Quantum Algorithm For K-Nearest Neighbors Classification Based On The Tensor Network Method

Quantum machine learning is an interdisciplinary subject produced by applying the basic characteristics of quantum computing to machine learning.Applying acceleration algorithms such as the principle of superposition of quantum states and quantum parallel algorithms to machine learning,it can be used to solve the difficulties of the current rapid increase in the amount of data in the era of big data and the slow training process of traditional machine learning,thereby realizing the acceleration of traditional classical algorithms.Research in this field can not only promote the rapid development of machine learning,improve the efficiency and accuracy of data mining and analysis,but also promote the application of quantum algorithms in classical algorithms.The current research in this field is not only to propose quantum machine learning algorithms such as quantum unsupervised clustering algorithms and quantum supervised classification algorithms,but also some algorithms have been implemented by algorithms,and have also been applied to many research fields such as image recognition.The k-nearest neighbor algorithm is a relatively simple and widely used supervised classification learning algorithm.In view of its large amount of calculation and low computational efficiency,researchers use the basic characteristics of quantum computing and quantum acceleration algorithms to propose the quantum k-nearest neighbor algorithm.By analyzing the existing quantum k-nearest neighbor algorithm,it is known that most of the algorithms are obscure and difficult to understand,and the readability is not strong.Based on this,we propose a quantum k-nearest neighbor algorithm,which uses Oracle operations to store all classical data in a quantum state,realizes distance calculation through quantum operations,and finally obtains the nearest k values,and achieves classification through voting.The quantum k nearest neighbor algorithm is superior to the classic k nearest neighbor algorithm in terms of classification efficiency and accuracy.At the same time,the categorical Tensor Network state graph data structure is used to describe the quantum k-nearest neighbor algorithm.Compared with the quantum k-nearest neighbor algorithm described by the quantum circuit,it can make the complex core structure of the algorithm more intuitive,clear and readable,while maintaining computational efficiency.