MLQAOA: Graph Learning Accelerated Hybrid Quantum-Classical Multilevel QAOA

TL;DR

This paper introduces MLQAOA, a multilevel hybrid quantum-classical algorithm enhanced with spectral graph learning, significantly improving large-scale graph maximum cut solutions with faster computation and higher quality.

Contribution

It presents a novel multilevel algorithm combined with spectral graph learning to accelerate and improve QAOA-based combinatorial optimization on large graphs.

Findings

Achieved high-quality solutions faster on large graphs.

Enhanced QAOA performance with spectral graph representation learning.

Demonstrated scalability and effectiveness of the approach.

Abstract

Learning the problem structure at multiple levels of coarseness to inform the decomposition-based hybrid quantum-classical combinatorial optimization solvers is a promising approach to scaling up variational approaches. We introduce a multilevel algorithm reinforced with the spectral graph representation learning-based accelerator to tackle large-scale graph maximum cut instances and fused with several versions of the quantum approximate optimization algorithm (QAOA) and QAOA-inspired algorithms. The graph representation learning model utilizes the idea of QAOA variational parameters concentration and substantially improves the performance of QAOA. We demonstrate the potential of using multilevel QAOA and representation learning-based approaches on very large graphs by achieving high-quality solutions in a much faster time. Reproducibility: Our source code and results are available at https://github.com/bachbao/MLQAOA