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arXiv · 2601.13195

Quantum Data Structure for Range Minimum Query

Qisheng Wang·Zhean Xu·Zhicheng Zhang
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Abstract

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 $\widetilde \Theta(\sqrt{nq})$ for performing $q = O(n)$ operations without preprocessing, compared to the classical $\widetilde\Theta(n+q)$. As an application, we obtain a time-efficient quantum algorithm for $k$-minimum finding without the use of quantum random access memory.

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Qisheng Wang, Zhean Xu, Zhicheng Zhang. 2026-01-19. Quantum Data Structure for Range Minimum Query. https://doi.org/10.1016/j.jcss.2026.103756

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