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

Coupling Majorana qubits with other qubits is an absolute essential in storing, manipulating and transferring informations for topological quantum computing. We theoretically propose a manner to coupling Majorana qubits with solitons, another kind of topological impurities, which was first studied in the spinless Su-Schrieffer-Heeger (SSH) model. We presents a NOT operation on the Majorana qubit with moving the complementary soliton through heterostructure adiabatically. Based on these two topological impurities, the operation is robust against local disorder. Furthermore, we find that the soliton may carry decimal electric charge instead of fractional charge $1/2$, because of the breaking of gauge invariance induced by superconducting proximity.