量子机器学习算法综述

A Survey on Quantum Machine Learning

机器学习在过去十几年里不断发展,并对其他领域产生了深远的影响.近几年,研究人员发现结合量子计算特性的新型机器学习算法可实现对传统算法的加速,该类成果引起了广泛的关注和研究.因此,文中对近十年的量子机器学习算法进行总结、梳理.首先,介绍了量子计算和机器学习的基本概念;其次,从四个方面分别介绍了量子机器学习,分别是量子无监督聚类算法、量子有监督分类算法、量子降维算法、量子深度学习;同时,对比分析量子机器学习算法与传统机器学习算法的区别和联系;最后,总结该领域存在的问题及挑战,并对量子机器学习未来的工作进行展望.

With tremendous development of classical machine learning in past decades, it has influenced on many different fields as an essential part of data science. Recent years, as an innovative type of machine learning algorithms, quantum machine learning plays high parallel performance based on quantum mechanics. Consequently, it speeds up some of conventional algorithms. Researchers in quantum machine learning focus on improving performance of classical machine learning through quantum computation and exploring the possibility of combination of machine learning with quantum mechanics, and presenting some new algorithms. The framework of quantum machine learning mainly contains three steps.. （1） Load and input classical data. It is converting classical information into quantum information. Making full use of high performance of quantum computation, it is necessary to encode classical data to quantum data according to quantum representation. （2） Construct series of unitary operators and use them to process quantum data. The basic principle of quantum computation is that all the operations must follow the unitary characteristics. Thereby, it is not possible to revise all classicai algorithms to quantum environment, and not all the quantum algorithms can provide exponential speed-up. （3） Read and output the learning result. After the first two steps, the quantum machine learning results are quantum states. In order to read and output the useful learning result, it needs some necessary measurements to extract relevant information. There are three kinds of research in this field. （1） Use quantum computing accelerates the costly part of traditional algorithm. This work is the hybrid of classical algorithm and quantum parts. There is no change of the main idea of learning algorithm. But complex parts are running on quantum devices, and it makes full use of quantum computing to speed up counterparts. （2） Borrow the physics concept to propose new algorithms. It is based on the mathematical framework of quantum mechanics. And researchers develop more efficient methods to solve optimization problem. （3） Use machine learning methods to solve some physics issues, such as quantum tomography by using compress sensing. With the power of machine learning, researchers can explore quantum world from another perspective, vice versa. Quantum machine learning solves classical data mining and data analysis problems from another perspective. There are some difficulties in building general quantum computer, researchers still make solid progress. With the development of quantum techniques, practical quantum machine learning algorithms will increasingly be presented. Therefore, some typical algorithms of quantum machine learning are surveyed in this paper. Firstly, it introduces the fundamental concepts of quantum computation and classical machine learning, including quantum states, quantum gate, and measurement. Secondly, it summarizes the quantum machine learning algorithms from four aspects including quantum unsupervised clustering algorithm, quantum supervised classification algorithm, quantum dimension reduction algorithm, quantum deep learning. It collects some typical algorithms for every part. Meanwhile, it analyzes and makes a comparison of computational complexity between classical machine learning and quantum machine learning. Finally, it reconfirms the problems, challenges and future research works for quantum machine learning along with an insight of quantum computation for big data.