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 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 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.

Article：2405.05973v1