Primitive quantum gates for an SU(2) discrete subgroup: Binary octahedral

We construct a primitive gate set for the digital quantum simulation of the 48-element binary octahedral (BO) group. This non-Abelian discrete group better approximates SU(2) lattice gauge theory than previous work on the binary tetrahedral group at the cost of one additional qubit-for a total of six-per gauge link. The necessary primitives are the inversion gate, the group multiplication gate, the trace gate, and the BO Fourier transform.