Quantum Approximate Optimization Algorithm (QAOA) has emerged as a promising solution for combinatorial optimization problems using a hybrid quantum-classical framework. Among combinatorial optimization problems, the Maximum Cut (Max-Cut) problem is particularly important due to its broad applicability in various domains. While QAOA-based Max-Cut solvers have been developed, they primarily favor solution accuracy over execution efficiency, which significantly limits their practicality for large-scale problems. To address the limitation, we propose ParaQAOA, a parallel divide-and-conquer QAOA framework that leverages parallel computing hardware to efficiently solve large Max-Cut problems. ParaQAOA significantly reduces runtime by partitioning large problems into subproblems and solving them in parallel while preserving solution quality. This design not only scales to graphs with tens of thousands of vertices but also provides tunable control over accuracy-efficiency trade-offs, making ParaQAOA adaptable to diverse performance requirements. Experimental results demonstrate that ParaQAOA achieves up to 1,600x speedup over state-of-the-art methods on Max-Cut problems with 400 vertices while maintaining solution accuracy within 2% of the best-known solutions. Furthermore, ParaQAOA solves a 16,000-vertex instance in 19 minutes, compared to over 13.6 days required by the best-known approach. These findings establish ParaQAOA as a practical and scalable framework for large-scale Max-Cut problems under stringent time constraints.

翻译：量子近似优化算法（QAOA）已成为采用混合量子-经典框架解决组合优化问题的有力方案。在各类组合优化问题中，最大割问题因其在多个领域的广泛适用性而尤为重要。尽管已有基于QAOA的最大割求解器被开发出来，这些方法主要侧重于解精度而牺牲执行效率，这严重制约了其在大规模问题中的实用性。针对这一局限，我们提出了ParaQAOA——一种并行分治QAOA框架，该框架利用并行计算硬件高效求解大规模最大割问题。ParaQAOA通过将大规模问题划分为子问题并对其进行并行求解，在保持解质量的同时显著缩短运行时间。该设计不仅能扩展至包含数万个顶点的图，还提供了对精度-效率权衡的可调控制，使ParaQAOA能够适应多样化的性能需求。实验结果表明，在包含400个顶点的最大割问题上，ParaQAOA相较于现有最优方法实现了高达1600倍的加速，同时将解精度控制在已知最优解的2%误差范围内。此外，ParaQAOA可在19分钟内求解一个包含16000个顶点的实例，而现有最优方法则需要超过13.6天。这些发现确立了ParaQAOA作为在严格时间约束下解决大规模最大割问题的实用且可扩展框架的地位。