ParaQAOA：用于超过10,000个顶点的大型最大切割问题的高效并行分治QAOA
ParaQAOA: Efficient Parallel Divide-and-Conquer QAOA for Large-Scale Max-Cut Problems Beyond 10,000 Vertices
AI总结：
ParaQAOA通过并行分治方法高效解决大规模最大切割问题，显著提升运行效率并保持解质量，实验显示在400顶点问题上达到1,600倍加速，适用于严格时间约束下的大规模问题。
摘要：
量子近似优化算法（QAOA）已作为混合量子-经典框架中求解组合优化问题的有希望解决方案。在组合优化问题中，最大切割（Max-Cut）问题因其在各种领域中的广泛应用而尤为重要。尽管已开发出基于QAOA的Max-Cut求解器，但它们主要以解的准确性为优先，这显著限制了其在大规模问题中的实用性。为解决这一限制，我们提出了ParaQAOA，一种利用并行计算硬件的并行分治QAOA框架，以高效解决大规模Max-Cut问题。ParaQAOA通过将大问题划分为子问题并在并行中求解，显著减少运行时间，同时保持解的质量。这种设计不仅可扩展到具有数万顶点的图，还能提供可调节的准确率-效率权衡，使ParaQAOA适应多样的性能需求。实验结果表明，ParaQAOA在400顶点的Max-Cut问题上相对于最先进的方法达到1,600倍的加速，同时保持解的准确性在最佳已知解的2%以内。此外，ParaQAOA在16,000个顶点的实例上仅需19分钟，而最佳已知方法则需要超过13.6天。这些发现确立了ParaQAOA作为在严格时间约束下处理大规模Max-Cut问题的实用且可扩展的框架。
英文摘要：
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.
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