  While fundamental scientific researchers are eagerly anticipating the
breakthroughs of quantum computing both in theory and technology, the current
quantum computer, i.e. noisy intermediate-scale quantum (NISQ) computer
encounters a bottleneck in how to deal with the noisy situation of the quantum
machine. It is still urgently required to construct more efficient and reliable
benchmarking protocols through which one can assess the noise level of a
quantum circuit that is designed for a quantum computing task. The existing
methods that are mainly constructed based on a sequence of random circuits,
such as randomized benchmarking (RB), have been commonly adopted as the
conventional approach owning to its reasonable resource consumption and
relatively acceptable reliability, compared with the average gate fidelity. To
more deeply understand the performances of the above different
randomized-framed benchmarking protocols, we design special random circuit
sequences to test the performances of the three selected standard
randomized-frame protocols under T1, T2, and coherent errors, which are
regarded to be more practical for a superconductor quantum computer. The
simulations indicate that MRB, DRB, and CRB sequentially overestimate the
average error rate in the presence of T1 and T2 noise, compared with the
conventional circuit's average error. Moreover, these methods exhibit almost
the same level of sensitivity to the coherent error. Furthermore, the DRB loses
its reliability when the strengths of T1 grow. More practically, the simulated
conclusion is verified by running the designed tasks for three protocols on the
Quafu quantum computation cloud platform. We find that MRB produces a more
precise assessment of a quantum circuit conditioned on limited resources.
However, the DRB provides a more stable estimation at a specific precision
while a more resource-consuming.
