A Quantum Algorithm for Minimising the Effective Graph Resistance upon Edge Addition
Finn de Ridder (Radboud Universiteit Nijmegen)
Niels Neumann (TNO)
Thijs Veugen (TNO, Centrum Wiskunde & Informatica (CWI))
Robert Kooij (Singapore University of Technology and Design, TU Delft - Network Architectures and Services)
More Info
expand_more
Other than for strictly personal use, it is not permitted to download, forward or distribute the text or part of it, without the consent of the author(s) and/or copyright holder(s), unless the work is under an open content license such as Creative Commons.
Abstract
In this work, we consider the following problem: given a graph, the addition of which single edge minimises the effective graph resistance of the resulting (or, augmented) graph. A graph’s effective graph resistance is inversely proportional to its robustness, which means the graph augmentation problem is relevant to, in particular, applications involving the robustness and augmentation of complex networks. On a classical computer, the best known algorithm for a graph with N vertices has time complexity (Formula Presented). We show that it is possible to do better: Dürr and Høyer’s quantum algorithm solves the problem in time (Formula Presented). We conclude with a simulation of the algorithm and solve ten small instances of the graph augmentation problem on the Quantum Inspire quantum computing platform.