Quantum Support Vector Machine for Multi Classification

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 counterpart. In this paper, we propose two quantum support vector machine algorithms for multi classification. One is the quantum version of 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 stored in 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.