We study strongly interacting topological Floquet systems in one dimension and symmetry class BDI and introduce two Floquet Green's-function-based topological invariants to characterize phases hosting Majorana zero modes and Majorana $\pi$ modes at the edge. While applicable also to interacting systems, these invariants reproduce winding numbers of noninteracting Floquet unitaries discussed in the literature. We further analytically evaluate the Green's function in interacting Kitaev-like Floquet chains (or equivalently transverse field Ising circuits) both in the bulk and at the edge at various analytically tractable points in parameter space corresponding to a variety of topological phases. Just as in the case of continuum time evolution, topological bands of Green's function zeros may also contribute to the topological invariant and display a bulk-boundary correspondence. However, contrary to the case of continuum time evolution, Floquet Green's functions can have zeros even in the absence of interactions. Finally, we also discuss an implementation of this Floquet system in a digital quantum emulator: We present a circuit which encodes the interaction under consideration and pinpoint the observables carrying information about the topological Green's function boundary zeros.

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• Quantum simulation
• Floquet systems
• Strongly correlated systems
• Green's function methods
• Topology