Cancelling second order frequency shifts in Ge hole spin qubits via bichromatic control

Abstract: Germanium quantum dot hole spin qubits are compatible with fully electrical control and are progressing toward multi-qubit operations. However, their coherence is limited by charge noise and driving field induced frequency shifts, and the resulting ensemble $1/f$ dephasing. Here we theoretically demonstrate that a bichromatic driving scheme cancels the second order frequency shift from the control field without sacrificing the electric dipole spin resonance (EDSR) rate, and without additional gate design or microwave engineering. Based on this property, we further demonstrate that bichromatic control creates a wide operating window that reduces sensitivity to quasi-static charge noise and thus enhances single qubit gate fidelity. This method provides a low-power route to a stabler frequency operation in germanium hole spin qubits and is readily transferable to other semiconductor spin qubit platforms.