  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
