In this paper, we study the string matching problem. We design a quantum string-matching algorithm for noisy intermediate-scale quantum (NISQ) computers, given the current leading quantum processing units (QPUs) having no more than a few hundred qubits [16]. We also compare the performance of classic algorithms and quantum algorithms under various combinations. Our study provides a comprehensive and quantitative guide for users to choose appropriate classic or quantum algorithms for their string matching problems.In this paper, we study the string matching problem. We design a quantum string-matching algorithm for noisy intermediate-scale quantum (NISQ) computers, given the current leading quantum processing units (QPUs) having no more than a few hundred qubits [16]. We also compare the performance of classic algorithms and quantum algorithms under various combinations. Our study provides a comprehensive and quantitative guide for users to choose appropriate classic or quantum algorithms for their string matching problems.

International Conference on Advanced Information Science and System (AISS)Nov 25, 20220 citations

Quantum Pattern Matching in Generalised Degenerate Strings

Massimo Equi, Md Rabiul Islam Khan, Veli Mäkinen

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

Quantum algorithm for polynomial multiplication and its applications

Shang Bing Gao, Rui‐Chen Huang, Bing‐Xin Liu +6 more

Polynomial multiplication is a fundamental operation in various fields of science and engineering. This paper proposes a quantum algorithm for polynomial multiplication that achieves improved efficiency over classical approaches. The core innovation is the use of a quantum Fourier transform with digital encoding. The practical utility and versatility of this algorithm are highlighted through its application to several related computational problems, including string matching, Toeplitz matrix-vector multiplication, and matrix decomposition algorithm. Furthermore, an enhanced version of the quantum polynomial multiplication algorithm is introduced, offering improvements in both execution process and time complexity.Polynomial multiplication is a fundamental operation in various fields of science and engineering. This paper proposes a quantum algorithm for polynomial multiplication that achieves improved efficiency over classical approaches. The core innovation is the use of a quantum Fourier transform with digital encoding. The practical utility and versatility of this algorithm are highlighted through its application to several related computational problems, including string matching, Toeplitz matrix-vector multiplication, and matrix decomposition algorithm. Furthermore, an enhanced version of the quantum polynomial multiplication algorithm is introduced, offering improvements in both execution process and time complexity.

EPJ Quantum TechnologyOct 15, 20250 citations

Quantum Algorithms for Matching Problems

Sebastian Dörn

Theory of Computing SystemsMay 29, 200819 citations

Practical Quantum Combinatorial String Matching

Domenico Aldo Cantone, Claudio Caudullo, Simone Faro +3 more

Lecture notes in networks and systemsJan 1, 20242 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.