Majorana Braiding Dynamics on Nanowires
  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. 
C\'assio Sozinho Amorim, Kazuto Ebihara, Ai Yamakage, Yukio Tanaka,   and Masatoshi Sato
cond-mat.mes-hall cond-mat.supr-con