发表机构
National University of Singapore; The Chinese University of Hong Kong; The Hong Kong University of Science and Technology (Guangzhou)（新加坡国立大学; 香港中文大学; 香港科技大学（广州））
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出量子范围查询（QRQ），通过混合量子-经典算法和量子索引变体，在轨迹数据上实现2.03至64.70倍的加速，为移动分析和LLM/GeoFM搜索提供基础原语。
AI 中文摘要
范围查询是地理空间数据搜索及许多其他下游应用中的一项基本任务。经典的范围查询通常依赖于基于树的空間索引，其查询速度取决于查询范围内被索引点的数量$k$。例如，经典的B+树在O(log N+k)时间内回答范围查询。长期以来，在经典数据库系统中，这一速度一直被认为渐近最优，直到最近量子计算的出现，使得量子B+树可能仅需O(log_B N)时间。本文通过一种混合量子-经典算法提出了量子范围查询（QRQ），以量子叠加态返回范围查询结果。在此背景下，QRQ旨在利用量子算法加速对时空语义轨迹地理数据的经典范围查询。具体而言，QRQ开发了R树、TB树和KD树的量子变体，其中节点的物理槽位（包括未使用的填充槽位）被视为一个数组，量子随机存取存储器（QRAM）可以以叠加态读取该数组。在三个常见轨迹数据集（即GeoLife、T-Drive和GDP Drifter）上的评估中，每个设置进行10,000次查询，QRQ在1%目标选择性下的加速比从2.03倍到64.70倍不等。更重要的是，QRQ在优化现有轨迹范围查询方面显示出巨大潜力，因此它成为人类移动性分析以及后续由大型语言模型（LLM）和地理基础模型（GeoFM）指定的搜索所依赖的共享原语。
英文摘要
Range query is a fundamental task in geospatial data search and many other downstream applications. Classic range queries often rely on tree-based spatial indexes, of which the query speed depends on the number of indexed points $k$ within the queried range. For instance, a classical B+ tree answers a range query in O(log N+k). For a long time, this speed has long been considered asymptotically optimal in classic database systems, until the recent emergence of quantum computing, where a quantum B+ tree may requires only O(log_B N). This paper presents Quantum Range Query (QRQ) via a hybrid quantum-classic algorithm to return the range query results in quantum superpositions. In this context, QRQ is designed to accelerate classic range query on spatial-temporal-semantic trajectory geodata using quantum algorithms. Specifically, QRQ develops quantum variants of R-tree, TB-tree and KD-tree, where the physical slots of a node, including unused padding slots, are treated as an array that a quantum random-access memory (QRAM) can read in superpositions. Evaluations on three common trajectory datasets, namely GeoLife, T-Drive, and GDP Drifter, and 10,000 queries per setting, the QRQ speedup at 1% target selectivity ranges from 2.03 times) to 64.70 times. More importantly, QRQ shows a great potential in optimizing existing trajectory range query, so it becomes the shared primitive on which human mobility analysis, and later searches specified by large language models (LLMs) and geo-foundation models (GeoFMs), can rest.
