用量子方法解决投资组合优化中的约束难题，比传统方法更准。
A Quantum Model for Constrained Markowitz Modern Portfolio Using Slack Variables to Process Mixed-Binary Optimization under QAOA
- 将松弛变量映射到量子辅助比特，直接嵌入哈密顿量中
- 模拟显示该方法在约束条件下始终找到最优解，传统方法失败
- 适合研究量子金融优化或想突破经典算法瓶颈的人
有效编码不等式约束是将量子算法应用于金融优化的主要障碍。本文提出一种马科维茨投资组合优化的量子模型，通过将松弛变量直接嵌入问题哈密顿量来解决此问题。该方法将每个松弛变量映射到一个专用辅助量子比特，将原问题转化为适用于量子近似优化算法（QAOA）的二次无约束二元优化（QUBO）形式。这一过程将约束内化于量子态中，改变问题的能量景观以促进优化。该模型通过模拟实证验证，显示其在标准惩罚法QAOA失效的情况下仍能持续找到最优投资组合。本工作表明，通过松弛-辅助比特方案修改哈密顿量架构，为在量子计算机上求解约束优化问题提供了一条稳健有效的路径。同时，还提出了投资组合风险与收益同时精确测量的根本量子限制。
原文摘要 · Abstract (English)
Effectively encoding inequality constraints is a primary obstacle in applying quantum algorithms to financial optimization. A quantum model for Markowitz portfolio optimization is presented that resolves this by embedding slack variables directly into the problem Hamiltonian. The method maps each slack variable to a dedicated ancilla qubit, transforming the problem into a Quadratic Unconstrained Binary Optimization (QUBO) formulation suitable for the Quantum Approximate Optimization Algorithm (QAOA). This process internalizes the constraints within the quantum state, altering the problem's energy landscape to facilitate optimization. The model is empirically validated through simulation, showing it consistently finds the optimal portfolio where a standard penalty-based QAOA fails. This work demonstrates that modifying the Hamiltonian architecture via a slack-ancilla scheme provides a robust and effective pathway for solving constrained optimization problems on quantum computers. A fundamental quantum limit on the simultaneous precision of portfolio risk and return is also posited.
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