Exploiting the Dynamics of Majorana Hybridisation

Qubits built out of Majorana-Zero Modes (MZMs) have long been theorised as a potential pathway toward fault-tolerant topological quantum computation. However, almost unavoidable in these processes are Majorana-Majorana wavefunction overlap that arise throughout the process and lead to qubit error, with precise dynamical predictions for the microscopic effects of hybridisation lacking from current literature. This work presents a method to track the dynamical evolution of the Majorana wavefunctions, allowing one to track transitions in the ground-state subspace and calculate time-dependent correlation functions that provide the output of quantum computations. This is compared to exact, time-dependent superconducting simulations utilising the method introduced in [1], to confirm the advantage of this approach to make accurate dynamical predictions without the need for full many-body calculations. We also show how Majorana hybridisation enable arbitrary quantum gates, including the magic-gate.