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arXiv:1307.0471 · Physical Review Letters

Quantum Support Vector Machine for Big Data Classification

Patrick Rebentrost, Masoud Mohseni, Seth Lloyd

Published Sep 25, 2014• 1,951 citations
arXivHTMLPDF

Abstract

Supervised machine learning is the classification of new data based on already classified training examples. In this work, we show that the support vector machine, an optimized binary classifier, can be implemented on a quantum computer, with complexity logarithmic in the size of the vectors and the number of training examples. In cases where classical sampling algorithms require polynomial time, an exponential speedup is obtained. At the core of this quantum big data algorithm is a nonsparse matrix exponentiation technique for efficiently performing a matrix inversion of the training data inner-product (kernel) matrix.

DOI
10.1103/physrevlett.113.130503

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Supervised machine learning is the classification of new data based on already classified training examples. In this work, we show that the support vector machine, an optimized binary classifier, can be implemented on a quantum computer, with complexity logarithmic in the size of the vectors and the number of training examples. In cases where classical sampling algorithms require polynomial time, an exponential speedup is obtained. At the core of this quantum big data algorithm is a nonsparse matrix exponentiation technique for efficiently performing a matrix inversion of the training data inner-product (kernel) matrix.
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The paper presents an influence of machine learning techniques that can be efficiently solved using quantum computer. Machine learning is considered as a core concept of modeling and mining large dimensionality data and visualizes data instances as a vector. Support vector is one of the trending methods that use supervised learning for classifying the data efficiently irrespective of linearity or non-linearity in data. As the quantum computations already proved to be inherently parallel and can become one of the key factors in order to reduce the complexities while dealing with the classical machine learning model. The quantum machine learning takes advantage of parallelism and can explore the number of vectors and their dimensions in logarithmic time, and hence it can achieve the computational speedup. Now, the main contribution of the paper is to discuss quantum fundamental, quantum algorithm and then to review over classical equivalent quantum support vector machine along with their training algorithm and the comparative analysis between algorithmic growths. At last, the paper justifies the quantum support vector as a highly efficient model that gains the computational speedup and also shows the possibility of further improvement.
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Abstract Classical machine learning algorithms seem to be totally incapable of processing tremendous data, while quantum machine learning algorithms could deal with big data unhurriedly and provide exponential acceleration over classical counterparts. In this paper, we propose two quantum support vector machine algorithms for multi classification. One is the quantum version of the directed acyclic graph support vector machine. The other one is to use the Grover search algorithm before measurement, which amplifies the amplitude of the phase storing of the classification result. For k classification, the former provides quadratic reduction in computational complexity when classifying. The latter accelerates the training speed significantly and more importantly, the classification result can be read out with a probability of at least 50% using only one measurement. We conduct numerical simulations on two algorithms, and their classification success rates are 96% and 88.7%, respectively.