Quantum Pattern Matching in Generalised Degenerate Strings

TL;DR

This paper extends pattern matching algorithms for generalized degenerate strings to quantum computing, significantly improving efficiency from classical to quantum models.

Contribution

It introduces a quantum algorithm for exact pattern matching in generalized degenerate strings with a faster running time.

Findings

Quantum algorithm achieves $ ilde{O}(\sqrt{mnN})$ time complexity.

Classical algorithm runs in $O(mn+N)$ time.

Quantum approach offers a quadratic speedup over classical methods.

Abstract

A degenerate string is a sequence of sets of characters. A generalized degenerate (GD) string extends this notion to the sequence of sets of strings, where strings of the same set are of equal length. Finding an exact match for a pattern string inside a GD string can be done in $O(mn+N)$ time (Ascone et al., WABI 2024), where $m$ is the pattern length, $n$ is the number of strings and $N$ the total length of strings constituting the GD string. We modify this algorithm to work under a quantum model of computation, achieving running time $\tilde{O}(\sqrt{mnN})$.