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We show how vortices that support Majorana fermions when placed on a periodicpinning array can be used for vortex exchange and independent braiding byperforming a series of specific moves with a probe tip. Using these braidingoperations, we demonstrate realizations of a Hadamard and a CNOT gate. Wespecifically consider the first matching field at which there is one vortex perpinning site, and we show that there are two basic dynamic operations, move andexchange, from which basic braiding operations can be constructed in order tocreate specific logic gates. The periodic pinning array permits both control ofthe world lines of the vortices and freedom for vortex manipulation using a setof specific moves of the probe during which the probe tip strength and heightremain unchanged. We measure the robustness of the different moves againstthermal effects and show that the three different operations produce distinctforce signatures on the moving tip.

Braiding Majorana Fermions and Creating Quantum Logic Gates with Vortices on a Periodic Pinning Structure