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，传统优化方法难以平衡收敛速度与全局探索能力。为此，本文首先提出一种基于增强夏普比率的模型，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。为高效求解所得的高维优化问题，我们提出一种量子混合差分进化算法，该算法将量子启发的概率行为整合到标准差分进化框架中。QHDE采用薛定谔启发的概率机制进行种群进化，实现更灵活、更多样化的解更新。为进一步提升性能，算法采用好点集-混沌反向学习策略生成分布良好的初始种群，并结合动态精英池与柯西-高斯混合扰动以增强全局探索能力并缓解早熟收敛。在CEC基准测试和涉及20至80项资产的真实投资组合上的实验验证表明，QHDE的性能提升最高达73.4%。相较于七种先进对比算法，该算法具有更快的收敛速度、更高的求解精度和更强的鲁棒性，从而证实了其处理复杂高维投资组合优化问题的适用性，并推动了计算金融领域量子启发进化研究的发展。