Practical Implementation of a Quantum String Matching Algorithm
Simone Faro, Francesco Pio Marino, and Antonio Scardace

This repository contains the official code for our paper on Exact String Matching.
In our paper, we present the implementation of a quantum ESM algorithm, which identifies occurrences of a specified pattern $x$ of length $m$, within a text $y$ of length $n$ $\geq$ $m$, where both sequences are composed of characters taken from an alphabet $\Sigma$ of size $\sigma$. Our article presents an initial practical implementation of a quantum circuit tailored to address the ESM problem, with a particular focus on binary strings.

A classical naïve approach exhibits a worst-case time complexity of $\mathcal{O}(n+m)$, contrasting with the capability of quantum computation to achieve a $\tilde{O}(\sqrt{n})$ complexity using Grover's search.

We use the Qiskit open-source toolkit developed by IBM. While current real-world hardware often struggles to produce valid results due to decoherence and quantum errors, this study presents experimental results from a circuit simulation on classical hardware, validating the proposed implementation's efficacy.

Citation

Please, reference this publication if you find this code useful:

@inproceedings{10.1145/3660318.3660327,
    author = {Marino, Francesco Pio and Faro, Simone and Scardace, Antonio},
    title = {Practical Implementation of a Quantum String Matching Algorithm},
    year = {2024},
    publisher = {Association for Computing Machinery},
    url = {https://doi.org/10.1145/3660318.3660327}
}