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QAOA Parameter Transferability for Maximum Independent Set using Graph Attention Networks

Hanjing Xu, Xiaoyuan Liu, Alex Pothen, Ilya Safro

TL;DR

The paper tackles the MIS problem on graphs in the NISQ era by addressing the bottleneck of QAOA parameter optimization. It introduces a Graph Attention Network (GAT) based parameter transfer scheme to reuse optimized MIS-QAOA parameters across related instances, and couples this with HyDRA-MIS, a distributed, resource-aware MIS solver that partitions large graphs and processes subproblems on heterogeneous quantum hardware. The methods are validated on large graphs, showing competitive performance with KaMIS and superiority over separator-based DC in many cases, and demonstrate scalability up to thousands of vertices through distributed computation and parameter transfer. The work highlights the feasibility of combining graph-neural-network guided parameter transfer with distributed quantum-classical optimization to tackle large combinatorial problems on near-term hardware, with potential applications to other constrained graph problems and future hardware generations.

Abstract

The quantum approximate optimization algorithm (QAOA) is one of the promising variational approaches of quantum computing to solve combinatorial optimization problems. In QAOA, variational parameters need to be optimized by solving a series of nonlinear, nonconvex optimization programs. In this work, we propose a QAOA parameter transfer scheme using Graph Attention Networks (GAT) to solve Maximum Independent Set (MIS) problems. We prepare optimized parameters for graphs of 12 and 14 vertices and use GATs to transfer their parameters to larger graphs. Additionally, we design a hybrid distributed resource-aware algorithm for MIS (HyDRA-MIS), which decomposes large problems into smaller ones that can fit onto noisy intermediate-scale quantum (NISQ) computers. We integrate our GAT-based parameter transfer approach to HyDRA-MIS and demonstrate competitive results compared to KaMIS, a state-of-the-art classical MIS solver, on graphs with several thousands vertices.

QAOA Parameter Transferability for Maximum Independent Set using Graph Attention Networks

TL;DR

The paper tackles the MIS problem on graphs in the NISQ era by addressing the bottleneck of QAOA parameter optimization. It introduces a Graph Attention Network (GAT) based parameter transfer scheme to reuse optimized MIS-QAOA parameters across related instances, and couples this with HyDRA-MIS, a distributed, resource-aware MIS solver that partitions large graphs and processes subproblems on heterogeneous quantum hardware. The methods are validated on large graphs, showing competitive performance with KaMIS and superiority over separator-based DC in many cases, and demonstrate scalability up to thousands of vertices through distributed computation and parameter transfer. The work highlights the feasibility of combining graph-neural-network guided parameter transfer with distributed quantum-classical optimization to tackle large combinatorial problems on near-term hardware, with potential applications to other constrained graph problems and future hardware generations.

Abstract

The quantum approximate optimization algorithm (QAOA) is one of the promising variational approaches of quantum computing to solve combinatorial optimization problems. In QAOA, variational parameters need to be optimized by solving a series of nonlinear, nonconvex optimization programs. In this work, we propose a QAOA parameter transfer scheme using Graph Attention Networks (GAT) to solve Maximum Independent Set (MIS) problems. We prepare optimized parameters for graphs of 12 and 14 vertices and use GATs to transfer their parameters to larger graphs. Additionally, we design a hybrid distributed resource-aware algorithm for MIS (HyDRA-MIS), which decomposes large problems into smaller ones that can fit onto noisy intermediate-scale quantum (NISQ) computers. We integrate our GAT-based parameter transfer approach to HyDRA-MIS and demonstrate competitive results compared to KaMIS, a state-of-the-art classical MIS solver, on graphs with several thousands vertices.
Paper Structure (20 sections, 6 equations, 4 figures, 1 table, 1 algorithm)

This paper contains 20 sections, 6 equations, 4 figures, 1 table, 1 algorithm.

Table of Contents

  1. Introduction
  2. Background
  3. Graph Attention Networks
  4. Solving MIS with QAOA
  5. Related Work on QAOA Parameter Transfer
  6. Previous Quantum Solvers for Large MIS Instances
  7. Methods
  8. GAT for Transferring QAOA Parameters
  9. Training Preparations
  10. GAT Training
  11. Parameter Transfer
  12. Hybrid Distributed Resource-Aware Algorithm for MIS
  13. Computational Results
  14. Experimental Setup
  15. GAT-based QAOA Parameter Transfer Scaling
  16. ...and 5 more sections

Figures (4)

  • Figure 1: Approximation ratios of feasible samples from MIS QAOA circuits on graphs with varying sizes and densities. The parameters for each circuit are transferred via GATs.
  • Figure 2: Comparison of independent set cardinalities obtained from HyDRA-MIS and separator-based DC algorithm with different subproblem cutoffs. Each subproblem is solved using KaMIS since simulating QAOA circuits with more than 50 qubits is beyond our capabilities.
  • Figure 3: Comparison of independent set cardinalities obtained from HyDRA-MIS and separator-based DC algorithm. The y-axis tracks the ratios of solution cardinalities against the baseline solver, KaMIS. For each graph, we run KaMIS ten times and record the best solution.
  • Figure 4: Comparison of independent set cardinalities obtained from HyDRA-MIS using different cutoff sizes. Subproblems are solved via QAOA simulation (cutoff=25) and KaMIS (cutoff=200).