Primitive quantum gates for an SU(3) discrete subgroup: Σ(36×3)

We construct the primitive gate set for the digital quantum simulation of the 108-element Σ⁢(36 × 3) group. This is the first time a non-Abelian 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 Σ⁢(36 × 3) 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.