量子多标签k近邻
Quantum multi-label k-nearest neighbor
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中文总结 AI 辅助
针对多标签k近邻算法处理大规模数据集时时间复杂度高的问题，提出量子多标签k近邻算法，利用量子相位估计、格罗弗振幅放大等技术加速概率计算与邻居识别，经实验验证该算法能显著降低时间复杂度并提升性能。
中文摘要 AI 辅助
虽然多标签k近邻（ML-kNN）能利用局部邻域相似性有效解决多标签学习（MLL）问题，但对于大规模数据集，其时间复杂度几乎无法接受。为解决此问题，我们提出一种采用量子计算技术的新型ML-kNN算法，即量子多标签k近邻（QML-kNN）。具体而言，我们首先利用量子相位估计和格罗弗振幅放大加速先验概率的计算。然后，使用受控SWAP测试和量子k最大相似性搜索来有效识别邻居。随后，设计量子并行计数电路（QPCC）快速计算后验概率。实验结果表明，QML-kNN能够显著降低解决多标签问题的时间复杂度并提高性能，比经典MLL算法有大幅加速。
英文摘要
Although multi-label k-nearest neighbor (ML-kNN) is able to effectively solve multi-label learning (MLL) problem with local neighborhood similarity, its time complexity is nearly unacceptable with large-scale datasets. To solve this issue, we propose a novel ML-kNN algorithm with quantum computing techniques, which called quantum multi-label k-nearest neighbor (QML-kNN). In particular, we first accelerate the calculation of the prior probability by taking advantage of quantum phase estimation and Grover's amplitude amplification. Then, a controlled-SWAP test and a quantum k-maximal similarity search are used for efficiently identifying the neighbors. Subsequently, a quantum parallel counting circuit (QPCC) is designed to rapidly calculate the posterior probabilities. Experimental results demonstrate that QML-kNN is able to significantly reduce the time complexity of solving multi-label problems with performance improvement, achieving a substantial speedup over the classical MLL algorithm.
