Testing a QUBO Formulation of Core-periphery Partitioning on a Quantum Annealer

TL;DR

This paper introduces a QUBO formulation for core-periphery partitioning in networks, enabling the use of quantum annealing to improve partitioning performance compared to classical heuristics.

Contribution

It presents a novel QUBO-based objective function for core-periphery detection and demonstrates its application on a quantum annealer, including a sparsified version for larger problems.

Findings

Quantum annealing on D-Wave shows promising results

Sparsified QUBO increases problem size solvable by quantum annealer

QUBO approach outperforms some classical heuristics in optimizing the new metric

Abstract

We propose a new kernel that quantifies success for the task of computing a core-periphery partition for an undirected network. Finding the associated optimal partitioning may be expressed in the form of a quadratic unconstrained binary optimization (QUBO) problem, to which a state-of-the-art quantum annealer may be applied. We therefore make use of the new objective function to (a) judge the performance of a quantum annealer, and (b) compare this approach with existing heuristic core-periphery partitioning methods. The quantum annealing is performed on the commercially available D-Wave machine. The QUBO problem involves a full matrix even when the underlying network is sparse. Hence, we develop and test a sparsified version of the original QUBO which increases the available problem dimension for the quantum annealer. Results are provided on both synthetic and real data sets, and we conclude that the QUBO/quantum annealing approach offers benefits in terms of optimizing this new quantity of interest.