Quantum Data Structure for Range Minimum Query

Fuente: arXiv
Salvato in:
Dettagli Bibliografici
Autori principali: Wang, Qisheng, Xu, Zhean, Zhang, Zhicheng
Natura: Preprint
Pubblicazione: 2026
Soggetti:
Accesso online:
Tags: Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
_version_ 1866912841547644928
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