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.

Duke Scholars

Author Shuchen Zhu Mathematics