  We show how vortices that support Majorana fermions when placed on a periodic
pinning array can be used for vortex exchange and independent braiding by
performing a series of specific moves with a probe tip. Using these braiding
operations, we demonstrate realizations of a Hadamard and a CNOT gate. We
specifically consider the first matching field at which there is one vortex per
pinning site, and we show that there are two basic dynamic operations, move and
exchange, from which basic braiding operations can be constructed in order to
create specific logic gates. The periodic pinning array permits both control of
the world lines of the vortices and freedom for vortex manipulation using a set
of specific moves of the probe during which the probe tip strength and height
remain unchanged. We measure the robustness of the different moves against
thermal effects and show that the three different operations produce distinct
force signatures on the moving tip.
