  We analyze propagation of quantum information along chiral Majorana edge
states in two-dimensional topological materials. The use of edge states may
facilitate the braiding operation, an important ingredient in topological
quantum computations. For the edge of the Kitaev honeycomb model in a
topological phase, we discuss how the edge states can participate in
quantum-information processing, and consider a two-qubit logic gate between
distant external qubits coupled to the edge. Here we analyze the influence of
disorder and noise on properties of the edge states and quantum-gate fidelity.
We find that realistically weak disorder does not prevent one from
implementation of a high-fidelity operation via the edge.
