  We formulate the $O(3)$ non-linear sigma model in 1+1 dimensions as a limit
of a three-component scalar field theory restricted to the unit sphere in the
large squeezing limit. This allows us to describe the model in terms of the
continuous variable (CV) approach to quantum computing. We construct the ground
state and excited states using the coupled-cluster Ansatz and find excellent
agreement with the exact diagonalization results for a small number of lattice
sites. We then present the simulation protocol for the time evolution of the
model using CV gates and obtain numerical results using a photonic quantum
simulator. We expect that the methods developed in this work will be useful for
exploring interesting dynamics for a wide class of sigma models and gauge
theories, as well as for simulating scattering events on quantum hardware in
the coming decades.
