基于量子判别分析法的量子连续投资组合优化算法

Financial Portfolio Optimization Method Based on the Quantum Linear Discriminant Analysis

摘要: 利用马科维茨投资组合优化问题和量子线性判别分析（quantum linear discriminant analysis, QLDA）的相似性，将马科维茨投资组合优化问题规约为量子线性判别分析的优化问题，并通过解决QLDA的技术厄米特链积（hermitian chain product, HCP）以及密度矩阵指数化算法（density matrix exponentiation, DME）来求得马科维茨均值方差模型中夏普率最大的最优解。量子连续投资组合优化方案相比于经典方案可以实现准指数加速。

Abstract: This paper reduces the Markowitz’s model to the Quantum Linear Discriminant Analysis (QLDA) model. Hermitian Chain Product (HCP) and Density Matrix Exponentiation (DME) are used to solve the optimal solution with the largest Sharpe rate in the Markowitz mean-variance model. The quantum continuous portfolio optimization scheme can achieve quasi-exponential acceleration compared to the classical scheme.