  Efficient digitization is required for quantum simulations of gauge theories.
Schemes based on discrete subgroups use a smaller, fixed number of qubits at
the cost of systematic errors. We systematize this approach by deriving the
single plaquette action through matching the continuous group action to that of
a discrete one via group character expansions modulo the field fluctuation
contributions. We accompany this scheme by simulations of pure gauge over the
largest discrete crystal-like subgroup of $SU(3)$ up to the fifth-order in the
coupling constant.
