  Symmetry protected topological order in one dimension leads to protected
degeneracies between symmetry blocks of the reduced density matrix. In the
presence of periodic driving, topological Floquet phases can be identified in
terms of a cycling of these symmetry blocks between different charge quantum
numbers. We discuss an example of this phenomenon with an Ising $\mathbb{Z}_2$
symmetry, using both analytic methods and real quantum computers. By
adiabatically moving along the phase diagram, we demonstrate that the cycling
periodicity is broken in Floquet topological phase transitions. An equivalent
signature of the topological Floquet phase is identified as a computational
power allowing to teleport quantum information.
