Erik J. Gustafson, Yao Ji, Henry Lamm, Edison M. Murairi, Shuchen Zhu (May 13 2024).
Abstract: We construct the primitive gate set for the digital quantum simulation of the 108-element $\Sigma(36\times3)$ 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 $\Sigma(36\times3)$ 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.