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Quantum k-means algorithm based on Manhattan distance

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Abstract

Traditional k-means algorithm measures the Euclidean distance between any two data points, but it is not applicable in many scenarios, such as the path information between two cities, or when there are some obstacles between two data points. To solve the problems, we propose a quantum k-means algorithm based on Manhattan distance (QKMM). The main two steps of the QKMM algorithm are calculating the distance between each training vector and k cluster centroids, and choosing the closest cluster centroid. The quantum circuit is designed, and the time complexity is \(O(\log (Nd) + 2n +\sqrt{k})\), where N is number of training vectors, d is number of features for each training vector, n is number of bits for each feature, and k is the number of clustering classes. Different from other quantum k-means algorithms, our algorithm has wide applications and reduces the complexity. Compared with classical k-means algorithm, our algorithm reaches quadratic speedup.

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Acknowledgements

This work is supported by the Fundamental Research Funds for the Central Universities (No. 21620433) and Guangxi Key Laboratory of Cryptography and Information Security (No. GCIS201922).

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Authors and Affiliations

  1. College of Cyber Security, Jinan University, Guangzhou, 510632, China

    Zhihao Wu

  2. College of Information Science and Technology, Jinan University, Guangzhou, 510632, China

    Tingting Song & Yanbing Zhang

  3. Guangxi Key Laboratory of Cryptography and Information Security, Guilin, 541004, China

    Tingting Song

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  1. Zhihao Wu
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  2. Tingting Song
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  3. Yanbing Zhang
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Correspondence to Tingting Song.

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Wu, Z., Song, T. & Zhang, Y. Quantum k-means algorithm based on Manhattan distance. Quantum Inf Process 21, 19 (2022). https://doi.org/10.1007/s11128-021-03384-7

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