量子原型聚类  

Quantum Prototype Clustering

作　　者：刘翔 祝静[1] 仲国强 顾永建[2] 崔丽媛 LIU Xiang;ZHU Jing;ZHONG Guoqiang;GU Yongjian;CUI Liyuan(College of Computer Science and Technology,Ocean University of China,Qingdao,Shandong 266100,China;College of Physics and Optoelectronic Engineering,Ocean University of China,Qingdao,Shandong 266100,China;Innovation Center,Ocean University of China,Qingdao,Shandong 266100,China)

机构地区：[1]中国海洋大学计算机科学与技术学院,山东青岛266100 [2]中国海洋大学物理与光电工程学院,山东青岛266100 [3]中国海洋大学创新教育实践中心,山东青岛266100

出　　处：《计算机科学》2023年第8期27-36,共10页Computer Science

基　　金：国家重点研发计划(2018AAA0100400);山东省自然科学基金(ZR2020MF131);山东省重大基础研究项目(ZR2021ZD19);青岛市科技计划项目(21-1-4-ny-19-nsh)。

摘　　要：经典机器学习算法的量子化重构是量子机器学习领域的一个重要研究方向。聚类作为一类在机器学习领域被广泛应用的算法,其量子化重构也拥有较高的研究价值。目前的量子机器学习算法大多存在复现难度大、难以与经典算法形成直观对比等问题。为解决这些问题,提出了一种量子原型聚类算法(Quantum Prototype Clustering,QPC),该算法可以很方便地在现有的通用性量子计算设备上部署。该方法首先结合单量子位旋转特性,寻找信息损失最小的特征映射方式,使用双维度特征数据制造单量子位旋转;然后,基于多量子位纠缠及纠缠系统坍缩的特性,设计了一种用于制造特定量子纠缠系统和测量纠缠系统坍缩结果的量子线路。根据纠缠系统中受控量子位旋转角和纠缠系统坍缩结果的关系,并结合闵可夫斯基距离的定义,推导了一种用于评估输入样本相似性的量子距离。该量子距离测量模块与经典计算机中的距离计算模块具有相同的输入输出形式,可以不加修改地替换掉原型聚类中的闵可夫斯基距离计算,从而将经典的原型聚类算法重构为QPC。在来自kaggle和scikit-learn的多组公开数据集上进行的多次重复实验表明,在平均样本中心距等评价指标上,QPC与经典的原型聚类算法无明显差别。Quantitative reconstruction of classical machine learning algorithms is one of the significant research directions in the field of quantum machine learning.The quantitative implementation of clustering algorithm,which has been widely used in the machine learning area,is worth studying.Most of the current quantum machine learning algorithms suffer from the difficulty of reproduction and the difficulty of forming direct comparisons with classical algorithms.To address these problems,this paper proposes the quantum prototype clustering algorithm that can be easily deployed on existing general-purpose quantum computing devices.Combining the rotation property of single quantum bit(qubit),and finding the feature mapping method with minimal information loss,the single qubit rotation is created using two-dimensional feature data.Then,based on the properties of multi-qubit entanglement and the collapse of the entangled system,a quantum circuit is designed for generating a specific quantum entangled system and measuring the collapsed result of entangled system.Based on the relationship between the rotation angle of controlled qubits in the entangled system and the collapse result of the entangled system,and combined with the definition of Minkowski distance,a quantum distance for evaluating the similarity of input samples is then derived.Both the quantum distance calculation module and its counterpart in classic computer have the same forms of input and output,so that the latter can be replaced by the former without modification,hence the prototype clustering algorithm is quantitatively reconstructed into QPC.Several replicated experiments on multiple publicly available datasets from kaggle and scikit-learn show that the QPC performs similarly to classic prototype clustering algorithm in terms of many evaluation metrics,such as the mean sample-centroid distance.

关 键 词：量子计算 量子机器学习 聚类算法 原型聚类 

分 类 号：TP181[自动化与计算机技术—控制理论与控制工程]