High-dimensional portfolio optimization faces significant computational challenges under complex constraints, with traditional optimization methods struggling to balance convergence speed and global exploration capability. To address this, firstly, we introduce an enhanced Sharpe ratio-based model that incorporates all constraints into the objective function using adaptive penalty terms, transforming the original constrained problem into an unconstrained single-objective formulation. This approach preserves financial interpretability while simplifying algorithmic implementation. To efficiently solve the resulting high-dimensional optimization problem, we propose a Quantum Hybrid Differential Evolution (QHDE) algorithm, which integrates Quantum-inspired probabilistic behavior into the standard DE framework. QHDE employs a Schrodinger-inspired probabilistic mechanism for population evolution, enabling more flexible and diversified solution updates. To further enhance performance, a good point set-chaos reverse learning strategy is adopted to generate a well-dispersed initial population, and a dynamic elite pool combined with Cauchy-Gaussian hybrid perturbations strengthens global exploration and mitigates premature convergence. Experimental validation on CEC benchmarks and real-world portfolios involving 20 to 80 assets demonstrates that QHDE's performance improves by up to 73.4%. It attains faster convergence, higher solution precision, and greater robustness than seven state-of-the-art counterparts, thereby confirming its suitability for complex, high-dimensional portfolio optimization and advancing quantum-inspired evolutionary research in computational finance.

翻译：高维投资组合优化在复杂约束下面临显著的计算挑战，传统优化方法难以兼顾收敛速度与全局探索能力。为此，首先我们引入一种增强型夏普比率模型，通过自适应惩罚项将所有约束纳入目标函数，将原始约束问题转化为无约束单目标形式。该方法在保持金融可解释性的同时简化了算法实现。为高效求解由此产生的高维优化问题，我们提出量子混合差分进化算法，将量子启发概率行为融入标准差分进化框架。QHDE采用薛定谔启发概率机制进行种群进化，实现更灵活多样化的解更新。为进一步提升性能，采用好点集-混沌反向学习策略生成分布良好的初始种群，同时动态精英池结合柯西-高斯混合扰动增强全局探索能力并缓解早熟收敛。在CEC基准测试及包含20至80个资产的实际投资组合上的实验验证表明，QHDE性能提升高达73.4%。相比七种前沿算法，该算法收敛更快、解精度更高、鲁棒性更强，从而证实其适用于复杂高维投资组合优化，并推动了计算金融中量子启发进化研究的发展。