Primitive Quantum Gates for an SU(3) Discrete Subgroup: $Σ(36\times3)$

• URL: http://arxiv.org/abs/2405.05973v4
• Date: Fri, 6 Sep 2024 21:34:44 GMT
• Title: Primitive Quantum Gates for an SU(3) Discrete Subgroup: $Σ(36\times3)$
• Authors: Erik J. Gustafson, Yao Ji, Henry Lamm, Edison M. Murairi, Sebastian Osorio Perez, Shuchen Zhu,
• Abstract summary: We construct the primitive gate set for the digital quantum simulation of the 108-element $Sigma(36times3)$ group. This is the first time a nonabelian crystal-like subgroup of $SU(3)$ has been constructed for quantum simulation.
• Score: 1.1545092788508224
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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