  Majorana zero modes are a promising platform for topologically protected
quantum information processing. Their non-Abelian nature, which is key for
performing quantum gates, is most prominently exhibited through braiding. While
originally formulated for two-dimensional (2d) systems, it has been shown that
braiding can also be realized using one-dimensional (1d) wires by forming an
essentially two-dimensional network. Here, we show that in driven systems far
from equilibrium, one can do away with the second spatial dimension altogether
by instead using quasienergy as the second dimension. To realize this, we use a
Floquet topological superconductor which can exhibit Majorana modes at two
special eigenvalues of the evolution operator, 0 and pi, 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 pi modes as auxiliary degrees of
freedom.
