Precise certification of a qubit space

Abstract: 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.