  We construct a qubit regularization of the $O(3)$ non-linear sigma model in
two and three spatial dimensions using a quantum Hamiltonian with two qubits
per lattice site. Using a worldline formulation and worm algorithms, we show
that in two spatial dimensions our model has a quantum critical point where the
well-known scale-invariant physics of the three-dimensional Wilson-Fisher fixed
point is reproduced. In three spatial dimensions, we recover mean-field
critical exponents at a similar quantum critical point. These results show that
our qubit Hamiltonian is in the same universality class as the traditional
classical lattice model close to the critical points. Simple modifications to
our model also allow us to study the physics of traditional lattice models with
$O(2)$ and $Z_2$ symmetries close to the corresponding critical points.
