-particle Schroedinger equation containing a complex nonlinearity. We introduce a nonlinear unitary transformation which permits us to linearize the…
Continuum mechanics simulators, numerically solving one or more partial differential equations, are essential tools in many areas of science and engineering, but their performance often limits application in practice. Recent modern machine…
Graph embedding techniques are useful to characterize spectral signature relations for hyperspectral images. However, such images consists of disjoint classes due to spatial details that are often ignored by existing graph computing tools.…
Probabilistic graphical models play a crucial role in machine learning and have wide applications in various fields. One pivotal subset is undirected graphical models, also known as Markov random fields. In this work, we investigate the…
In this work, we propose novel families of positional encodings tailored to graph neural networks obtained with quantum computers. These encodings leverage the long-range correlations inherent in quantum systems that arise from mapping the…
We use the recently introduced concept of a Scaled Relative Graph (SRG) to develop a graphical analysis of input-output properties of feedback systems. The SRG of a nonlinear operator generalizes the Nyquist diagram of an LTI system. In the…
We are concerned with the nonlinear Schr\"odinger equation with an $L^2$ mass constraint on both finite and locally finite graphs and prove that the equation has a normalized solution by employing variational methods. We also pay attention…
Quantum Graphity is an approach to quantum gravity based on a background independent formulation of condensed matter systems on graphs. We summarize recent results obtained on the notion of emergent geometry from the point of view of a…
The simulation of dense fermionic matters is a long-standing problem in lattice gauge theory. One hopeful solution would be the use of quantum computers. In this paper, digital quantum simulation is designed for lattice gauge theory at…
Dynamic programming is a cornerstone of graph-based optimization. While effective, it scales unfavorably with problem size. In this work, we present QuantGraph, a two-stage quantum-enhanced framework that casts local and global…
This report provides an (updated) overview of {\sl Grafalgo}, an open-source library of graph algorithms and the data structures used to implement them. The programs in this library were originally written to support a graduate class in…
We establish general non-uniqueness results for normalized ground states of nonlinear Schr\"odinger equations with power nonlinearity on metric graphs. Basically, we show that, whenever in the $L^2$-subcritical regime a graph hosts ground…
Quantum walks are at the heart of modern quantum technologies. They allow to deal with quantum transport phenomena and are an advanced tool for constructing novel quantum algorithms. Quantum walks on graphs are fundamentally different from…
Representing and learning from graphs is essential for developing effective machine learning models tailored to non-Euclidean data. While Graph Neural Networks (GNNs) strive to address the challenges posed by complex, high-dimensional graph…
While stabilizer tableaus have proven useful as a descriptive tool for additive quantum codes, they otherwise offer little guidance for concrete constructions or algorithm analysis. We introduce a representation of stabilizer codes as…
In this paper, the space complexity of nonuniform quantum computations is investigated. The model chosen for this are quantum branching programs, which provide a graphic description of sequential quantum algorithms. In the first part of the…