Solving large Minimum Vertex Cover problems on a quantum annealer

TL;DR

This paper introduces a decomposition algorithm for solving large minimum vertex cover problems on quantum annealers by recursively dividing problems and applying pruning techniques, enabling solutions despite hardware connectivity limitations.

Contribution

The paper presents a novel recursive decomposition algorithm with pruning methods to efficiently solve large minimum vertex cover problems on quantum annealers.

Findings

Algorithm successfully decomposes large problems for quantum annealing

Pruning techniques improve decomposition efficiency

Simulation results demonstrate practical applicability

Abstract

We consider the minimum vertex cover problem having applications in e.g. biochemistry and network security. Quantum annealers can find the optimum solution of such NP-hard problems, given they can be embedded on the hardware. This is often infeasible due to limitations of the hardware connectivity structure. This paper presents a decomposition algorithm for the minimum vertex cover problem: The algorithm recursively divides an arbitrary problem until the generated subproblems can be embedded and solved on the annealer. To speed up the decomposition, we propose several pruning and reduction techniques. The performance of our algorithm is assessed in a simulation study.