  Chiral Majorana fermion is a massless self-conjugate fermion which can arise
as the edge state of certain two-dimensonal topological matters. It has been
theoretically predicted and experimentally observed in a hybrid device of
quantum anomalous Hall insulator and a conventional superconductor. Its closely
related cousin, Majorana zero mode in the bulk of the corresponding topological
matter, is known to be applicable in topological quantum computations. Here we
show that the propagation of chiral Majorana fermions lead to the same unitary
transformation as that in the braiding of Majorana zero modes, and propose a
new platform to perform quantum computation with chiral Majorana fermions. A
Corbino ring junction of the hybrid device can utilize quantum coherent chiral
Majorana fermions to implement the Hadamard gate and the phase gate, and the
junction conductance yields a natural readout for the qubit state.
