  We provide a systematic approach for constructing approximate quantum
many-body scars (QMBS) starting from two-layer Floquet automaton circuits that
exhibit trivial many-body revivals. We do so by applying successively more
restrictions that force local gates of the automaton circuit to commute
concomitantly more accurately when acting on select scar states. With these
rules in place, an effective local, Floquet Hamiltonian is seen to capture
dynamics of the automaton over a long prethermal window. We provide numerical
evidence for such a picture and use our construction to derive several QMBS
models, including the celebrated PXP model.
