We introduce Quantum Hamiltonian Descent as a novel approach to solve the graph partition problem. By reformulating graph partition as a Quadratic Unconstrained Binary Optimization (QUBO) problem, we leverage QHD's quantum-inspired dynamics to identify optimal community structures. Our method implements a multi-level refinement strategy that alternates between QUBO formulation and QHD optimization to iteratively improve partition quality. Experimental results demonstrate that our QHD-based approach achieves superior modularity scores (up to 5.49\%) improvement with reduced computational overhead compared to traditional optimization methods. This work establishes QHD as an effective quantum-inspired framework for tackling graph partition challenges in large-scale networks.

翻译：本文提出量子哈密顿下降法作为一种解决图划分问题的新方法。通过将图划分问题重构为二次无约束二进制优化问题，我们利用QHD的量子启发动力学来识别最优社区结构。该方法实现了多级优化策略，在QUBO公式化和QHD优化之间交替进行，以迭代提升划分质量。实验结果表明，与传统优化方法相比，基于QHD的方法在降低计算开销的同时获得了更优的模块度分数（最高提升5.49%）。本工作确立了QHD作为处理大规模网络图划分挑战的有效量子启发框架。