Quantum Circuits for Fixed Substring Matching Problems

TL;DR

This paper introduces quantum algorithms for fixed substring matching problems that significantly outperform classical methods by achieving polylogarithmic complexity for string comparison tasks.

Contribution

The study presents novel quantum algorithms for fixed-length substring matching, providing polylogarithmic solutions that surpass classical linear-time algorithms.

Findings

Quantum algorithms achieve polylogarithmic complexity.

Solutions outperform classical linear algorithms.

Applicable to text processing and sequence analysis.

Abstract

Quantum computation represents a computational paradigm whose distinctive attributes confer the ability to devise algorithms with asymptotic performance levels significantly superior to those achievable via classical computation. Recent strides have been taken to apply this computational framework in tackling and resolving various issues related to text processing. The resultant solutions demonstrate marked advantages over their classical counterparts. This study employs quantum computation to efficaciously surmount text processing challenges, particularly those involving string comparison. The focus is on the alignment of fixed-length substrings within two input strings. Specifically, given two input strings, $x$ and $y$, both of length $n$, and a value $d \leq n$, we want to verify the following conditions: the existence of a common prefix of length $d$, the presence of a common substring of length $d$ beginning at position $j$ (with $0 \leq j < n$) and, the presence of any common substring of length $d$ beginning in both strings at the same position. Such problems find applications as sub-procedures in a variety of problems concerning text processing and sequence analysis. Notably, our approach furnishes polylogarithmic solutions, a stark contrast to the linear complexity inherent in the best classical alternatives.