The increasing complexity of financial models has highlighted the limitations of classical computing, positioning quantum computing as a promising solution for addressing these challenges. This paper explores the potential of quantum computing in finance, with a focus on portfolio optimization, a crucial task for investment management. We present a state-of-the-art review of quantum algorithms, emphasizing their application to financial problems. Through practical implementation using Qiskit, this work compares the Quantum Approximate Optimization Algorithm (QAOA) with classical optimization methods, particularly backtracking algorithms. The study investigates the efficiency of QAOA in solving portfolio optimization problems, such as maximizing returns while minimizing risk, and highlights its potential for faster convergence compared to classical approaches. Despite the promise of quantum computing, the integration of quantum systems into the financial sector faces significant challenges, including high costs and complex maintenance. The results suggest that while quantum computing offers substantial speedups in solving financial optimization problems, practical implementation remains hindered by resource-intensive requirements. This paper aims to contribute to the growing intersection of quantum computing and finance, shedding light on both the technological advancements and the financial implications of quantum solutions in the sector.