# A Quantum Algorithm for Minimising the Effective Graph Resistance upon Edge Addition

A Quantum Algorithm for Minimising the Effective Graph Resistance upon Edge Addition

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: Durr 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. © 2019, Springer Nature Switzerland AG.

SubjectDurr and Høyer’s algorithm

Effective graph resistance

Graph augmentation

Quantum Inspire

Optimization

Quantum computers

Quantum theory

Simulation platform

Best-known algorithms

Following problem

Graph augmentation

Quantum algorithms

Quantum Inspire

S-algorithms

Time complexity

Complex networks

http://resolver.tudelft.nl/uuid:ec8767f6-88a1-48c4-bf88-a618a8e406d8

TNO identifier866718

9783030140816

3029-743

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 1st International Workshop on Quantum Technology and Optimization Problems, QTOP 2019 was held in conjunction with the International Conference on Networked Systems, NetSys 2019, 18 March 2019 through 18 March 2019, 63-73

Document typeconference paper

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