This thesis explores pathways to scalable, fault-tolerant quantum computing by focusing on two leading qubit platforms—spin qubits and Majorana qubits—and developing simulation-based methods to speed up their design and optimization. Spin qubits utilize advanced semiconductor fabrication but remain susceptible to decoherence from charge noise and environmental disturbances, while Majorana qubits offer intrinsic topological protection through non-Abelian quasiparticles yet face significant experimental challenges in initialization and braiding. To address these issues, the work introduces numerical modeling techniques and customized optimization frameworks to improve gate designs for spin qubit arrays and Majorana trijunctions, while systematically analyzing the effects of disorder and identifying operational regimes that support stable quantum behavior. ... Read more

Braiding of Majorana states demonstrates their non-Abelian exchange statistics. One implementation of braiding requires control of the pairwise couplings between all Majorana states in a trijunction device. To have adiabaticity, a trijunction device requires the desired pair coupling to be sufficiently large and the undesired couplings to vanish. In this work, we design and simulate a trijunction device in a two-dimensional electron gas with a focus on the normal region that connects three Majorana states. We use an optimisation approach to find the operational regime of the device in a multi-dimensional voltage space. Using the optimization results, we simulate a braiding experiment by adiabatically coupling different pairs of Majorana states without closing the topological gap. We then evaluate the feasibility of braiding in a trijunction device for different shapes and disorder strengths. ... Read more