A Quantum String‐Matching Algorithm - Prousalis, Konstantinos; Kydros, Asimakis; Konofaos, Nikos (Advanced quantum technologies (Online), 2025)
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(N+log(N)+6N2)$O( {N + log( N ) + 6{N^2}} )$ and a space complexity of O(log(2N))$O( {log( {2N} )} )$, demonstrating a clear advantage in quantum computational efficiency. A string‐matching quantum algorithm is introduced, offering significant improvements in computational complexity. The algorithm employs a quantum image denoising method applied to a quantum‐generated dot‐matrix plot view, to identify regions of similarity between two input strings of lengths N and M. For strings of equal length, the algorithm achieves an improved time complexity of O(N+log(N)+6N2)$O( {N + log( N ) + 6{N^2}} )$ and space complexity of O(log(2N))$O( {log( {2N} )} )$.