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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.
Plos One
|July 14, 2022
Summary
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.
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.
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