A Note on Quantum Divide and Conquer for Minimal String Rotation
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2022
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866915161873317888 |
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| author | Wang, Qisheng |
| author_facet | Wang, Qisheng |
| contents | Lexicographically minimal string rotation is a fundamental problem in string processing that has recently garnered significant attention in quantum computing. Near-optimal quantum algorithms have been proposed for solving this problem, utilizing a divide-and-conquer structure. In this note, we show that its quantum query complexity is $\sqrt{n} \cdot 2^{O(\sqrt{\log n})}$, improving the prior result of $\sqrt{n} \cdot 2^{(\log n)^{1/2+\varepsilon}}$ due to Akmal and Jin (SODA 2022). Notably, this improvement is quasi-polylogarithmic, which is achieved by only logarithmic level-wise optimization using fault-tolerant quantum minimum finding. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2210_09149 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | A Note on Quantum Divide and Conquer for Minimal String Rotation Wang, Qisheng Quantum Physics Data Structures and Algorithms Lexicographically minimal string rotation is a fundamental problem in string processing that has recently garnered significant attention in quantum computing. Near-optimal quantum algorithms have been proposed for solving this problem, utilizing a divide-and-conquer structure. In this note, we show that its quantum query complexity is $\sqrt{n} \cdot 2^{O(\sqrt{\log n})}$, improving the prior result of $\sqrt{n} \cdot 2^{(\log n)^{1/2+\varepsilon}}$ due to Akmal and Jin (SODA 2022). Notably, this improvement is quasi-polylogarithmic, which is achieved by only logarithmic level-wise optimization using fault-tolerant quantum minimum finding. |
| title | A Note on Quantum Divide and Conquer for Minimal String Rotation |
| topic | Quantum Physics Data Structures and Algorithms |
| url | https://arxiv.org/abs/2210.09149 |