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Graph Learning for Parameter Prediction of Quantum Approximate Optimization Algorithm

Zhiding Liang, Gang Liu, Zheyuan Liu, Jinglei Cheng, Tianyi Hao, Kecheng Liu, Hang Ren, Zhixin Song, Ji Liu, Fanny Ye, Yiyu Shi

TL;DR

GNN’s potential in improving QAOA performance is shown, opening new avenues for hybrid quantum-classical approaches in quantum computing and contributing to practical applications, as well as highlighting the synergy between quantum algorithms and machine learning.

Abstract

In recent years, quantum computing has emerged as a transformative force in the field of combinatorial optimization, offering novel approaches to tackling complex problems that have long challenged classical computational methods. Among these, the Quantum Approximate Optimization Algorithm (QAOA) stands out for its potential to efficiently solve the Max-Cut problem, a quintessential example of combinatorial optimization. However, practical application faces challenges due to current limitations on quantum computational resource. Our work optimizes QAOA initialization, using Graph Neural Networks (GNN) as a warm-start technique. This sacrifices affordable computational resource on classical computer to reduce quantum computational resource overhead, enhancing QAOA's effectiveness. Experiments with various GNN architectures demonstrate the adaptability and stability of our framework, highlighting the synergy between quantum algorithms and machine learning. Our findings show GNN's potential in improving QAOA performance, opening new avenues for hybrid quantum-classical approaches in quantum computing and contributing to practical applications.

Graph Learning for Parameter Prediction of Quantum Approximate Optimization Algorithm

TL;DR

GNN’s potential in improving QAOA performance is shown, opening new avenues for hybrid quantum-classical approaches in quantum computing and contributing to practical applications, as well as highlighting the synergy between quantum algorithms and machine learning.

Abstract

In recent years, quantum computing has emerged as a transformative force in the field of combinatorial optimization, offering novel approaches to tackling complex problems that have long challenged classical computational methods. Among these, the Quantum Approximate Optimization Algorithm (QAOA) stands out for its potential to efficiently solve the Max-Cut problem, a quintessential example of combinatorial optimization. However, practical application faces challenges due to current limitations on quantum computational resource. Our work optimizes QAOA initialization, using Graph Neural Networks (GNN) as a warm-start technique. This sacrifices affordable computational resource on classical computer to reduce quantum computational resource overhead, enhancing QAOA's effectiveness. Experiments with various GNN architectures demonstrate the adaptability and stability of our framework, highlighting the synergy between quantum algorithms and machine learning. Our findings show GNN's potential in improving QAOA performance, opening new avenues for hybrid quantum-classical approaches in quantum computing and contributing to practical applications.
Paper Structure (13 sections, 9 equations, 5 figures, 1 table)

This paper contains 13 sections, 9 equations, 5 figures, 1 table.

Table of Contents

  1. Introduction
  2. Motivation
  3. Methodologoy
  4. Data Processing:
  5. Model Preparation:
  6. Improvement of Data Quality:
  7. Experiments
  8. Experiment Setup
  9. Result Analysis
  10. Related Work
  11. Conclusion
  12. Future Works and Limitations
  13. Acknowledgment

Figures (5)

  • Figure 1: The overview of the framework that uses the GNN to do the parameter "warm-start".
  • Figure 2: Degree and graph size distributions of the target dataset.
  • Figure 3: Possible Approximation Ratio by Graph Size
  • Figure 4: Possible Approximation Ratio by Degree Number
  • Figure 5: Comparison of Approximation Ratio between random initialisation and various GNN benchmarks. From left to right, the order is GAT, GCN, GIN and GraphSAGE.