  The 1+1D O(3) non-linear {\sigma}-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.
