  We explore if space-time symmetric lattice field theory models with a finite
Hilbert space per lattice site can reproduce asymptotic freedom in the
two-dimensional $O(4)$ model. We focus on a simple class of such models with a
five dimensional local Hilbert space. We demonstrate how even the simplest
model reproduces asymptotic freedom within the D-theory formalism but at the
cost of increasing the size of the Hilbert space through coupling several
layers of a two-dimensional lattice. We then argue that qubit regularization
can be viewed as an effective field theory (EFT) even if the continuum limit
cannot be reached, as long as we can tune the model close enough to the
continuum limit where perturbation theory, or other analytical techniques,
become viable. We construct a simple lattice model on a single layer with a
four dimensional local Hilbert space that acts like an excellent EFT of the
original theory.
