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

Po-Hsuan Huang, Xie-Ru Li, Chi Chuang, Chia-Heng Tu, Shih-Hao Hung

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.

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

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.

Paper Structure

This paper contains 32 sections, 6 equations, 14 figures, 3 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Background and Motivation
  3. Maximum Cut Problem
  4. Quantum Approximate Optimization Algorithm
  5. Classical Simulation of QAOA
  6. Divide-and-Conquer QAOA for Solving Max-Cut Problems
  7. A Divide-and-Conquer QAOA Example
  8. Existing Graph Partitioning Strategies
  9. Limitations of Existing Divide-and-Conquer QAOA Approaches
  10. Motivation
  11. ParaQAOA
  12. Framework Overview
  13. Graph Partition
  14. Partitioning Constraints
  15. Partitioning Algorithm
  16. ...and 17 more sections

Figures (14)

  • Figure 1: A divide-and-conquer QAOA example for solving the Max-Cut problem.
  • Figure 2: Graphs and their corresponding bitstring representations under different partitions.
  • Figure 3: ParaQAOA framework overview.
  • Figure 4: Comparing random partitioning and proposed connectivity-preserving partitioning algorithms.
  • Figure 5: The proposed parallelized QAOA execution workflow integrated with a multi-GPU system.
  • ...and 9 more figures