Quantum-Guided Cluster Algorithms for Combinatorial Optimization

This article introduces Quantum-Guided Cluster Algorithms (QGCA), a hybrid approach combining quantum and classical methods for solving complex combinatorial optimization problems.

• QGCA uses precomputed correlations from quantum algorithms to guide collective spin updates in optimization
• Addresses limitations of simulated annealing on rugged optimization landscapes with many local minima
• Clusters are built probabilistically based on correlation strength, avoiding percolation issues of traditional cluster methods
• Demonstrated on Max-Cut problems using QAOA-derived correlations from classical simulation
• Outperforms simulated annealing on certain graph instances, particularly those with high frustration
• Experiments show performance improves with deeper QAOA circuits providing better correlation guidance
• Future work includes scaling to larger problems and testing with quantum hardware as it advances

QGCA represents a practical hybrid approach leveraging quantum-derived information to improve classical optimization for scheduling, routing, and network design problems.