Simple Quantum Algorithm for Approximate $k$-Mismatch Problem
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866911365267980288 |
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| author | Habib, Ruhan Shahriar, Shadman |
| author_facet | Habib, Ruhan Shahriar, Shadman |
| contents | In the $k$-mismatch problem, given a pattern and a text of length $n$ and $m$ respectively, we have to find if the text has a sub-string with a Hamming distance of at most $k$ from the pattern. This has been studied in the classical setting since 1982 and recently in the quantum computational setting by Jin and Nogler and Kociumaka, Nogler, and Wellnitz. We provide a simple quantum algorithm that solves the problem in an approximate manner, given a parameter $ε\in (0, 1]$. It returns an occurrence as a match only if it is a $\left(1+ε\right)k$-mismatch. If it does not return any occurrence, then there is no $k$-mismatch. This algorithm has a time (size) complexity of $\tilde{O}\left( ε^{-1} \sqrt{\frac{mn}{k}} \right)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_02399 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Simple Quantum Algorithm for Approximate $k$-Mismatch Problem Habib, Ruhan Shahriar, Shadman Quantum Physics Data Structures and Algorithms In the $k$-mismatch problem, given a pattern and a text of length $n$ and $m$ respectively, we have to find if the text has a sub-string with a Hamming distance of at most $k$ from the pattern. This has been studied in the classical setting since 1982 and recently in the quantum computational setting by Jin and Nogler and Kociumaka, Nogler, and Wellnitz. We provide a simple quantum algorithm that solves the problem in an approximate manner, given a parameter $ε\in (0, 1]$. It returns an occurrence as a match only if it is a $\left(1+ε\right)k$-mismatch. If it does not return any occurrence, then there is no $k$-mismatch. This algorithm has a time (size) complexity of $\tilde{O}\left( ε^{-1} \sqrt{\frac{mn}{k}} \right)$. |
| title | Simple Quantum Algorithm for Approximate $k$-Mismatch Problem |
| topic | Quantum Physics Data Structures and Algorithms |
| url | https://arxiv.org/abs/2510.02399 |