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Quantum gates in experiment are inherently prone to errors that need to becharacterized before they can be corrected. Full characterization via quantumprocess tomography is impractical and often unnecessary. For most practicalpurposes, it is enough to estimate more general quantities such as the averagefidelity. Here we use a unitary 2-design and twirling protocol for efficientlyestimating the average fidelity of Clifford gates, to certify a 7-qubitentangling gate in a nuclear magnetic resonance quantum processor. Comparedwith more than $10^8$ experiments required by full process tomography, weconducted 1656 experiments to satisfy a statistical confidence level of 99%.The average fidelity of this Clifford gate in experiment is 55.1%, and rises to87.5% if the infidelity due to decoherence is removed. The entire protocol ofcertifying Clifford gates is efficient and scalable, and can easily be extendedto any general quantum information processor with minor modifications.

Experimental Estimation of Average Fidelity of a Clifford Gate on a 7-qubit Quantum Processor