Simultaneous Randomized Benchmarking

Motivations

Definition of a protocol that quantifies the rate of cross-talk errors arising during the parallel execution of quantum gates.
Evaluation of the correlations in the error rates.

We illustrate the protocol for the case of single-qubit Clifford group simultaneous RB on a two-qubit chip.

The protocol begins with the standard RB protocol performed for each qubit (see Step 1): A single-qubit Clifford RB is executed on one qubit while others are kept idle. The decay parameters \(\alpha_1\) and \(\alpha_2\) are then extracted respectively for qubit 1 and qubit 2.
In a second step, a single-qubit RB is run simultaneously on both qubits, enabling the extraction of three decay parameters (see Step 2): \(\alpha_{1 \vert 2}\), \(\alpha_{2 \vert 1}\) and \(\alpha_{12}\). The parameters \(\alpha_{1 \vert 2}\) and \(\alpha_{2 \vert 1}\) are obtained from measurements of the first and second qubit. The joint decay parameter \(\alpha_{12}\) is retrieved from the measurements of qubit 1 and 2.
The values \(\alpha_{1}\) and \(\alpha_{1 \vert 2}\) (resp. \(\alpha_{2}\) and \(\alpha_{2 \vert 1}\)) can be used to measure the errors added on qubit 1 (resp. 2) due to simultaneous quantum gates operations on qubit 2 (resp. 1).
Potential correlations in the errors are obtained with the value \(\alpha_{12} -\alpha_{1 \vert 2} \alpha_{2 \vert 1}\).

Litterature: [1], [2], [3]

[1]J. M. Gambetta et al., “Characterization of Addressability by Simultaneous Randomized Benchmarking,” Physical Review Letters, vol. 109, no. 24, Dec. 2012, doi: 10.1103/physrevlett.109.240504. [Online]. Available at: http://dx.doi.org/10.1103/PhysRevLett.109.240504
[2]D. C. McKay, S. Sheldon, J. A. Smolin, J. M. Chow, and J. M. Gambetta, “Three-Qubit Randomized Benchmarking,” Physical Review Letters, vol. 122, no. 20, May 2019, doi: 10.1103/physrevlett.122.200502. [Online]. Available at: http://dx.doi.org/10.1103/PhysRevLett.122.200502
[3]D. C. McKay, I. Hincks, E. J. Pritchett, M. Carroll, L. C. G. Govia, and S. T. Merkel, “Benchmarking quantum processor performance at scale,” arXiv preprint arXiv:2311.05933, 2023.