Topological edge states are robust against symmetry-preserving perturbations and noise, making them promising for quantum information and computation, particularly in topological quantum computation through braiding operations of Majorana quasiparticles. Realizing these applications requires fast and high-fidelity dynamic control of edge states. In this work, we theoretically propose a high-fidelity method for transferring topological edge states by dynamically moving a domain wall between two regions of different topological numbers in one dimension. This method fundamentally relies on Lorentz invariance and relativistic effects, because the moving the domain wall at a constant speed is described by a mass term with the uniform linear motion in the Dirac equation. We demonstrate effectiveness of our method in transferring edge states with high fidelity using a one-dimensional quantum walk with two internal states, which is feasible with current experimental technology. We also investigate how bit-flip and dephasing dissipation to environment affects transfer efficiency. Remarkably, bit (dephasing) dissipation does not affect the efficiency at slow (fast) transfer limits, which can be explained by the relativistic effects on the edge states.

Reference:
Y. Kanda, Y. Fujisawa, K. Yakubo, N. Kawakami, and H. Obuse, arXiv:2505.16606