Optimization of gate operations in quantum dot hybrid qubits formed from Ge holes

Quantum dot hybrid qubits are conventionally formed of three electrons in a double quantum dot, which can be tuned to a spin-like or charge-like regime [1,2]. In Si-based devices, unpredictable valley splittings can be a concern. An interesting, valley-free alternative would be to use hole spins in Ge quantum wells. However, spin-orbit coupling (SOC) is much stronger in this system, with potential consequences for gate operations. Here, we theoretically explore the possibility of SOC causing leakage to states outside the computational subspace during gate operations of a hybrid qubit. We use an effective model involving just the heavy hole states, as appropriate for strained Ge/SiGe heterostructures, yielding a SOC that is cubic in momentum. We find that leakage in this system depends on both the tunnel coupling and the detuning parameters, suggesting the possibility of suppressing leakage via gate optimization. Our results describe a path towards improving the fidelity of multi-hole spin qubits in Ge.

[1] Shi, Z. et al. Phys. Rev. Lett. 108, 140503 (2012).

[2] Kim, D. et al. Nature 511, 70-74 (2014).