  Superconductors hosting long-sought excitations called Majorana fermions may
be ultimately used as qubits of fault-tolerant topological quantum computers. A
crucial challenge toward the topological quantum computer is to implement
quantum operation of nearly degenerate quantum states as a dynamical process of
Majorana fermions. In this paper, we investigate the braiding dynamics of
Majorana fermions on superconducting nanowires. In a finite size system, a non-
adiabatic dynamical process dominates the non-Abelian braiding that operates
qubits of Majorana fermions. Our simulations clarify how qubits behave in the
real-time braiding process, and elucidate the optimum condition of
superconducting nanowires for efficient topological quantum operation.
