In this talk I present a new approach called wave function matching for solving quantum many-body systems and recent results for ab initio calculations of nuclear structure. The method is applied to lattice Monte Carlo simulations of light nuclei, medium-mass nuclei, neutron matter, and nuclear matter. The goal of method is to ensure that the perturbative corrections used in the lattice calculations converge quickly. We use interactions at next-to-next-to-next-to-leading order in the framework of chiral effective field theory and we find that the method is producing good results for the binding energies and charge radii of light and medium mass nuclei as well as the equation of state for pure neutron matter and symmetric nuclear matter saturation. Also, these results are accompanied by new insights on the nuclear interactions that may help to resolve long-standing challenges in accurately reproducing nuclear binding energies, charge radii, and nuclear matter saturation in ab initio calculations.