Hybrid Quantum-Classical Multilevel Approach for Maximum Cuts on Graphs

TL;DR

This paper presents a scalable hybrid quantum-classical multilevel method for solving large Max-Cut problems, demonstrating competitive performance of QAOA-based approaches compared to classical solvers.

Contribution

It introduces a novel multilevel hybrid approach that effectively integrates quantum algorithms with classical solvers for large-scale Max-Cut problems.

Findings

Hybrid approach achieves performance comparable to classical solvers.

QAOA integration demonstrates potential for practical quantum advantage.

Scalable method applicable to large problem instances.

Abstract

Combinatorial optimization is one of the fields where near term quantum devices are being utilized with hybrid quantum-classical algorithms to demonstrate potentially practical applications of quantum computing. One of the most well studied problems in combinatorial optimization is the Max-Cut problem. The problem is also highly relevant to quantum and other types of "post Moore" architectures due to its similarity with the Ising model and other reasons. In this paper, we introduce a scalable hybrid multilevel approach to solve large instances of Max-Cut using both classical only solvers and quantum approximate optimization algorithm (QAOA). We compare the results of our solver to existing state of the art large-scale Max-Cut solvers. We demonstrate excellent performance of both classical and hybrid quantum-classical approaches and show that using QAOA within our framework is comparable to classical approaches.