Quantum Hamiltonian Descent for Graph Partition

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.