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

The traditional approach of characterizing a given quantum gate via quantum process tomography (QPT) requires exponential number of experiments. Therefore, estimating the average fidelity of the quantum gate by QPT is not practical for large-scale systems. In this talk, I will discuss about how to certify a Clifford gate within polynomial complexity using a twirling protocol. In particular, we adopted this method in NMR and certified a 7-qubit quantum Clifford gate with only 1600 experiments (in contrast, QPT requires millions of experiments). This Clifford gate is important as it generates maximal coherence from single coherence, and non-trivial for benchmarking the coherent control in experiment. We show that the average fidelity of this gate is over 87\% after accounting for the decoherence effect, and to date this is the largest experimental gate-characterization. This twirling protocol is efficient and scalable, and can also be extended to other systems straightforwardly.