We investigate the non-adiabatic processes occurring during the manipulations
of Majorana qubits in 1-D semiconducting wires with proximity induced
superconductivity. Majorana qubits are usually protected by the excitation gap.
Yet, manipulations performed at a finite pace can introduce both decoherence
and renormalization effects. Though exponentially small for slow manipulations,
these effects are important as they may constitute the ultimate decoherence
mechanism. Moreover, as adiabatic topological manipulations fail to produce a
universal set of quantum gates, non-adiabatic manipulations might be necessary
to perform quantum computation.Comment: 14 pages, 5 figure
