  We demonstrate an implementation of the precise test of dimension on the
qubit, using the public IBM quantum computer, using the determinant dimension
witness. The accuracy is below $10^{-3}$ comparing to maximal possible value of
the witness in higher dimension. The test involving minimal independent sets of
preparation and measurement operations (gates) is applied both for specific
configurations and parametric ones. The test is be robust against nonidealities
such as incoherent leakage and erroneous gate execution. Two of the IBM devices
failed the test by more than $5$ standard deviations, which has no simple
explanation.
