  Qubit regularization provides a rich framework to explore quantum field
theories. The freedom to choose how the important symmetries of the theory are
embedded in the qubit regularization scheme allows us to construct new lattice
models with rich phase diagrams. Some of the phases can contain topological
terms which lead to critical phases. In this work we introduce and study the
SU(3)-F qubit regularization scheme to embed the SO(3) spin-symmetry. We argue
that qubit models in this regularization scheme contain several phases
including a critical phase which describes the k = 1 Wess-Zumino-Witten (WZW)
conformal field theory (CFT) at long distances, and two massive phases one of
which is trvially gapped and the other which breaks the lattice translation
symmetry. We construct a simple space-time Euclidean lattice model with a
single coupling U and study it using the Monte Carlo method. We show the model
has a critical phase at small U and a trivially massive phase at large U with a
first order transition separating the two. Another feature of our model is that
it is symmetric under space-time rotations, which means the temporal and
spatial lattice spacing are connected to each other. The unitary time evolution
operator obtained by a Wick rotation of the transfer matrix of our model can
help us compute the physics of the k = 1 WZW CFT in real time without the need
for tuning the temporal lattice spacing to zero. We use this idea to introduce
the concept of a relativistic quantum circuit on a discrete space-time lattice.
