Three Qubit Randomized Benchmarking

TL;DR

This paper demonstrates three-qubit randomized benchmarking on transmon qubits, establishing a scalable fidelity metric and revealing how errors scale with different gate configurations and coherent errors.

Contribution

It introduces three-qubit RB for fixed-frequency transmon qubits and shows how three-qubit errors relate to one- and two-qubit errors, highlighting its uniqueness as a multiqubit metric.

Findings

Measured three-qubit error per Clifford: 0.106 (all-to-all), 0.207 (linear)

Predicted three-qubit errors from one- and two-qubit errors using simultaneous RB

Coherent errors can significantly increase three-qubit errors beyond predictions

Abstract

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.