As quantum circuits increase in size, it is critical to establish scalable multiqubit fidelity metrics. Here we investigate three-qubit randomized benchmarking (RB) with fixed-frequency transmon qubits coupled to a common bus with pairwise microwave-activated interactions (cross-resonance). We measure, for the first time, a three-qubit error per Clifford of 0.106 for all-to-all gate connectivity and 0.207 for linear gate connectivity. Furthermore, by introducing mixed dimensionality simultaneous RB --- simultaneous one- and two-qubit RB --- we show that the three-qubit errors can be predicted from the one- and two-qubit errors. However, by introducing certain coherent errors to the gates we can increase the three-qubit error to 0.302, an increase that is not predicted by a proportionate increase in the one- and two-qubit errors from simultaneous RB. This demonstrates three-qubit RB as a unique multiqubit metric.
@article{arxiv.1712.06550,
title = {Three Qubit Randomized Benchmarking},
author = {David C. McKay and Sarah Sheldon and John A. Smolin and Jerry M. Chow and Jay M. Gambetta},
journal= {arXiv preprint arXiv:1712.06550},
year = {2019}
}
Comments
6 pages, 2 figures V2: Fixed an error in Eqn. 1 of V1 and added supplementary information