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Main Authors: Xia, Shuyin, Tian, Xiaojiang, Yuan, Suzhen, Deng, Jeremiah D.
Format: Preprint
Published: 2025
Subjects:
Online Access:https://arxiv.org/abs/2505.23066
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author Xia, Shuyin
Tian, Xiaojiang
Yuan, Suzhen
Deng, Jeremiah D.
author_facet Xia, Shuyin
Tian, Xiaojiang
Yuan, Suzhen
Deng, Jeremiah D.
contents High time complexity is one of the biggest challenges faced by $k$-Nearest Neighbors ($k$NN). Although current classical and quantum $k$NN algorithms have made some improvements, they still have a speed bottleneck when facing large amounts of data. To address this issue, we propose an innovative algorithm called Granular-Ball based Quantum $k$NN(GB-Q$k$NN). This approach achieves higher efficiency by first employing granular-balls, which reduces the data size needed to processed. The search process is then accelerated by adopting a Hierarchical Navigable Small World (HNSW) method. Moreover, we optimize the time-consuming steps, such as distance calculation, of the HNSW via quantization, further reducing the time complexity of the construct and search process. By combining the use of granular-balls and quantization of the HNSW method, our approach manages to take advantage of these treatments and significantly reduces the time complexity of the $k$NN-like algorithms, as revealed by a comprehensive complexity analysis.
format Preprint
id arxiv_https___arxiv_org_abs_2505_23066
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Efficient Quantum Approximate $k$NN Algorithm via Granular-Ball Computing
Xia, Shuyin
Tian, Xiaojiang
Yuan, Suzhen
Deng, Jeremiah D.
Quantum Physics
Artificial Intelligence
Machine Learning
High time complexity is one of the biggest challenges faced by $k$-Nearest Neighbors ($k$NN). Although current classical and quantum $k$NN algorithms have made some improvements, they still have a speed bottleneck when facing large amounts of data. To address this issue, we propose an innovative algorithm called Granular-Ball based Quantum $k$NN(GB-Q$k$NN). This approach achieves higher efficiency by first employing granular-balls, which reduces the data size needed to processed. The search process is then accelerated by adopting a Hierarchical Navigable Small World (HNSW) method. Moreover, we optimize the time-consuming steps, such as distance calculation, of the HNSW via quantization, further reducing the time complexity of the construct and search process. By combining the use of granular-balls and quantization of the HNSW method, our approach manages to take advantage of these treatments and significantly reduces the time complexity of the $k$NN-like algorithms, as revealed by a comprehensive complexity analysis.
title Efficient Quantum Approximate $k$NN Algorithm via Granular-Ball Computing
topic Quantum Physics
Artificial Intelligence
Machine Learning
url https://arxiv.org/abs/2505.23066