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))
Rob Kooij (TU Delft - Network Architectures and Services, Singapore University of Technology and Design)
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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.