Quantum Support Vector Machine for Big Data Classification Patrick RebentrostMasoud Mohseniand Seth Lloyd Research Laboratory of Electronics,Massachusetts Institte of Technology,Cambridge,Massachusetts 02139,USA Google Research,Venice,California 90291,USA Department of Mechanical Engineering,Massachusetts Institte of Technology,Cambridge,Massachusetts 02139,USA (Received 12 February 2014;published 25 September 2014) 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