Enhancing Knapsack-Based Financial Portfolio Optimization Using Quantum Approximate Optimization Algorithm

Abstract

Portfolio optimization is a primary component of the decision-making process in finance, aiming to tactfully allocate assets to achieve optimal returns while considering various constraints. Herein, we proposed a method that uses the knapsack-based portfolio optimization problem and incorporates the quantum computing capabilities of the quantum walk mixer with the quantum approximate optimization algorithm (QAOA) to address the challenges presented by the NP-hard problem. Additionally, we present the sequential procedure of our suggested approach and demonstrate empirical proof to illustrate the effectiveness of the proposed method in finding the optimal asset allocations across various constraints and asset choices. Moreover, we discuss the effectiveness of the QAOA components in relation to our proposed method. Consequently, our study successfully achieves the approximate ratio of the portfolio optimization technique using a circuit layer of $p\geqslant 3$ , compared to the classical best-known solution of the knapsack problem. Our proposed methods potentially contribute to the growing field of quantum finance by offering insights into the potential benefits of employing quantum algorithms for complex optimization tasks in financial portfolio management.

Keywords

• Best-known solution (BKS)
• portfolio optimization
• knapsack problem
• quantum approximate optimization algorithm (QAOA)