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

  • Finn de RidderEmail author
  • Niels Neumann
  • Thijs Veugen
  • Robert Kooij
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11413)


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 \(\mathcal {O}(N^5)\). We show that it is possible to do better: Dürr and Høyer’s quantum algorithm solves the problem in time \(\mathcal {O}(N^4)\). 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.


Graph augmentation Effective graph resistance Dürr and Høyer’s algorithm Quantum Inspire 


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Authors and Affiliations

  • Finn de Ridder
    • 1
    Email author
  • Niels Neumann
    • 2
  • Thijs Veugen
    • 2
    • 3
  • Robert Kooij
    • 4
    • 5
  1. 1.Radboud UniversityNijmegenThe Netherlands
  2. 2.TNOThe HagueThe Netherlands
  3. 3.CWIAmsterdamThe Netherlands
  4. 4.iTrust Centre for Research in Cyber SecuritySingapore University of Technology and DesignSingaporeSingapore
  5. 5.Faculty of Electrical Engineering, Mathematics and Computer ScienceDelft University of TechnologyDelftThe Netherlands

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