Application of quantum computing in discrete portfolio optimization

Abstract

This study proposes a novel and more efficient quantum algorithm for portfolio optimization using quantum combinatorial optimization (QCO) techniques. A recent construction developed in 2021 has sparked the field of financial portfolio optimization through the Quantum Walk Optimization Algorithm (QWOA). In this study, we investigated the complexity and efficiency of quantum optimization algorithms with a special interest in QWOA. The objective is to minimize investment risk by having a good combination of assets in the portfolio. We also focused on reducing the number of iterations while attaining a high-quality resolution through contraction of the solution space to ease computations. The concept of QWOA was extended by constructing a newly outperforming scheme known as the “Quantum Mix Optimization Algorithm (QMOA).” QMOA algorithm codes were provided for the implementation and simulation of numerical results. In addition, the efficiency of QMOA, which is better than the existing QCO algorithms, was discussed. For instance, the least QWOA number of computations required to execute the initial state equation was p > 2, whereas this value was p ≥ 2 in the proposed QMOA.