  We discuss lattice simulations of light nuclei at leading order in chiral
effective field theory. Using lattice pion fields and auxiliary fields, we
include the physics of instantaneous one-pion exchange and the leading-order
S-wave contact interactions. We also consider higher-derivative contact
interactions which adjust the S-wave scattering amplitude at higher momenta. By
construction our lattice path integral is positive definite in the limit of
exact Wigner SU(4) symmetry for any even number of nucleons. This SU(4)
positivity and the approximate SU(4) symmetry of the low-energy interactions
play an important role in suppressing sign and phase oscillations in Monte
Carlo simulations. We assess the computational scaling of the lattice algorithm
for light nuclei with up to eight nucleons and analyze in detail calculations
of the deuteron, triton, and helium-4.
