Adaptive Quantum-Inspired Sorting Algorithm with Entropy-Based Recursion Control and AI-Optimized Partitioning

Sorting is a fundamental problem in computer science, critical for database indexing, numerical computations, and large-scale data processing. Traditional sorting algorithms, such as Quicksort and Merge Sort, achieve O(n log n) complexity but suffer from inefficiencies in pivot selection, recursion overhead, and memory usage. This paper introduces Adaptive Quantum-Inspired Sorting Algorithm with Entropy-Based Recursion Control and AI-Optimized Partitioning (AQSort), a novel hybrid algorithm that integrates quantum-inspired pivot selection, entropy-driven recursion control, and AI-assisted partitioning to optimize sorting efficiency. AQSort dynamically adjusts recursion depth based on data entropy, minimizing redundant operations and memory overhead. By leveraging probabilistic pivot selection inspired by Grover's algorithm and parallel acceleration via SIMD and CUDA, AQSort achieves an average-case complexity of O(n log log n), outperforming traditional sorting techniques in large-scale applications. Benchmark results demonstrate significant improvements in execution time and memory efficiency, making AQSort highly suitable for high-performance computing environments. This research contributes to adaptive sorting methodologies by bridging quantum-inspired computing and classical sorting, paving the way for efficient large-scale data processing.