High-Fidelity Single-Qubit Gates for Two-Electron Spin Qubits in GaAs

Single-qubit operations on singlet-triplet qubits in GaAs double quantum dots have not yet reached the fidelities required for fault-tolerant quantum information processing. Considering experimentally important constraints and using measured noise spectra, we numerically minimize the effect of decoherence (including high-frequency $1/f$-like noise) and show, theoretically, that quantum gates with fidelities higher than 99.9% are achievable. We also present a self-consistent tuning protocol which should allow the elimination of individual systematic gate errors directly in an experiment.

Figure 1

Left: energy diagram of the computational subspace (black) as a function of $\epsilon$. The transfer function $J(\epsilon )$ is nonlinear and modeled as $J(\epsilon )=J_0\exp (\epsilon /{\epsilon }_0)$. Right: Bloch sphere convention.

Figure 2

(a) $\pi /2_x$ gate with $\mathcal{I}=1-\mathcal{F}=1.5\times {10}^{-3}$ (b) $\pi /2_y$ gate with $\mathcal{I}=1.6\times {10}^{-3}$. Rectangular $J$ pulses are shown in green, black lines show $J(t)$ when accounting for finite rise times, and $\mathrm{\Delta }{B}_z$ is shown in blue. The corresponding Bloch sphere trajectories for both pulses are plotted for selected initial states (green dot).

Figure 3

Infidelities of $\pi /2_x$ gates. (a) Best solutions for different number of pure $\mathrm{\Delta }{B}_z$ rotations and number of $\epsilon$ pulses. (b) Maximum deterioration of the infidelity (only considering the contributions from noise) for model errors in $J_0$, ${\epsilon }_0$, and ${\tau }_{\text{rise}}$ as large as 20%.

Figure 4

(a) The self-consistent tuning protocol converges even for bad initial infidelities ${\mathcal{I}}_s$. (b) The infidelity from noise ${\mathcal{I}}_n$ of the final calibrated gates (dots) is on average close to ${\mathcal{I}}_n$ of the perfect gates (dashed lines), and sometimes better because small systematic errors are now allowed. The error bars show the 10th and 90th percentile of the distribution of ${\mathcal{I}}_n$ over 100 runs per bin for different starting gates.