  Projection Monte Carlo calculations of lattice Chiral Effective Field Theory
suffer from sign oscillations to a varying degree dependent on the number of
protons and neutrons. Hence, such studies have hitherto been concentrated on
nuclei with equal numbers of protons and neutrons, and especially on the alpha
nuclei where the sign oscillations are smallest. Here, we introduce the
"symmetry-sign extrapolation" method, which allows us to use the approximate
Wigner SU(4) symmetry of the nuclear interaction to systematically extend the
Projection Monte Carlo calculations to nuclear systems where the sign problem
is severe. We benchmark this method by calculating the ground-state energies of
the $^{12}$C, $^6$He and $^6$Be nuclei, and discuss its potential for studies
of neutron-rich halo nuclei and asymmetric nuclear matter.
