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We construct a primitive gate set for the digital quantum simulation of the48-element binary octahedral ($\mathbb{BO}$) group. This nonabelian discretegroup better approximates $SU(2)$ lattice gauge theory than previous work onthe binary tetrahedral group at the cost of one additional qubit -- for a totalof six -- per gauge link. The necessary primitives are the inversion gate, thegroup multiplication gate, the trace gate, and the $\mathbb{BO}$ Fouriertransform.

Primitive Quantum Gates for an $SU(2)$ Discrete Subgroup: Binary Octahedral