Three-Qubit Randomized Benchmarking

As quantum circuits increase in size, it is critical to establish scalable multiqubit fidelity metrics. Here we investigate, for the first time, three-qubit randomized benchmarking (RB) on a quantum device consisting of three fixed-frequency transmon qubits with pairwise microwave-activated interactions (cross-resonance). We measure 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 the importance of multiqubit metrics, such as three-qubit RB, on evaluating overall device performance.

Figure 1

(a) Schematic of the experimental setup and connectivity of the cnot $2Q$ gates (control $\to$ target). (b) $1Q$ simultaneous RB $\{[0],[1],[2]\}$, (c) $2Q\text{−}1Q$ simultaneous RB $\{[0,1],[2]\}$, and (c) $3Q$ RB $\{[0,1,2]\}$. Under each is a sample (b) $1Q$, (c) $2Q$, and (d) $3Q$ Clifford gate.

Figure 2

Qubit 0 experimental data from different RB sequences for calibration $A$. Black lines are exponential fits to the data, and the gray points are from the individual trials. Red squares (blue diamonds) are the averages over these trials for the light gray (dark gray) points. (a) $1Q$ RB from simultaneous $1Q$ (red squares) and $2Q\text{−}1Q$ RB (blue diamonds). (b) $2Q$ RB for the 01 pair performed in isolation (red square) and simultaneously with $1Q$ RB on Q2 (blue diamonds). (c) $3Q$ RB for all-to-all connectivity (red squares) and for limited (no ${\mathrm{CNOT}}_{12}$) connectivity (blue squares). The decay parameters from these fits are given in Ref. [43].