ParaQAOA: Efficient Parallel Divide-and-Conquer QAOA for Large-Scale Max-Cut Problems Beyond 10,000 Vertices

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.

💡 Research Summary

This paper introduces “ParaQAOA,” a novel parallel divide-and-conquer framework designed to overcome the scalability limitations of the Quantum Approximate Optimization Algorithm (QAOA) for solving large-scale Maximum Cut (Max-Cut) problems. The Max-Cut problem, an NP-hard combinatorial optimization problem with applications in VLSI design, social network analysis, and wireless communications, becomes computationally prohibitive for classical and standard quantum-inspired methods as graph sizes increase into the tens of thousands of vertices.

Existing QAOA-based solvers and even recent divide-and-conquer approaches primarily prioritize solution accuracy, often leading to impractically long runtimes for large instances. ParaQAOA addresses this efficiency bottleneck by strategically partitioning the input graph into smaller, manageable subgraphs. The key innovation lies in its parallel execution pipeline: these subproblems are solved independently and concurrently on classical parallel computing hardware (e.g., multi-core CPUs, GPUs), and their solutions are subsequently merged to reconstruct a global solution for the original problem. This architecture dramatically reduces wall-clock time.

The framework is built around four core components: 1) a linear-time graph partitioning algorithm for efficient decomposition of large graphs, 2) a parallelized pipeline for subproblem solving and solution reconstruction, 3) a parameterized design that allows users to tune the trade-off between execution speed and solution quality (e.g., by controlling subproblem size), and 4) a novel unified evaluation metric called the Performance Efficiency Index (PEI), which integrates approximation ratio and runtime to facilitate holistic comparisons between different Max-Cut solvers.

Comprehensive experimental results demonstrate ParaQAOA’s transformative performance. On medium-scale problems with 400 vertices, it achieves speedups of up to 1,600x compared to state-of-the-art methods while maintaining solution quality within 2% of the best-known results. Most strikingly, for a very large-scale instance with 16,000 vertices, ParaQAOA obtains a solution in just 19 minutes, whereas the best prior approach is projected to require over 13.6 days. These findings establish ParaQAOA as a practical, scalable, and highly efficient framework for solving large-scale Max-Cut problems, particularly under stringent time constraints where timely solutions are valued. The paper concludes by discussing future directions, including adaptation for execution on real quantum hardware and extension to other combinatorial optimization problems.