Hole-based spin qubits in strained planar germanium quantum wells have received considerable attention due to their favorable properties and remarkable experimental progress. The sizeable spin-orbit interaction in this structure allows for efficient qubit operations with electric fields. However, it also couples the qubit to electrical noise. In this work, we perform simulations of a heterostructure hosting these hole spin qubits. We solve the effective mass equations for a realistic heterostructure, provide a set of analytical basis wavefunctions, and compute the effective g-factor of the heavy-hole ground state. Our investigations reveal a strong impact of highly excited light-hole states located outside the quantum well on the g-factor. We find that sweet spots, points of operations that are least susceptible to charge noise, for out-of-plane magnetic fields are shifted to impractically large electric fields. However, for magnetic fields close to in-plane alignment, partial sweet spots at low electric fields are recovered. Furthermore, sweet spots with respect to multiple fluctuating charge traps can be found under certain circumstances for different magnetic field alignments. This work will be helpful in understanding and improving the coherence of germanium hole spin qubits.

应变平面锗量子阱中的空穴自旋量子比特因其良好的特性和显着的实验进展而受到了相当大的关注。这种结构中相当大的自旋-轨道相互作用允许对电场进行高效的量子比特操作。但是，它还会将量子比特耦合到电噪声。在这项工作中，我们对托管这些空穴自旋量子比特的异质结构进行了模拟。我们求解了真实异质结构的有效质量方程，提供了一组解析基波函数，并计算了重空穴基态的有效 g 因子。我们的研究揭示了位于量子阱外的高激发轻空态对 g 因子的强烈影响。我们发现，面外磁场的最佳点，即最不容易受到电荷噪声影响的操作点被转移到不切实际的大电场。然而，对于接近面内对准的磁场，可以恢复低电场下的部分甜蜜点。此外，在某些情况下，对于不同的磁场对准，可以找到多个波动电荷陷阱的最佳位置。这项工作将有助于理解和改进锗空穴自旋量子比特的相干性。