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

TL;DR

This paper compares the performance of three randomized benchmarking protocols under T1, T2, and coherent errors, revealing their overestimation tendencies and reliability issues, with practical validation on a quantum cloud platform.

Contribution

It provides a comparative analysis of MRB, DRB, and CRB protocols under realistic error models, highlighting their strengths and limitations in noisy intermediate-scale quantum computers.

Findings

MRB overestimates error rates more accurately with limited resources

DRB offers stable estimates but is more resource-intensive

All protocols show similar sensitivity to coherent errors

Abstract

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.