  We construct the primitive gate set for the digital quantum simulation of the
108-element $\Sigma(36\times3)$ group. This is the first time a nonabelian
crystal-like subgroup of $SU(3)$ has been constructed for quantum simulation.
The gauge link registers and necessary primitives -- the inversion gate, the
group multiplication gate, the trace gate, and the $\Sigma(36\times3)$ Fourier
transform -- are presented for both an eight-qubit encoding and a heterogeneous
three-qutrit plus two-qubit register. For the latter, a specialized compiler
was developed for decomposing arbitrary unitaries onto this architecture.
