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arXiv · 2405.05973

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

Erik J. Gustafson·Yao Ji·Henry Lamm·Edison M. Murairi·Sebastian Osorio Perez·Shuchen Zhu
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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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Erik J. Gustafson, Yao Ji, Henry Lamm, Edison M. Murairi, Sebastian Osorio Perez, Shuchen Zhu. 2024-04-30. Primitive Quantum Gates for an SU(3) Discrete Subgroup: $\Sigma(36\times3)$. https://doi.org/10.1103/physrevd.110.034515

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