量子聚类分析和量子图像识别

发布时间：2018-05-03 17:25

本文选题：量子机器学习 + 量子k-means算法　；参考：《南京信息工程大学》2017年硕士论文

【摘要】：量子计算作为一种新型的计算模式,已成为解决摩尔律失效问题的一个可能的解决方法。随着对量子计算和机器学习的深入研究,量子机器学习也应运而生。本文探讨和研究量子机器学习中的量子聚类算法(量子k-means算法)和量子图像识别。主要研究内容如下:(1)基于经典的k-means算法,提出了一个高效的基于距离最小化原则的量子k-means算法。将经典k-means算法的部分步骤使用量子算法来实现,利用量子叠加态和量子并行计算的特性来实现,与经典的k-means算法相比带来了指数加速。算法中,为了计算待分类点与聚类中心之间距离,通过增加一个辅助粒子构造聚类中心与待分类点的纠缠态,并对辅助粒子进行投影测量,进而依据测量结果计算出两点之间距离。算法的目的是将待分类的点按距离最小原则分到相应的聚类中。(2)提出了比较两幅量子图像相似度的算法,并给出算法的量子线路图。所提出的比较算法,是在不连接图像的基础上,将图像用量子态表示,进行控制交换(c-Swap)操作,再进行量子测量,根据测量结果判断两幅图像的相似度。(3)将所提的量子相似度比较算法应用到量子手势识别中。在经典领域中,手势识别的流程比较复杂。而在量子领域中,无需提取手势的颜色、纹理、特征等步骤,直接可以将手势进行二值化表示,再根据(2)中所提的图像相似度算法来实现手势识别。
[Abstract]:As a new computational model, quantum computing has become a possible solution to the problem of molar law failure. With the further study of quantum computing and machine learning, quantum machine learning has emerged as the times require. Quantum clustering algorithm (quantum k-means algorithm) and quantum image recognition in quantum machine learning are discussed and studied in this paper. The main contents are as follows: (1) based on the classical k-means algorithm, an efficient quantum k-means algorithm based on the principle of distance minimization is proposed. Some steps of classical k-means algorithm are implemented by quantum algorithm and quantum superposition state and quantum parallel computation. Compared with classical k-means algorithm, it brings exponential acceleration. In order to calculate the distance between the points to be classified and the centers of clustering, the entangled states between the centers of clustering and the points to be classified are constructed by adding an auxiliary particle, and the projection measurements of the auxiliary particles are carried out. Then the distance between two points is calculated according to the measurement results. The purpose of the algorithm is to divide the points to be classified into the corresponding cluster according to the principle of minimum distance. (2) an algorithm to compare the similarity between two quantum images is proposed, and the quantum circuit diagram of the algorithm is given. The proposed comparison algorithm is based on the disconnection of the image, the image is represented by quantum state, the control switching c-Swap-operation is carried out, and then the quantum measurement is carried out. The proposed quantum similarity comparison algorithm is applied to quantum gesture recognition. In the classical field, the process of gesture recognition is complicated. In the quantum field, without extracting the color, texture and features of the gesture, the gesture can be directly binary representation, and then the gesture recognition can be realized according to the image similarity algorithm proposed in X2).
【学位授予单位】：南京信息工程大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TP391.41;TP18

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