Error generation and propagation in Majorana-based topological qubits

We investigate dynamical evolution of a topological memory that consists of two p-wave superconducting wires separated by a nontopological junction, focusing on the primary errors (i.e., qubit loss) and secondary errors (bit and phase flip) that arise due to nonadiabaticity. On the question of qubit loss we examine the system's response to both periodic boundary driving and deliberate shuttling of the Majorana bound states. In the former scenario, we show how the frequency-dependent rate of qubit loss is strongly correlated with the local density of states at the edge of wire, a fact that can make systems with a larger gap more susceptible to high-frequency noise. In the second scenario we confirm previous predictions concerning superadiabaticity and critical velocity, but see no evidence that the coordinated movement of edge boundaries reduces qubit loss. Our analysis on secondary bit-flip errors shows that it is necessary that nonadiabaticity occurs in both wires and that interwire tunneling be present for this error channel to be open. We also demonstrate how such processes can be minimized by disordering central regions of both wires. Finally, we identify an error channel for phase-flip errors, which can occur due to mismatches in the energies of states with bulk excitations. In the noninteracting system considered here, this error systematically opposes the expected phase rotation due to finite-size splitting in the qubit subspace.