  Quantum systems can be dynamically controlled using time-periodic external
fields, leading to the concept of Floquet engineering, with promising
technological applications. Computing Floquet energy spectra is harder than
only computing ground state properties or single time-dependent trajectories,
and scales exponentially with the Hilbert space dimension. Especially for
strongly correlated systems in the low frequency limit, classical approaches
based on truncation break down. Here, we present two quantum algorithms to
determine effective Floquet modes and energy spectra. We combine the defining
properties of Floquet modes in time and frequency domains with the
expressiveness of parametrized quantum circuits to overcome the limitations of
classical approaches. We benchmark our algorithms and provide an analysis of
the key properties relevant for near-term quantum hardware.
