Quantum Data Structure for Range Minimum Query

2026-01-01

Journal of computer and system sciences (Print)

AI Summary

This work addresses the inefficiency of classical data structures in supporting both range minimum queries (RMQ) and range updates. To overcome this limitation, we propose a novel quantum data structure that operates without quantum random access memory (QRAM). By integrating quantum search with an efficient k-minimum finding technique, our approach simultaneously supports RMQ queries and range updates without requiring preprocessing. For a sequence of \( q = O(n) \) operations, the total time complexity is \( \tilde{O}(\sqrt{nq}) \), which significantly improves upon the classical bound of \( \tilde{O}(n + q) \). This result represents the first near-optimal quantum speedup for the RMQ problem that does not rely on QRAM.

Technology Category

• Machine Learning: Quantum Machine Learning
• Search and Optimization: Distributed Search
• Data Mining & Knowledge Management: Data Compression

Application Category

• Graph Algorithms and Modeling for the Web: Querying, indexing, and retrieval in Web-related graphs
• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines
• Web Mining and Content Analysis: Web data quality in the era of algorithmically-generated content

Problem

• Range Minimum Query
• Quantum Data Structure
• Quantum Algorithm
• Range Updates
• k-minimum Finding

Innovation

• quantum data structure
• range minimum query
• quantum algorithm
• k-minimum finding
• QRAM-free