Related papers: A Quantum Algorithm for the Sub-Graph Isomorphism …
The Bandwidth Problem seeks for a simultaneous permutation of the rows and columns of the adjacency matrix of a graph such that all nonzero entries are as close as possible to the main diagonal. This work focuses on investigating novel…
The rise of graph analytic systems has created a need for ways to measure and compare the capabilities of these systems. Graph analytics present unique scalability difficulties. The machine learning, high performance computing, and visual…
Given an undirected, unweighted graph with $n$ vertices and $m$ edges, the maximum cut problem is to find a partition of the $n$ vertices into disjoint subsets $V_1$ and $V_2$ such that the number of edges between them is as large as…
Subgraph queries also known as subgraph isomorphism search is a fundamental problem in querying graph-like structured data. It consists to enumerate the subgraphs of a data graph that match a query graph. This problem arises in many…
This paper introduces a novel architecture for Quantum Graph Neural Networks, which is significantly different from previous approaches found in the literature. The proposed approach produces similar outcomes with respect to previous models…
Large scale complex systems, such as social networks, electrical power grid, database structure, consumption pattern or brain connectivity, are often modeled using network graphs. Valuable insight can be gained by measuring the similarity…
In this paper we study the viability of solving the Chinese Postman Problem, a graph routing optimization problem, and many of its variants on a quantum annealing device. Routing problem variants considered include graph type, directionally…
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…
The computational cost of simulating quantum many-body systems can often be reduced by taking advantage of physical symmetries. While methods exist for specific symmetry classes, a general algorithm to find the full permutation symmetry…
We derive an intuitive and novel method to represent nodes in a graph with special unitary operators, or quantum operators, which does not require parameter training and is competitive with classical methods on scoring similarity between…
In the context of the graph matching problem we propose a novel method for projecting a matrix $Q$, which may be a doubly stochastic matrix, to a permutation matrix $P.$ We observe that there is an intuitve mapping, depending on a given…
We study polynomial-time approximation algorithms for the Quantum Max-Cut (QMC) problem. Given an edge-weighted graph $G$ on n vertices, the QMC problem is to determine the largest eigenvalue of a particular $2^n \times 2^n$ matrix that…
It is well-known that the graph isomorphism problem can be posed as an equivalent problem of determining whether an auxiliary graph structure contains a clique of specific order. However, the algorithms that have been developed so far for…
Quantum computing promises solutions to classically difficult and new-found problems through controlling the subtleties of quantum computing. The Quantum Approximate Optimisation Algorithm (QAOA) is a recently proposed quantum algorithm…
The subgraph isomorphism finding problem is a well-studied problem in the field of computer science and graph theory, and it aims to enumerate all instances of a query graph in the respective data graph. In this paper, we propose an…
We present quantum complexity lower and upper bounds for independent set problems in graphs. In particular, we give quantum algorithms for computing a maximal and a maximum independent set in a graph. We present applications of these…
We investigate classical and quantum physics-based algorithms for solving the graph isomorphism problem. Our work integrates and extends previous work by Gudkov et al. (cond-mat/0209112) and by Rudolph (quant-ph/0206068). Gudkov et al.…
This work shows that minimizing the depth of a quantum circuit composed of commuting operations reduces to a vertex coloring problem on an appropriately constructed graph, where gates correspond to vertices and edges encode…
We demonstrate that a quantum annealer can be used to solve the NP-complete problem of graph partitioning into subgraphs containing Hamiltonian cycles of constrained length. We present a method to find a partition of a given directed graph…
Quantum circuit transformation aims to produce equivalent circuits while optimizing for various aspects such as circuit depth, gate count, and compatibility with modern Noisy Intermediate Scale Quantum (NISQ) devices. There are two…