  Floquet topological matter has emerged as one exciting platform to explore
rich physics and game-changing applications of topological phases. As one
remarkable and recently discovered feature of Floquet symmetry protected
topological (SPT) phases, in principle a simple periodically driven system can
host an arbitrary number of topological protected zero edge modes and pi edge
modes, with Majorana zero modes and Majorana pi modes as examples protected by
the particle-hole symmetry. This work advocates a new route to holonomic
quantum computation by exploiting the co-existence of many Floquet SPT edge
modes, all of which have trivial dynamical phases during a computation
protocol. As compelling evidence supporting this ambitious goal, three pairs of
Majorana edge modes, hosted by a periodically driven one-dimensional (1D)
superconducting superlattice, are shown to suffice to encode two logical
qubits, realize quantum gate operations, and execute two simple quantum
algorithms through adiabatic lattice deformation. When compared with early
studies on quantum computation based on Majorana zero modes of topological
quantum wires, significant resource saving is now made possible by use of
Floquet SPT phases. This paper is thus hoped to motivate a series of future
studies on the potential of Floquet topological matter in quantum computation.
