  An unknown unitary gates, which is secretly chosen from several known ones,
can always be distinguished perfectly. In this paper, we implement such a task
on IBM's quantum processor. More precisely, we experimentally demonstrate the
discrimination of two qubit unitary gates, the identity gate and the
$\frac{2}{3}\pi$-phase shift gate, using two discrimination schemes -- the
parallel scheme and the sequential scheme. We program these two schemes on the
\emph{ibmqx4}, a $5$-qubit superconducting quantum processor via IBM cloud,
with the help of the $QSI$ modules [S. Liu et al.,~arXiv:1710.09500, 2017]. We
report that both discrimination schemes achieve success probabilities at least
85%.
