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Quantum Control Electronics System Integration

Quantum Data Structure for Range Minimum Query

arXiv
Authors: Qisheng Wang, Zhean Xu, Zhicheng Zhang

Year

2026

Paper ID

3632

Status

Preprint

Abstract Read

~2 min

Abstract Words

107

Citations

N/A

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 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.

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  • This paper contributes to the Quantum Control Electronics & System Integration research area in the Quantum Articles archive.
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  • 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...

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References & Citation Signals

[1] DOI https://doi.org/arXiv:2601.13195 [2] arXiv https://arxiv.org/abs/2601.13195 [3] Publisher https://arxiv.org/abs/2601.13195

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