Since its proposal, quantum computing has made significant strides in various domains. Among the different emerging techniques, Variational Quantum Algorithms (VQAs) have become one of the most promising approaches in the current era, where quantum computational resources are limited. VQAs aim to harness the potential of near-term quantum devices through quantum-classical hybrid frameworks, where parameterized quantum circuits are optimized using classical methods. These algorithms have been applied to diverse areas, including quantum chemistry, optimization, and machine learning.

Despite the promise of VQAs, recent studies have highlighted their limitations, particularly in terms of trainability, which is the ability to train quantum circuits. Furthermore, it is also questioned whether classical algorithms can fully replicate the trainable VQAs.

This thesis addresses two main objectives. First, it investigates the application of quantum neural networks in classification and generative tasks, providing a comprehensive analysis of Quantum Machine Learning (QML). In particular, it developed novel methodologies for applying VQAs to the domain of image analysis. The second objective addresses the inherent limitations of quantum computing. This includes a deep exploration of the vanishing gradient problem, also known as the barren plateau, which is a critical challenge in VQAs. The thesis concludes by comparing the resource efficiency of quantum simulations with their classical counterparts, providing insights into the practical feasibility of quantum advantage.