Quantum-Inspired Sparse Optimization Algorithms for High-Dimensional Problems

Abstract

The curse of dimensionality in high-dimensional optimization: It is inherently seen that the dimensionality of feature space presents a fundamental challenge to high-dimensional optimization: as dimensionality increases, feature space becomes computationally inefficient, overfitted and model interpretability declines, thus requiring highly robust sparsity-based solutions. To find a solution to these problems, a new quantum-inspired framework of sparse optimization is proposed in this study, which combines probabilistic Q-bit representation and L1-regularized optimization to efficiently consider large solution spaces but with a sparsity constraint. The suggested method builds on quantum-inspired search algorithms such as initiation by superposition and rotation gate updates to the search to improved exploration and exploitation ratio, leading to a better convergence process. Experimental analyses show that the framework produces better optimization accuracy, indicated by much lower Mean Squared Error (MSE) and convergence rates than classical and met heuristic baselines, with the framework also having a higher level of sparsity in the solution space. These results highlight the effectiveness of the proposed method in handling high-dimensional problems, making it particularly suitable for applications in signal processing, machine learning-based feature selection, and large-scale scientific computing tasks.