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A QUBO formulation for top-τ eigencentrality nodes.

Prosper D Akrobotu1,2, Tamsin E James2, Christian F A Negre3

  • 1Department of Mathematical Sciences, The University of Texas at Dallas, Richardson, TX, United States of America.

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|July 14, 2022
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Summary
This summary is machine-generated.

This study introduces a quantum computing approach to calculate eigenvector centrality, a key metric for network analysis. Quantum algorithms effectively identify the most important nodes in large networks.

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Area of Science:

  • Quantum Computing
  • Network Science
  • Computational Mathematics

Background:

  • Calculating node centrality in large networks is crucial for data analysis.
  • Eigenvector centrality (eigencentrality) is a valuable metric due to its simplicity and accuracy.
  • Existing methods face challenges with increasing data scale.

Purpose of the Study:

  • To develop and validate quantum computational methods for solving the eigencentrality problem.
  • To reformulate network node ranking as a Quadratic Unconstrained Binary Optimization (QUBO) problem.
  • To assess the performance of quantum algorithms on D-Wave and IBM quantum computers.

Main Methods:

  • Reformulation of the eigencentrality problem as a QUBO problem.
  • Implementation and execution of the QUBO formulation on quantum annealing (D-Wave) and gate-based (IBM) quantum computers.
  • Analysis of quantum solutions to identify the top-τ highest eigencentrality nodes.

Main Results:

  • Demonstrated the feasibility of using quantum computing for eigencentrality calculation.
  • Successfully identified the most important nodes in various networks using quantum algorithms.
  • Validated the sparse vector solution of the QUBO formulation on quantum hardware.

Conclusions:

  • Quantum computing offers a promising paradigm for efficient network centrality analysis.
  • The QUBO formulation provides a pathway for solving eigencentrality on current quantum architectures.
  • This work lays the groundwork for future quantum-enhanced network science applications.