Physalis peruviana Is hardy in US hardiness zones 10 - 12. You will have to grow it in a pot and bring it in for the winter or grow it as an annual, like tomatoes. In zone 6, the ground is going to freeze to some depth, too cold for roots.
PS: The other problem you might run into if you decide to tree it as an annual is season leagth. If you are really determined to grow that particular ground cherry, I suggest you look into ways to extend the growing season: cold frames, small greenhouse.... .