The 1+1D O(3) non-linear σ-model is a model system for future quantum lattice simulations of other
asymptotically-free theories, such as non-Abelian gauge theories. We find that utilizing dimensional reduction
can make efficient use of two-dimensional layouts presently available on cold atom quantum simulators. A
new definition of the renormalized coupling is introduced, which is applicable to systems with open boundary
conditions and can be measured using analog quantum simulators. Monte Carlo and tensor network calculations
are performed to determine the quantum resources required to reproduce perturbative short-distance observables.
In particular, we show that a rectangular array of 48 Rydberg atoms with existing quantum hardware capabilities
should be able to adiabatically prepare low-energy states of the perturbatively-matched theory. These states can
then be used to simulate non-perturbative observables in the continuum limit that lie beyond the reach of classical
computers.