In recent years, germanium hole spin qubits have become a research hotspot for semiconductor quantum dot quantum computing. Their strong spin-orbit coupling gives rise to an anisotropic exchange interaction. The exchange interaction plays an important role in implementing two-qubit gates for electron/hole spin qubits. Currently, the modeling, control, and optimization of exchange interaction primarily focus on the isotropic type between electron spins. Strategies for making full use of the anisotropic exchange interaction to implement high-fidelity two-qubit gates remain immature. In this thesis, we focus on germanium hole spin qubits and utilize the anisotropic exchange interaction between them to implement two-qubit gates protected against errors by means of composite pulse technique.

Quantum computers hold the potential to revolutionize computation by harnessing the unique properties of qubits. However, qubits are highly susceptible to errors, posing a major challenge in building reliable quantum systems. To address this, the development of quantum error correction codes is essential. The surface code has become a well-known code, using a 2D square grid to encode qubits. However, its high qubit overhead may be improved by alternative codes with more efficient encoding schemes. This thesis focuses on the small stellated dodecahedron code, previously outperformed by the surface code, and proposes a new approach to optimize its performance by developing an algorithm that finds interleaved measurement schedules. The developed algorithm is tested on both the surface code and a code based on the Tetrahemi hexahedron, correctly providing interleaved schedules for both. Applying the algorithm to the small stellated dodecahedron reduces the number of time steps required from 10 to 6, significantly boosting error correction performance. Simulations under a depolarizing noise model confirm the fault tolerance of these new schedules and demonstrate a 2.6x improvement in the code’s pseudo-threshold compared to the original sequential schedule. While the surface code remains more effective at protecting against errors, performing 1.26 times better, the stellated dodecahedron code offers a compelling alternative for near-term research, requiring fewer qubits while maintaining strong performance.