  In this paper, we have discussed a quantum approach for the all-pair
multiclass classification problem. We have shown that the multiclass support
vector machine for big data classification with a quantum all-pair approach can
be implemented in logarithm runtime complexity on a quantum computer. In an
all-pair approach, there is one binary classification problem for each pair of
classes, and so there are k (k-1)/2 classifiers for a k-class problem. As
compared to the classical multiclass support vector machine that can be
implemented with polynomial run time complexity, our approach exhibits
exponential speed up in the quantum version. The quantum all-pair algorithm can
be used with other classification algorithms, and a speed up gain can be
achieved as compared to their classical counterparts.
