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

翻译：学习问题在不同粗化层次上的结构信息，以指导基于分解的混合量子-经典组合优化求解器，是扩展变分方法的一种有前景的策略。我们引入了一种多层级算法，该算法结合了基于谱图表示学习的加速器，用于处理大规模图最大割实例，并与多个版本的量子近似优化算法（QAOA）及受QAOA启发的算法进行了融合。图表示学习模型利用了QAOA变分参数集中化的思想，显著提升了QAOA的性能。我们通过在极短的时间内获得高质量解，展示了将多层级QAOA与基于表示学习方法应用于超大规模图的潜力。可复现性：我们的源代码和结果可在 https://github.com/bachbao/MLQAOA 获取。