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

2026-03-27

AI Summary

This work addresses the challenge of balancing accuracy and efficiency in solving large-scale Max-Cut problems with the standard Quantum Approximate Optimization Algorithm (QAOA). To overcome this limitation, the authors propose ParaQAOA, a novel framework that scales efficiently to graphs with up to 16,000 vertices. The approach decomposes the problem via graph partitioning into subgraphs, which are then optimized in parallel using a hybrid quantum-classical architecture. ParaQAOA enables flexible trade-offs between solution quality and computational speed, achieving up to a 1,600× acceleration on 400-vertex instances with less than 2% accuracy loss. Notably, it solves a 16,000-vertex instance in just 19 minutes—over three orders of magnitude faster than existing methods, which require more than 13.6 days for the same task.

Abstract

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.

Problem

• QAOA
• Max-Cut
• large-scale optimization
• execution efficiency
• combinatorial optimization

Innovation

• Parallel QAOA
• Divide-and-Conquer
• Large-Scale Max-Cut
• Quantum-Classical Hybrid
• Scalable Optimization