A NOT operation on Majorana qubits with mobilizable solitons in an extended Su–Schrieffer–Heeger model

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 nonuniversal fractional electric charge instead of fractional charge $1/2$ , because of the breaking of gauge invariance induced by superconducting proximity.