<![CDATA[Quantum machine learning has emerged as a promising paradigm for addressing the limitations of classical learning models in handling data with exponentially growing dimensionality. In particular, many problems in physics, chemistry, and quantum information are naturally represented in high-dimensional Hilbert spaces, where classical neural networks face significant challenges related to representation efficiency and scalability. This study aims to analyze the advantages of quantum neural networks in processing data embedded in high-dimensional Hilbert spaces and to clarify the structural sources of their potential superiority over classical architectures. The research adopts a theoretical–computational approach that combines analytical modeling with numerical simulations of variational quantum circuits and comparable classical neural network models across increasing dimensional regimes. Performance is evaluated in terms of learning fidelity, parameter scaling behavior, and stability under dimensional growth. The results show that quantum neural networks consistently maintain higher fidelity with substantially fewer parameters as Hilbert space dimensionality increases, while classical models exhibit rapid performance degradation and escalating complexity. These findings indicate that quantum neural networks benefit from intrinsic alignment with Hilbert space geometry through superposition and entanglement. In conclusion, the study demonstrates that quantum neural networks constitute a distinct and scalable learning framework for high-dimensional data, supporting their relevance for future quantum-enhanced machine learning applications..]]>
