Characterizing Dynamic Majorana Hybridization for Universal Quantum Computing

Qubits built out of Majorana zero modes (MZMs) have long been theorized as a potential pathway toward fault-tolerant topological quantum computation. Almost unavoidable in these processes is Majorana wavefunction overlap, known as hybridization, which arise throughout the process when Majorana modes get close to each other. This breaks the ground state degeneracy, leading to qubit errors in the braiding process. This work presents a simple but precise method to predict qubit errors for dynamic hybridization which varies in space and time. This includes hybridization between four or more MZMs through topological or trivial regions, or both of them. As an illustration, we characterize qubit-errors for an X-gate. We demonstrate how to utilize the hybridization to implement not only arbitrary one-qubit rotations but also a two-qubit controlled variable phase gate, providing a demonstration of universal quantum computing.