SAPO: Improving the Scalability and Accuracy of Quantum Linear Solver for Portfolio Optimization

Portfolio optimization is one of the most important financial problem, suffering from huge computational pressure due to arithmetic complexity. Quantum computing offers polynomial or even exponential speedup that turns out to be a promising approach. However, existing quantum methods is fundamentally limited by either poor scalability or insufficient accuracy. In this paper, we propose SAPO, which formally articulates the quantum circuit that seamlessly integrates financial theory and historical data characteristics with quantum algebra. The circuit design is extended from the HHL algorithm incorporating mean-variance theory, which promotes scalability by equivalent transformation. Then, we present a min-max eigenvalue model that leverages historical financial information to refine parameter settings with high accuracy. Experiments conducted on market data demonstrate that SAPO can effectively reduce the complexity by $\mathbf{3 6. 9 4 \%}$ compared to basic HHL [1], [2] and improve the accuracy by $1.46 \times$ compared to hybrid HHL [3].