  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 >= 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.
