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arXiv · 2505.23066

Efficient Quantum Approximate $k$NN Algorithm via Granular-Ball Computing

Shuyin Xia·Xiaojiang Tian·Suzhen Yuan·Jeremiah D. Deng
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Abstract

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.

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Shuyin Xia, Xiaojiang Tian, Suzhen Yuan, Jeremiah D. Deng. 2025-05-29. Efficient Quantum Approximate $k$NN Algorithm via Granular-Ball Computing. https://arxiv.org/abs/2505.23066

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