Quantum Machine Learning

Machine learning techniques are applied for solving a large variety of practical problems. The tasks attacked by machine learning algorithms include classification, regression, pattern recognition, etc. Traditionally, machine learning algorithms are divided into two groups depending on the nature of training data: supervised and unsupervised. Supervised machine learning algorithms take on the input labeled samples and learn how to predict labels for new data points. Unsupervised learning algorithms like the ones for clustering, pattern recognition, on the other hand, take on the input unlabeled data and try to discover the hidden structure in the data. Algorithms of machine learning manipulate large amounts of data represented in a form of arrays of vectors of high dimension. These algorithms become practically intractable for classical computers as the amount of data grows rapidly [4], whereas quantum computing potentially provides an exponential speed up [11]. So far, a large number of quantum machine learning algorithm has been developed, for example, the algorithm for solving systems of linear equations HHL [10] is used for generic classification problems as perceptron or linear regression training, there were developed quantum algorithms for nearest centroid, k-nearest neighbours and support vector machines classsification [2]. In this review we will focus on the supervised classification quantum algorithm of nearest centroid, presented in [11]. Quantum computational model helps to overcome the main bottleneck of the algorithm: calculation of the distances between the vectors in highly dimensional space. Methods of computing distances similar to the one presented in the context of nearest centroid algorithm can be used in many other practical applications, and the first experimental results on implementation of this algorithm on a small-scale quantum photonic computer can be found in [4].