  We test a possible digitization of $\mathrm{SU}(2)$ lattice gauge theories
based on partitionings of the sphere $S_3$. In our construction the link
operators are unitary and diagonal, with eigenvalues determined by the vertices
of the partitioning. The canonical momenta are finite difference operators
approximating the Lie derivatives on the manifold. In this formalism we
implement the standard Wilson Hamiltonian. We show results for a 2-site
Schwinger-type model in 1D and a single-plaquette system in 2D. Our
calculations are performed on a classical computer, though in principle they
can be implemented also on a quantum device.
