The curse of dimensionality remains a significant challenge in machine learning, degrading model performance in high-dimensional data analysis and leading to issues such as sparsity, computational inefficiency, and overfitting. Dimensionality reduction overcomes this problem as it transforms high-dimensional data into a lower-dimensional space and preserves its essential features. In this regard, problem domain is mapped with classical and its equivalent quantum-based solutions through hierarchical framework. Based on quantum effective design strategies and application specific use cases, this research presents the quantum-enhanced algorithmic advancements for dimensionality reduction. For critical assessment, quantum algorithms are standardized and independently analyzed for their computational complexity, and equivalent quantum circuits are realized using quantum simulation. A comparative evaluation highlights the exponential speedup achievable with quantum approaches for the high-dimensional datasets. This work establishes a comprehensive and foundational framework for advancing quantum-based dimensionality reduction techniques, serving as a unified and reliable resource for their seamless integration into next-generation machine learning systems.