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Semiconductor double quantum dot hybrid qubits are promising candidates forhigh-fidelity quantum computing. However, their performance is limited bycharge noise, which is ubiquitous in solid-state devices, and phonon-induceddephasing. Here we explore methods for improving the quantum operations of ahybrid qubit, using strong microwave driving to enable gate operations that aremuch faster than decoherence processes. Using numerical simulations and atheoretical method based on a cumulant expansion, we analyze qubit dynamics inthe presence of $1/f$ charge noise, which forms the dominant decoherencemechanism in many solid-state devices. We show that, while strong-drivingeffects and charge noise both reduce the quantum gate fidelity, simplepulse-shaping techniques effectively suppress the strong-driving effects.Moreover, a broad AC sweet spot emerges when the detuning parameter and thetunneling coupling are driven simultaneously. Taking into accountphonon-mediated noise, we find that it should be possible to achieve $X_{\pi}$gates with fidelities higher than $99.9\%$.

High-fidelity single-qubit gates in a strongly driven quantum dot hybrid qubit with $1/f$ charge noise