He Yi; Zheng Kou-Quan; Jing Feng; Zhang Yi-Jun; Wang Xun; Liu Ying; Zhao Le

doi:10.7498/aps.73.20241265

Abstract

The paper proposes a quantum enhanced solution method based on quantum K-means for platform clustering and grouping in joint operations campaigns. The method first calculates the number of categories for platform clustering based on the determined number of task clusters, and sets the number of clustering categories in the classical K-means algorithm. By using the location information of the tasks, the clustering center points are calculated and derived. Secondly, the Euclidean distance is used as an indicator to measure the distance between the platform data and each cluster center point. The platform data are quantized and transformed into their corresponding quantum state representations. According to theoretical derivation, the Euclidean distance solution is transformed into the quantum state inner product solution. By designing and constructing a universal quantum state inner product solution quantum circuit, the Euclidean distance solution is completed. Then, based on the sum of squared errors of the clustering dataset, the corresponding quantum circuits are constructed through calculation and deduction. The experimental results show that compared with the classical K-means algorithm, the proposed method not only effectively solves the platform clustering and grouping problem on such action scales, but also significantly reduces the time and space complexity of the algorithm.

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Corresponding author: Zhang Yi-Jun, zhangyijun_gfkjdx@163.com

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数据集	样本数	特征维度数	类别数
Haberman	306	3	2
Iris	150	4	3
Diabetes	768	8	2
Wine	178	13	3

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算法1. 基于QK-means的量子增强求解方法的伪代码
输入: 输入数据集S(N, M, K), 其中N表示数据集样本数量, M表示数据样本维度, K表示数据分类个数. 初始化量子软件开发环境与量子云平台
输出: K个聚类分簇以及每个分簇所包含的数据样本
初始化量子软件开发环境${Q_r}$与量子比特数量
1) 根据输入数据集分类个数确定聚类中心数为K
2) 结合公共数据集实际情况, 根据3.1节中所述选取聚类中心点的方法, 将每个分簇数据集合的平均值作为初始聚类中心点位置
3) 对数据样本和聚类中心点进行量子化, 并给SSE赋一个较大值
4) while SSE值$ \geqslant $阈值 do
5) 通过基于QK-means的量子线路制备量子态, 计算数据样本与各聚类中心点之间的欧氏距离$D\left( {{x_i}, {c_k}} \right)$
6) 根据$D\left( {{x_i}, {c_k}} \right)$, 当$D\left( {{x_i}, {c_k}} \right)$取到$\mathop {\min }\limits_{i, k} D\left( {{x_i}, {c_k}} \right)$时, 将${x_i} \to {C_k}$
7) 计算每个${N_k}$, 并求该聚类分簇的平均值${c'_k} = \dfrac1{{{N_k}}}{{\displaystyle\sum\limits_{{x_i} \in {C_k}} {{x_i}} }}$
8) 通过${c'_k}$更新聚类中心位置
9) 求解整个聚类数据集的残差平方和${\text{SSE}} = {\displaystyle\sum\limits_{k = 1}^K {\displaystyle\sum\limits_{{x_i} \in {C_k}} {\left\| {D\left( {{x_i}, {c_k}} \right)} \right\|} } ^2}$
10) end while
11) 输出每个${C_k}$

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Vol. 73, Issue 23 - 2024-12-05

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