Precise certification of a qubit space

TL;DR

This paper demonstrates a precise method for testing the dimension of a qubit using IBM quantum computers, achieving high accuracy and robustness against nonidealities, and reveals some devices fail the test unexpectedly.

Contribution

It introduces a precise dimension test for qubits using the determinant dimension witness on IBM quantum computers, with robustness against common errors.

Findings

Achieved accuracy below 10^{-3} in dimension testing.

Two IBM devices failed the test significantly, with no clear explanation.

Test is robust against incoherent leakage and gate errors.

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.