Researching | Quantum K-means algorithm based on parameterized angle encoding

Chinese Journal of Quantum Electronics, Volume. 41, Issue 1, 113(2024)

Quantum K-means algorithm based on parameterized angle encoding

FENG Weijun... GUO Gongde and LIN Song* |Show fewer author(s)

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College of Computer and Cyber Security, Fujian Normal University, Fuzhou 350007, China

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Fig. 1. Quantum circuit diagram from classical data to quantum state

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Fig. 2. Circuit diagram with 3-auxiliary qubits

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Fig. 3. Circuit diagram of multi-quantum phase estimation

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Fig. 4. Probability distribution of two-dimensional data points to two centroids

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Table 1. Comparison between K-means algorithms

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Table 1. Comparison between K-means algorithms

Algorithm	Implementation mode	Time complexity
Classical K-means algorithm	/	$O (K M N)$
The proposed algorithm	Angle encoding	$O ((N + p o l y (l o g_{2} K M)) \sqrt[]{K M})$
Lloyd'algorithm^[19]	QRAM	$O (l o g_{2} K M N)$
Kerenidis'algorithm^[20]	QRAM	$O (\frac{K^{2} N η^{2.5}}{δ^{3}} p o l y (l o g M))$

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Weijun FENG, Gongde GUO, Song LIN. Quantum K-means algorithm based on parameterized angle encoding[J]. Chinese Journal of Quantum Electronics, 2024, 41(1): 113

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Paper Information

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Received: Mar. 29, 2022

Accepted: --

Published Online: Mar. 19, 2024

The Author Email: LIN Song (lins95@fjnu.edu.cn)

DOI:10.3969/j.issn.1007-5461.2024.01.011

Topics

laser devices and laser physics

Lasers and Laser Optics

laser manufacturing

Instrumentation, Measurement and Metrology