Randomized benchmarking (RB) is a widely used tool in quantum information science to determine qubit fidelity and to characterize individual qubit gates. It is also an excellent example of a quantum experiment with advanced requirements on the control hardware and software. For an RB experiment, we apply random sequences of unitary gates to the qubit. The sequences are chosen such that the final gate always inverts all the preceding ones. This means that in the ideal case, where all the gates are perfect and there is no decoherence, the initial state of the qubit remains unchanged after we have applied all gates. Gate errors and decoherence will however lead to changes in the final qubit state and will have more influence for longer sequences of gates. We perform the RB experiment by varying the number of random gates M, where we choose the unitary gates from the Clifford group. For each sequence length M, we also choose k different random sequences. Finally, for each random sequence we apply the final recovery gate, which in the ideal case would take the qubit back to its initial state. We experimentally determine the probability of finding the qubit in its initial state and plot the average of the return probability for all k random sequences as a function of the sequence length M. An exponential fit to the return probability as a function of the sequence length M provides a general measure of qubit fidelity, which can be understood as an estimate of the average error rate per qubit operation. Benchmarking qubits in this way is largely independent of state-preparation and measurement errors, making RB the preferred method for benchmarking individual qubits for many research groups worldwide.
