  We study time-dependent electron transport and quantum noise in a ballistic
graphene field effect transistor driven by an ac gate potential. The non-linear
response to the ac signal is computed through Floquet theory for scattering
states and Landauer-B\"uttiker theory for charge current and its fluctuations.
Photon-assisted excitation of a quasibound state in the top-gate barrier leads
to resonances in transmission that strongly influence the noise properties. For
strong doping of graphene under source and drain contacts, when electrons are
transmitted through the channel via evanescent waves, the resonance leads to a
substantial suppression of noise. The Fano factor is then reduced well below
the pseudo-diffusive value, $F<1/3$, also for strong ac drive. The good
signal-to-noise ratio (small Fano factor) on resonance suggests that the device
is a good candidate for high-frequency (THz) radiation detection. We show
analytically that Klein tunneling (total suppression of back-reflection)
persists for perpendicular incidence also when the barrier is driven
harmonically. Although the transmission is inelastic and distributed among
sideband energies, a sum rule leads to total suppression of shot noise.
