  Topological edge states are recently attracting intense interest due to their
robustness in the presence of disorder and defects. However, most approaches
for manipulating such states require global modulations of the system's
Hamiltonian. In this work, we develop a method to control edge states using
local interactions of a four-node junction between cross-one-dimensional
topological atomic chains. These junction interactions can give rise to tunable
couplings between the hybridized edge states within different geometric
symmetry, allowing us to implement robust quantum state transfer and SWAP gate
between the two topological chains, where the edge states are pair-encoded as a
single qubit. Moreover, when the atoms are precisely positioned to couple
waveguides, the correlated decay caused by the environment enables the
anti-symmetric edge states to present subradiant dynamics and thus show
extremely long coherence time. These findings open up new possibilities for
quantum technologies with topological edge states in the future.
