Randomized benchmarking does not measure average infidelity of gates
Jiaan Qi, Hui Khoon Ng · arXiv (Cornell University) · 2018
Randomized benchmarking (RB) is a popular procedure used to gauge the performance of a set of gates useful for quantum information processing (QIP). Recently, Proctor et al. [Phys. Rev. Lett. 119, 130502 (2017)] demonstrated a practically relevant example where the RB measurements give a number $r$ very different from the actual average gate-set infidelity $\epsilon$, despite past theoretical assurances that the two should be equal. Here, we derive formulas for $\epsilon$, and for $r$ from the RB protocol, in a manner permitting easy comparison of the two. We show that $r eq \epsilon$, i.e., RB does not measure average infidelity, and, in fact, neither one bounds the other. We give several examples, all plausible in real experiments, to illustrate the differences in $\epsilon$ and $r$. Many recent papers on experimental implementations of QIP have claimed the ability to perform high-fidelity gates because they demonstrated small $r$ values using RB. Our analysis shows that such a conclusion cannot be drawn from RB alone.