Majorana braiding in realistic nanowire Y-junctions and tuning forks

Majorana fermions are predicted to arise at the ends of nanowire devices which combine superconductivity, strong spin-orbit coupling, and an external magnetic field. By manipulating networks of these devices with suitable gating, it has been suggested that braiding operations may be performed which act as logic operations, suitable for quantum computation. However, the unavoidable misalignment of the magnetic field in any realistic device geometry has raised questions about the feasibility of such braiding. In this paper, we numerically simulate braiding operations in devices with Y-junction and tuning-fork geometries using an experimentally motivated nanowire model. We study how the static and dynamical features vary with geometric parameters and identify parameter choices that optimize the probability of a successful braid. Notably, we find that there is an optimal Y-junction half-angle (about 20 degrees for our parameter values), which balances two competing mechanisms that reduce the energy gap to excitations. In addition, we find that a tuning-fork geometry has significant advantages over a Y-junction geometry, as it substantially reduces the effect of dynamical phase oscillations that complicate the braiding process. Our results suggest that performing a successful braid is in principle possible with such devices and is within experimental reach.