Optimized driving of superconducting artificial atoms for improved single-qubit gates

We employ simultaneous shaping of in-phase and out-of-phase resonant microwave drives to reduce single-qubit gate errors arising from the weak anharmonicity of transmon superconducting artificial atoms. To reduce the effect of higher levels present in the transmon spectrum, we apply Gaussian and derivative-of-Gaussian envelopes to the in-phase and out-of-phase quadratures, respectively, and optimize over their relative amplitude. Using randomized benchmarking, we obtain a minimum average error per gate of $0.007\pm 0.005$ using 4-ns-wide pulses, which is limited by decoherence. This simple optimization technique works for multiple transmons coupled to a single microwave resonator in a quantum bus architecture.

Figure 1

(a) Gaussian and derivative pulse shapes applied to the in-phase and quadrature control channels, respectively, for implementing DRAG to first order. (b) Measured $\langle {\sigma }_z\rangle$ on transmon L [semitransparent red (lightly shaded) bars], after applying the indicated pairs of $\pi$ and $\pi /2$ rotations to the ground state. The slash-filled bars correspond to a master-equation simulation of a three-level system with parameters of the sample tested. The gray (darker shaded) bars reflect ideal values. (c) Similarly measured $\langle {\sigma }_z\rangle$ on transmon L but using DRAG pulses with derivative scale factor ${\beta }^{\mathrm{L}}=0.4$ [semitransparent (lightly shaded) bars], also overlaid on the ideal values [gray (darker shaded) bars].

Figure 2

Randomized benchmarking for transmon L with $\sigma =1\hspace{0.5em}\mathrm{ns}$ using (a) Gaussian pulses, and (b) additional Gaussian derivative pulses on the quadrature channel. The scattered gray points are extracted fidelities for 32 RB sequences, truncated at different numbers of gates. A remarkable reduction in the extracted average EPG (black squares) of the benchmarking results is observed going from (a) to (b). The error bars indicate the variance of all the RB sequences and are smaller than the squares in (b).

Figure 3

Comparison of single-qubit gate errors with and without DRAG. EPG for the left qubit extracted from RB for different gate lengths using both Gaussian pulses (red squares) and first-order DRAG pulses (blue dots) down to $\sigma =1\hspace{0.5em}\mathrm{ns}$, the shortest permissible by the arbitrary waveform generator. Excellent overlap of the EPG with theory (black solid line) suggests that the DRAG pulses successfully eliminate the errors due to the presence of higher levels. Using DRAG, we reach EPG down to $0.007$, which is otherwise unattainable on this sample with Gaussian pulses.

Figure 4

Measured two-qubit Pauli sets for state $|1,1\rangle$ with (a) Gaussian pulses and (b) DRAG pulses (${\beta }^{\mathrm{L}}=0.4$, ${\beta }^{\mathrm{R}}=0.25$) applied to the quadrature channels of both transmons L and R. The ideal Pauli set is shown in dark gray.