Related papers: Graph Approach to Quantum Systems
Antidot lattices, defined on a two-dimensional electron gas at a semiconductor heterostructure, are a well-studied class of man-made structures with intriguing physical properties. We point out that a closely related system, graphene sheets…
Current applications have produced graphs on the order of hundreds of thousands of nodes and millions of edges. To take advantage of such graphs, one must be able to find patterns, outliers and communities. These tasks are better performed…
Finding the ground state of spin glasses is a challenging problem with broad implications. Many hard optimization problems, including NP-complete problems, can be mapped, for instance, to the Ising spin glass model. We present a graph-based…
Spin network states are a powerful tool for constructing the $SU(2)$ gauge theories on a graph. In loop quantum gravity (LQG), they have yielded many promising predictions, although progress has been limited by the computational challenge…
Graph embedding is a popular algorithmic approach for creating vector representations for individual vertices in networks. Training these algorithms at scale is important for creating embeddings that can be used for classification, ranking,…
An important topic in quantum information is the theory of error correction codes. Practical situations often involve quantum systems with states in an infinite dimensional Hilbert space, for example coherent states. Motivated by these…
In this paper, we propose a new way to represent graphs in quantum space. In that approach, we replace the rows of the adjacency matrix of the graph by state vectors in the occupation number representation. Unlike the traditional definition…
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…
We introduce the concept of hypergraphs to describe quantum optical experiments with probabilistic multi-photon sources. Every hyperedge represents a correlated photon source, and every vertex stands for an optical output path. Such general…
Construction of graphs with equal eigenvalues (co-spectral graphs) is an interesting problem in spectral graph theory. Seidel switching is a well-known method for generating co-spectral graphs. From a matrix theoretic point of view, Seidel…
We study an array of graphene nano sheets that form a two-dimensional S = 1/2 Kagome spin lattice used for quantum computation. The edge states of the graphene nano sheets are used to form quantum dots to confine electrons and perform the…
Knowledge graphs (KGs) are powerful tools for representing and reasoning over structured information. Their main components include schema, identity, and context. While schema and identity matching are well-established in ontology and…
When two or more subsystems of a quantum system interact with each other they can become entangled. In this case the individual subsystems can no longer be described as pure quantum states. For systems with only 2 subsystems this…
An experimental scheme is proposed for building massively multipartite entangled states using both the spatial and the frequency modes of an optical parametric oscillator. We provide analytical forms of the entangled states using the…
Applying a method of Godsil and McKay \cite{GM} to some graphs related to the symplectic graph, a series of new infinite families of strongly regular graphs with parameters…
Quantum-mechanical phenomena are playing an increasing role in information processing, as transistor sizes approach the nanometer level, and quantum circuits and data encoding methods appear in the securest forms of communication.…
In this article we further investigate the construction of graph coherent states, first introduced in [1], in the context of loop quantum gravity. We specifically investigate the possibility of defining a family of graph coherent states…
Graph states are a central resource in measurement-based quantum information processing. In the photonic qubit architecture based on Gottesman-Kitaev-Preskill (GKP) encoding, the generation of high-fidelity graph states composed of…
The transition to 100% renewable energy requires new techniques for managing energy networks, such as dividing them into sensible subsets of prosumers called micro-grids. Doing so in an optimal manner is a difficult optimization problem, as…
We introduce an open-source software library Graphix, which optimizes and simulates measurement-based quantum computation (MBQC). By combining the measurement calculus with an efficient graph state simulator, Graphix allows the classical…