Quantum Data Structure for Range Minimum Query
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866912841547644928 |
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| author | Wang, Qisheng Xu, Zhean Zhang, Zhicheng |
| author_facet | Wang, Qisheng Xu, Zhean Zhang, Zhicheng |
| contents | Given an array $a[1..n]$, the Range Minimum Query (RMQ) problem is to maintain a data structure that supports RMQ queries: given a range $[l, r]$, find the index of the minimum element among $a[l..r]$, i.e., $\operatorname{argmin}_{i \in [l, r]} a[i]$. In this paper, we propose a quantum data structure that supports RMQ queries and range updates, with an optimal time complexity $\widetilde Θ(\sqrt{nq})$ for performing $q = O(n)$ operations without preprocessing, compared to the classical $\widetildeΘ(n+q)$. As an application, we obtain a time-efficient quantum algorithm for $k$-minimum finding without the use of quantum random access memory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_13195 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Quantum Data Structure for Range Minimum Query Wang, Qisheng Xu, Zhean Zhang, Zhicheng Quantum Physics Data Structures and Algorithms Given an array $a[1..n]$, the Range Minimum Query (RMQ) problem is to maintain a data structure that supports RMQ queries: given a range $[l, r]$, find the index of the minimum element among $a[l..r]$, i.e., $\operatorname{argmin}_{i \in [l, r]} a[i]$. In this paper, we propose a quantum data structure that supports RMQ queries and range updates, with an optimal time complexity $\widetilde Θ(\sqrt{nq})$ for performing $q = O(n)$ operations without preprocessing, compared to the classical $\widetildeΘ(n+q)$. As an application, we obtain a time-efficient quantum algorithm for $k$-minimum finding without the use of quantum random access memory. |
| title | Quantum Data Structure for Range Minimum Query |
| topic | Quantum Physics Data Structures and Algorithms |
| url | https://arxiv.org/abs/2601.13195 |