Papers › A Quantum Genetic Algorithm Framework for the MaxCut Problem
A Quantum Genetic Algorithm Framework for the MaxCut Problem
Paulo A. Viana, Fernando M. de Paula Neto
The archive published only this paper's code-link row. Authors, date and abstract are from arXiv's metadata (CC0), read from the Kaggle arXiv metadata snapshot of 2026-09-12 where its title matched the archive's; the title is the archive's.
The MaxCut problem is a fundamental problem in Combinatorial Optimization, with significant implications across diverse domains such as logistics, network design, and statistical physics. The algorithm represents innovative approaches that balance theoretical rigor with practical scalability. The proposed method introduces a Quantum Genetic Algorithm (QGA) using a Grover-based evolutionary framework and divide-and-conquer principles. By partitioning graphs into manageable subgraphs, optimizing each independently, and applying graph contraction to merge the solutions, the method exploits the inherent binary symmetry of MaxCut to ensure computational efficiency and robust approximation performance. Theoretical analysis establishes a foundation for the efficiency of the algorithm, while empirical evaluations provide quantitative evidence of its effectiveness. On complete graphs, the proposed method consistently achieves the true optimal MaxCut values, outperforming the Semidefinite Programming (SDP) approach, which provides up to 99.7\% of the optimal solution for larger graphs. On Erd\H{o}s-R\'{e}nyi random graphs, the QGA demonstrates competitive performance, achieving median solutions within 92-96\% of the SDP results. These results showcase the potential of the QGA framework to deliver competitive solutions, even under heuristic constraints, while demonstrating its promise for scalability as quantum hardware evolves.
Code
Repository list and official/mentioned flags are the archive's, frozen 2025-07-28. Reachability, where shown, is from one Syntology probe window (2026-09-16 to 2026-09-18); repositories not probed show nothing. GitHub stars are not tracked.
Code Syntology ran Syntology
Not run by Syntology. Nothing on this page verifies that the listed code works.
Results from the paper archive 2025-07-28
No leaderboard rows for this paper in the archive.
Report a problem or propose a change · a person checks every report against the paper or source before anything changes; decisions are listed on /corrections