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. This is the best classical algorithm achieved so far, and no matching lower bound, neither unconditional nor conditional, has been shown. We make progress on this problem proposing a quantum algorithm that achieves running time $\tilde{O}(\sqrt{mnN})$ , thus beating the current best classical solution. To the best of our knowledge, this is the first quantum algorithm proposed in the context of GD strings. We present our results starting from the framework of classical parallel computing, which we believe makes them intuitive to understand and possibly easy to generalise to other similar structures.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. This is the best classical algorithm achieved so far, and no matching lower bound, neither unconditional nor conditional, has been shown. We make progress on this problem proposing a quantum algorithm that achieves running time $\tilde{O}(\sqrt{mnN})$, thus beating the current best classical solution. To the best of our knowledge, this is the first quantum algorithm proposed in the context of GD strings. We present our results starting from the framework of classical parallel computing, which we believe makes them intuitive to understand and possibly easy to generalise to other similar structures.

quant-pharXiv:2603.16297Mar 18, 20260 citations

String matching in O(n+m) quantum time

H. Ramesh, V Vinay

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Quantum Algorithm for the Multiple String Matching Problem

Kamil Ravilevich Khadiev, Danil Serov

arXiv:2411.14850Lecture notes in computer scienceJan 1, 20253 citations

A quantum algorithm for string matching.

Evangelos Tzanis

IADIS ACJan 1, 20050 citations

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. This is the best classical algorithm achieved so far, and no matching lower bound, neither unconditional nor conditional, has been shown. We make progress on this problem proposing a quantum algorithm that achieves running time

\tilde{O}(\sqrt{mnN})

, thus beating the current best classical solution. To the best of our knowledge, this is the first quantum algorithm proposed in the context of GD strings. We present our results starting from the framework of classical parallel computing, which we believe makes them intuitive to understand and possibly easy to generalise to other similar structures.