Braiding a novel kind of Majorana-like quasiparticles in nanowire quantum dots

For an electrically driven electron confined in a nanowire quantum dot with spin-orbit coupling (SOC), we find a SOC-magnetism phase-locked condition under which we derive a complete set of Schr\"odinger kitten states which contains some novel degenerate ground states with oscillating wave packets or stationary double packets in undriven case. We identify such wave packets as Majorana-like quasiparticles and demonstrate that they obey non-Abelian statistics and behave similarly to neutral particles. The braiding operations based on the interchanges of the degenerate non-Abelian quasiparticles are shown, which shift the system between different ground states and may be insensitive to perturbations and weak noise from the environment. The results could be tested experimentally in the existing setups and could be treated as the leading-order results to directly extended to an array of weakly coupled single-electron quantum dots for topological quantum computation.