  The identification of an unknown quantum gate is a significant issue in
quantum technology. In this paper, we propose a quantum gate identification
method within the framework of quantum process tomography. In this method, a
series of pure states are inputted to the gate and then a fast state tomography
on the output states is performed and the data are used to reconstruct the
quantum gate. Our algorithm has computational complexity $O(d^3)$ with the
system dimension $d$. The algorithm is compared with maximum likelihood
estimation method for the running time, which shows the efficiency advantage of
our method. An error upper bound is established for the identification
algorithm and the robustness of the algorithm against the purity of input
states is also tested. We perform quantum optical experiment on single-qubit
Hadamard gate to verify the effectiveness of the identification algorithm.
