  We develop an efficient method for certifying single-qubit quantum gates in a
black-box scenario, assuming only the dimension of the quantum system is known.
The method is based on testing the outcomes of exact quantum computations on a
single qubit, with no auxiliary systems required. We prove that the method's
sample complexity grows as $\mathrm{O}(\varepsilon^{-1})$ with respect to the
average gate infidelity $\varepsilon$ for the certification of a relevant
single-qubit gate, which experimentally corresponds to a $\pi/2$-pulse.
Furthermore, we show that the proposed method can be used to certify a gate set
universal for single-qubit quantum computation. Our approach takes a first step
in bridging the gap between strong notions of certification from self-testing
and practically highly relevant approaches from quantum system
characterization.
