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Random features are a central technique for scalable learning algorithms based on kernel methods. A recent work has shown that an algorithm for machine learning by quantum computer, quantum machine learning (QML), can exponentially speed up sampling of optimized random features, even without imposing restrictive assumptions on sparsity and low-rankness of matrices that had limited applicability of conventional QML algorithms; this QML algorithm makes it possible to significantly reduce and provably minimize the required number of features for regression tasks. However, a major interest in the field of QML is how widely the advantages of quantum computation can be exploited, not only in the regression tasks. We here construct a QML algorithm for a classification task accelerated by the optimized random features. We prove that the QML algorithm for sampling optimized random features, combined with stochastic gradient descent (SGD), can achieve state-of-the-art exponential convergence speed of reducing classification error in a classification task under a low-noise condition; at the same time, our algorithm with optimized random features can take advantage of the significant reduction of the required number of features so as to accelerate each iteration in the SGD and evaluation of the classifier obtained from our algorithm. These results discover a promising application of QML to significant acceleration of the leading classification algorithm based on kernel methods, without ruining its applicability to a practical class of data sets and the exponential error-convergence speed.
Kernel methods augmented with random features give scalable algorithms for learning from big data. But it has been computationally hard to sample random features according to a probability distribution that is optimized for the data, so as to minimiz
Although kernel methods are widely used in many learning problems, they have poor scalability to large datasets. To address this problem, sketching and stochastic gradient methods are the most commonly used techniques to derive efficient large-scale
The use of quantum computing for machine learning is among the most exciting prospective applications of quantum technologies. However, machine learning tasks where data is provided can be considerably different than commonly studied computational ta
Quantum computers promise to enhance machine learning for practical applications. Quantum machine learning for real-world data has to handle extensive amounts of high-dimensional data. However, conventional methods for measuring quantum kernels are i
We study generalised linear regression and classification for a synthetically generated dataset encompassing different problems of interest, such as learning with random features, neural networks in the lazy training regime, and the hidden manifold m