Superconducting Qubit Gates Robust to Parameter Fluctuations

Abstract

State-of-the-art single-qubit gates on superconducting transmon qubits can achieve the fidelities required for error-corrected computations. However, parameter fluctuations due to qubit instabilities, environmental changes, and control inaccuracies make it difficult to maintain this performance. To mitigate the effects of these parameter variations, we numerically derive gates robust to amplitude and frequency errors using gradient ascent pulse engineering (GRAPE). We analyze how fluctuations in qubit frequency, drive amplitude, and coherence affect gate performance over time. The robust pulses suppress coherent errors from drive amplitude drifts over 15 times more than a Gaussian pulse with derivative removal by adiabatic gate (DRAG) corrections. Furthermore, the robust gates, originally designed to compensate for quasi-static errors, also demonstrate resilience to stochastic, time-dependent noise, which is reflected in the dephasing time. They suppress added errors during increases in dephasing by up to 1.7 times more than DRAG.

Figures (8)

• Figure 1: Pulse envelopes for (a) FROG and (b) AROG. The pulses are given by Eq. \ref{['eq:Wright-FourierPulse']}. Randomized benchmarking sequence error $1 - F_\text{seq}$ as a function of frequency error $\delta$ and amplitude error $\gamma$ for the (c) DRAG, (d) FROG, and (e) AROG gates. Simulations of the three gates performed using Eq. \ref{['eq:Wright-Hamiltonian']} are shown in (f)-(h) for comparison. While the colourbar shows sequence error, the contour lines correspond to gate errors $\mathcal{E}_g = 5\times 10^{-3}$ and $\mathcal{E}_g = 1\times 10^{-2}$, estimated from the sequence error using Eq. \ref{['eq:Wright-ORBIT']}. The yellow line and box indicate the range of errors over which FROG and AROG are optimized. The arrows indicate linecuts at zero amplitude error and at zero frequency error, with the corresponding line plots shown in Fig. \ref{['fig:linecuts']}.
• Figure 2: Randomized benchmarking sequence error $1 - F_\text{seq}$ for (a) amplitude errors $\gamma$ and (b) frequency errors $\delta$ for the DRAG, FROG, and AROG gates. Each panel shows a line cut from the 2D plots shown in Fig. \ref{['fig:landscapes']}, along the directions indicated by the grey arrows. The error bars reflect the standard deviation across different randomizations The data are fitted with Gaussian functions. The horizontal line indicates a gate error $\mathcal{E}_g = 10^{-2}$, estimated from the sequence fidelity using Eq. \ref{['eq:Wright-ORBIT']}.
• Figure 3: (a) Gate error $\mathcal{E}_g$ for the DRAG, FROG, and AROG gates extracted from RB experiments for 10 hours each day for 11 days. RB curves for (b) day 6 and (c) day 10 are connected by lines to time points of interest in (a). The error bars at each sequence length $N_C$ reflect the standard deviation across different randomizations, and the insets show the mean standard deviation $\langle \sigma \rangle_g$ over all sequence lengths.
• Figure 4: (a) Amplitude error $\gamma$ for an $X_{\pi/2}$ gate extracted from error amplification experiments and (b) internal temperature for the device used to generate the drive signals, measured independently for 10 hours each day for 11 days.
• Figure 5: (a) Qubit frequency extracted from Ramsey experiments for 10 hours each day in an 11 day period. The two distinct frequency regions indicate the even (blue circle) and odd (red triangle) parity states of the qubit.