基于并行欧氏距离估计的量子K-median算法
Quantum K-medians Algorithm Using Parallel Euclidean Distance Estimator
摘要：
量子机器学习虽然还处于初始阶段，但与现有的经典方法相比，它已经证明了它有可能加快一些昂贵的机器学习计算。在众多具有挑战性的子程序中，经典的k-中值聚类算法计算高维大数据集之间的距离就是其中之一。为了解决这个问题，本文提出了一个有效的量子k-中位数聚类算法使用强大的量子欧氏估计算法。与经典算法相比，量子k-median算法的速度有指数级的提高，当且仅当输入和输出矢量都是量子态时.在第三方模块QISKit的帮助下，在python中处理所提出的算法实现。实现的量子算法通过云在IBM Quantum模拟器上执行。实验和仿真结果表明，量子距离估计算法可以为其他基于距离的机器学习算法，如k-最近邻分类，支持向量机，层次聚类和k-均值聚类带来好处。这项工作揭示了利用量子理论提供的指数加速的大数据时代的光明未来。
英文摘要：
Quantum machine learning, though in its initial stage, has demonstrated its potential to speed up some of the costly machine learning calculations when compared to the existing classical approaches. Among the challenging subroutines, computing distance between with the large and high-dimensional data sets by the classical k-medians clustering algorithm is one of them. To tackle this challenge, this paper proposes an efficient quantum k-medians clustering algorithm using the powerful quantum Euclidean estimator algorithm. The proposed quantum k-medians algorithm has provided an exponential speed up as compared to the classical version of it. If and only if we allow the input and the output vectors to be quantum states. The proposed algorithm implementation handled in python with the help of third-party module known as QISKit. The implemented quantum algorithm was executed on the IBM Quantum simulators through cloud. The results from the experiment and simulation suggest that quantum distance estimator algorithms could give benefits for other distance-based machine learning algorithms like k-nearest neighbor classification, support vector machine, hierarchical clustering and k-means clustering. This work sheds light on the bright future of the age of big data making use of exponential speed up provided by quantum theory.
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