  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 when classical sampling algorithms require
polynomial time, an exponential speed-up is obtained. At the core of this
quantum big data algorithm is a non-sparse matrix exponentiation technique for
efficiently performing a matrix inversion of the training data inner-product
(kernel) matrix.
