  Primordial non-Gaussianities (PNGs) are signatures in the density field that
encode particle physics processes from the inflationary epoch. Such signatures
have been extensively studied using the Cosmic Microwave Background, through
constraining the amplitudes, $f^{X}_{\rm NL}$, with future improvements
expected from large-scale structure surveys; specifically, the galaxy
correlation functions. We show that weak lensing fields can be used to achieve
competitive and complementary constraints. This is shown via the new Ulagam
suite of N-body simulations, a subset of which evolves primordial fields with
four types of PNGs. We create full-sky lensing maps and estimate the Fisher
information from three summary statistics measured on the maps: the moments,
the cumulative distribution function, and the 3-point correlation function. We
find that the year 10 sample from the Rubin Observatory Legacy Survey of Space
and Time (LSST) can constrain PNGs to $\sigma(f^{\rm\,eq}_{\rm NL}) \approx
110$, $\sigma(f^{\rm\,or,lss}_{\rm NL}) \approx 120$, $\sigma(f^{\rm\,loc}_{\rm
NL}) \approx 40$. For the former two, this is better than or comparable to
expected galaxy clustering-based constraints from the Dark Energy Spectroscopic
Instrument (DESI). The PNG information in lensing fields is on non-linear
scales and at low redshifts ($z \lesssim 1.25$), with a clear origin in the
evolution history of massive halos. The constraining power degrades by
$\sim\!\!60\%$ under scale cuts of $\gtrsim 20{\,\rm Mpc}$, showing there is
still significant information on scales mostly insensitive to small-scale
systematic effects (e.g. baryons). We publicly release the Ulagam suite to
enable more survey-focused analyses.
