A Quantum String-Matching Algorithm

Abstract

A novel quantum algorithm for string-matching is introduced that significantly enhances the complexity of this fundamental operation, essential in numerous computing applications. The algorithm is designed as a composite quantum denoising procedure applied to a quantum-generated dot-matrix plot, which is treated as an image. This approach effectively identifies regions of similarity between two input strings of lengths N and M. For strings of equal length, the algorithm achieves a time complexity of $O\left(N+log\left(N\right)+6N^2\right)$ and a space complexity of $O\left(log\left(2N\right)\right)$, demonstrating a clear advantage in quantum computational efficiency.