Quantum K-means algorithm based on parameterized angle encoding

FENG Weijun; GUO Gongde; LIN Song

doi:10.3969/j.issn.1007-5461.2024.01.011

Journals >Chinese Journal of Quantum Electronics >Volume 41 >Issue 1 >Page 113 > Article

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

Quantum K-means algorithm based on parameterized angle encoding

FENG Weijun, GUO Gongde, and LIN Song^*

Author Affiliations

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

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DOI: 10.3969/j.issn.1007-5461.2024.01.011 Cite this Article

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 Copy Citation Text

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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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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	$O (\frac{K^{2} N η^{2.5}}{δ^{3}} p o l y (l o g M))$

Table 1. Comparison between K-means algorithms

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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