  Using the properties of quantum superposition, we propose a quantum
classification algorithm to efficiently perform multi-class classification
tasks, where the training data are loaded into parameterized operators which
are applied to the basis of the quantum state in quantum circuit composed by
\emph{sample register} and \emph{label register}, and the parameters of quantum
gates are optimized by a hybrid quantum-classical method, which is composed of
a trainable quantum circuit and a gradient-based classical optimizer. After
several quantum-to-class repetitions, the quantum state is optimal that the
state in \emph{sample register} is the same as that in \emph{label register}.
%A structure of loading data many times is performed as a quantum version of
neural network to improve the expression ability of quantum circuit. For a
classification task of $L$-class, the analysis shows that the space and time
complexity of the quantum circuit are $O(L*logL)$ and $O(logL)$, respectively.
The numerical simulation results of 2-class task and 5-class task show that the
proposed algorithm has a higher classification accuracy, faster convergence and
higher expression ability. The classification accuracy and the speed of
converging can also be improved by increasing the number times of applying
multi-qubit controlled operators on the quantum circuit, especially for
multiple classes classification.
