The realization and manipulation of Majorana zero modes have drawn significant attention for their crucial role in enabling topological quantum computation. Conventional approaches to the braiding of Majorana zero modes rely on adiabatic processes. In this work, using a composite 2-Kitaev-chain system accommodating Majorana zero modes as a working example, we propose a nonadiabatic and non-Abelian geometry phase-based protocol to execute operations on these Majorana zero modes. This is possible by locally coupling the edge sites of both quantum chains with an embedded lattice defect, successfully simulating the braiding operation of two Majorana modes in a highly nonadiabatic fashion. To further enhance the robustness against control imperfections, we apply a multiple-pulse composite strategy to our quantum chain setting for second-order protection of the braiding operations. Our proposal can also support the fast and robust realization of the $\pi /8$ gate, an essential ingredient for universal quantum computation. This work hence offers a potential pathway toward the nonadiabatic and fault-tolerant control of Majorana zero modes.

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• Edge states
• Geometric & topological phases
• Quantum control
• Topological superconductors