Title: Braiding errors in interacting Majorana quantum wires,
Abstract: Avenues of Majorana bound states (MBSs) have become one of the primary
directions towards a possible realization of topological quantum computation.
For a Y-junction of Kitaev quantum wires, we numerically investigate the
braiding of MBSs while considering the full quasi-particle background. The two
central sources of braiding errors are found to be the fidelity loss due to the
incomplete adiabaticity of the braiding operation as well as the hybridization
of the MBS. The explicit extraction of the braiding phase in the low-energy
Majorana sector from the full many-particle Hilbert space allows us to analyze
the breakdown of the independent-particle picture of Majorana braiding.
Furthermore, we find nearest-neighbor interactions to significantly affect the
braiding performance to the better or worse, depending on the sign and
magnitude of the coupling.