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While fundamental scientific researchers are eagerly anticipating thebreakthroughs of quantum computing both in theory and technology, the currentquantum computer, i.e. noisy intermediate-scale quantum (NISQ) computerencounters a bottleneck in how to deal with the noisy situation of the quantummachine. It is still urgently required to construct more efficient and reliablebenchmarking protocols through which one can assess the noise level of aquantum circuit that is designed for a quantum computing task. The existingmethods that are mainly constructed based on a sequence of random circuits,such as randomized benchmarking (RB), have been commonly adopted as theconventional approach owning to its reasonable resource consumption andrelatively acceptable reliability, compared with the average gate fidelity. Tomore deeply understand the performances of the above differentrandomized-framed benchmarking protocols, we design special random circuitsequences to test the performances of the three selected standardrandomized-frame protocols under T1, T2, and coherent errors, which areregarded to be more practical for a superconductor quantum computer. Thesimulations indicate that MRB, DRB, and CRB sequentially overestimate theaverage error rate in the presence of T1 and T2 noise, compared with theconventional circuit's average error. Moreover, these methods exhibit almostthe same level of sensitivity to the coherent error. Furthermore, the DRB losesits reliability when the strengths of T1 grow. More practically, the simulatedconclusion is verified by running the designed tasks for three protocols on theQuafu quantum computation cloud platform. We find that MRB produces a moreprecise assessment of a quantum circuit conditioned on limited resources.However, the DRB provides a more stable estimation at a specific precisionwhile a more resource-consuming.

Comparisons among the Performances of Randomized-framed Benchmarking Protocols under T1, T2 and Coherent Error Models