Non-Abelian braiding, as a promising approach for topological quantum computation, is typically based on topologically protected quantum gates. However, existing braiding schemes have primarily focused on arrays constructed from periodic lattices, which provide limited types of quantum gates and lack flexibility in braiding path design. In this work, we propose two structurally distinct X junctions based on a one-dimensional single-particle tight-binding model, and present a braiding protocol that yields a topologically protected $X$ gate by adiabatically moving defects. The two proposed $\mathrm{X}$ junctions are introduced into the Stampfli-type quasicrystal, and each is successfully used to demonstrate non-Abelian braiding. Our braiding scheme allows for multimode braiding and flexible path design, providing a novel approach for designing non-Abelian devices in optical and acoustic platforms.

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• Quantum communication, protocols & technology
• Quantum control
• Quantum protocols
• Quantum simulation
• Quantum state transfer
• Topological quantum computing
• Quasicrystals
• Non-Abelian models