Related papers: Vertex coupling in quantum graphs: approximations …
Nuclear physics, whose underling theory is described by quantum gauge field coupled with matter, is fundamentally important and yet is formidably challenge for simulation with classical computers. Quantum computing provides a perhaps…
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…
Jaberi [7] presented approximation algorithms for the problem of computing a minimum size 2-vertex strongly biconnected subgraph in directed graphs. We have implemented approximation algorithms presented in [7] and we have tested the…
Decomposition of (finite-dimensional) operators in terms of orthogonal bases of matrices has been a standard method in quantum physics for decades. In recent years, it has become increasingly popular because of various methodologies applied…
We consider some simple examples of supersymmetric quantum mechanical systems and explore their possible geometric interpretation with the help of geometric aspects of real Clifford algebras. This leads to natural extensions of the…
Continuous-time quantum walks are natural tools for spatial search, where one searches for a marked vertex in a graph. Sometimes, the structure of the graph causes the walker to get trapped, such that the probability of finding the marked…
Connectivity is a fundamental property of quantum graphs, previously studied in the operator system model for matrix quantum graphs and via graph homomorphisms in the quantum adjacency matrix model. In this paper, we develop an algebraic…
In this paper, we propose a new type of graph, denoted as "embedded-graph", and its theory, which employs a distributed representation to describe the relations on the graph edges. Embedded-graphs can express linguistic and complicated…
We study the tailoring of structured random graph ensembles to real networks, with the objective of generating precise and practical mathematical tools for quantifying and comparing network topologies macroscopically, beyond the level of…
Graph states are a unique resource for quantum information processing, such as measurement-based quantum computation. Here, we theoretically investigate using continuous-variable graph states for single-parameter quantum metrology,…
The problem of vertex coloring in random graphs is studied using methods of statistical physics and probability. Our analytical results are compared to those obtained by exact enumeration and Monte-Carlo simulations. We critically discuss…
Recent years have witnessed rapid advances in graph representation learning, with the continuous embedding approach emerging as the dominant paradigm. However, such methods encounter issues regarding parameter efficiency, interpretability,…
Motivated by various data science applications including de-anonymizing user identities in social networks, we consider the graph alignment problem, where the goal is to identify the vertex/user correspondence between two correlated graphs.…
We develop a unified quantum framework for subgraph counting in graphs. We encode a graph on $N$ vertices into a quantum state on $2\lceil \log_2 N \rceil$ working qubits and $2$ ancilla qubits using its adjacency list, with worst-case gate…
We clarify the correspondence between the two approaches to quantum graphs: via quantum adjacency matrices and via quantum relations. We show how the choice of a (possibly non-tracial) weight manifests itself on the quantum relation side…
We initiate a study of the classification of approximation complexity of the eight-vertex model defined over 4-regular graphs. The eight-vertex model, together with its special case the six-vertex model, is one of the most extensively…
We give an overview of different approaches to measuring the similarity of, or the distance between, two graphs, highlighting connections between these approaches. We also discuss the complexity of computing the distances.
In this comprehensible article we develop, following Fantoni and Rosati formalism, a hypernetted chain approximation for one dimensional systems of fermions. Our scheme differs from previous treatments in the form that the whole set of…
Scaled relative graphs were recently introduced to analyze the convergence of optimization algorithms using two dimensional Euclidean geometry. In this paper, we connect scaled relative graphs to the classical theory of input/output…
We describe random loop models and their relations to a family of quantum spin systems on finite graphs. The family includes spin 1/2 Heisenberg models with possibly anisotropic spin interactions and certain spin 1 models with…