  We analyze the results of the test of $\pi/2$ qubit rotations on the public
quantum computer provided by IBM. We measure a single qubit rotated by $\pi/2$
about a random axis, and we accumulate vast statistics of the results. The test
performed on different devices shows systematic deviations from the theoretical
predictions, which appear at the level $10^{-3}$. Some of the differences,
beyond 5 standard deviations, cannot be explained by simple corrections due to
nonlinearities of pulse generations. The magnitude of the deviation is
comparable with the randomized benchmarking of the gate, but we additionally
observe a pronounced parametric dependence. We discuss other possible reasons
of the deviations, including states beyond the single-qubit space. The
deviations have a similar structure for various devices used at different
times, and so they can also serve as a diagnostic tool to eliminate imperfect
gate implementations, and faithful description of the involved physical
systems.
