1D Braiding Dynamics for Topological Qubits in the Finite-Time Regime

Topological nanowires have become a paradigmatic example for topological qubits. Alongside other topological qubit platforms, these systems are well studied and understood in the adiabatic regime, but to eventually make use of these platforms within a scalable system, we should advance our understanding into the more realistic, finite-time regime. Towards this goal, we first demonstrate here a tight-binding calculation for adiabatic manipulation of edge bound Majorana within Kitaev's chain model, focusing on domain wall control to implement 1D braiding and shuttling. We then relax the adiabatic assumption to compute finite-time dependence for the system to derive quantitative properties of the computational manifold, gate operations, and decoherence. This work supplements the ongoing experimental efforts by providing a more accurate predictive model for nanowire platforms as well as bridging the gap between physical qubit hardware and topological QC algorithms.