, and thus can realize four Majorana modes in a single, driven quantum wire. We describe and numerically evaluate a protocol that realizes a topologically protected exchange of two Majorana zero modes in a single wire by adiabatically modulating the Floquet drive and using the

\ensuremath{\pi}

modes as auxiliary degrees of freedom.

DOI: 10.1103/physrevb.100.041102

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\ensuremath{\pi}

\ensuremath{\pi}

modes as auxiliary degrees of freedom.

Z

rotations. We first design a topologically protected logical

Z

gate based entirely on local interactions within the 1DTS. Using an auxiliary qubit coupled to the topological superconductors, we extend the

Z

gate to non-Clifford single- and multiqubit arbitrary rotations with partial topological protection. Finally, to perform universal quantum computing, we introduce a scheme for performing arbitrary unitary rotations, albeit without topological protection. We develop a formalism based on unitary braids which creates transitions between different topological phases of the 1DTS system. The unitary formalism can be simply converted to an equivalent adiabatic scheme, which we numerically simulate, and we show that high-fidelity operations should be possible with reasonable parameters.