We demonstrate the successful simulation of $\sqrt{Z}$-, $\sqrt{X}$-, and $X$-quantum gates using Majorana zero modes (MZMs) that emerge in magnetic vortices located in topological superconductors. We compute the transition probabilities and geometric phase differences accounting for the full many-body dynamics and show that qubit states can be read out by fusing the vortex core MZMs and measuring the resulting charge density. We visualize the gate processes using the time- and energy-dependent nonequilibrium local density of states. Our results demonstrate the feasibility of employing vortex core MZMs for the realization of fault-tolerant topological quantum computing.

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• Magnetic vortices
• Majorana bound states
• Vortices in superconductors
• Topological superconductors
• Bogoliubov-de Gennes equations