Xiong, Y (reprint author), Nanjing Normal Univ, Dept Phys, Nanjing 210023, Jiangsu, Peoples R China.
Coupling Majorana qubits with other qubits is absolutely essential for storing, manipulating and transferring information for topological quantum computing. We theoretically propose a manner to couple Majorana qubits with solitons, another kind of topological impurity, which was first studied in the spinless Su-Schrieffer-Heeger model. We present a NOT operation on the Majorana qubit by moving the soliton through a heterostructure adiabatically. Based on these two topological impurities, the operation is robust against local disorder. Furthermore, we find that the soliton may carry non-universal fractional electric charge instead of fractional charge 1/2, because of the breaking of gauge invariance induced by superconducting proximity.