  Based on the notion of quantum trajectory, we present a stochastic
theoretical framework for Floquet quantum heat engines. As an application, the
large deviation functions of two types of stochastic efficiencies for a
two-level Floquet quantum heat engine are investigated. We find that the
statistics of one efficiency agree well with the predictions of the universal
theory of efficiency fluctuations developed by Verley et al. [Phys. Rev. E {\bf
90}, 052145 (2014)], whereas the statistics of the other efficiency do not. The
reason for this discrepancy is attributed to the lack of fluctuation theorems
for the latter type of efficiency.
