Primitive Quantum Gates for an SU(3) Discrete Subgroup: $Σ(36\times3)$
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arXiv
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| Main Authors: | , , , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866917770574168064 |
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| author | Gustafson, Erik J. Ji, Yao Lamm, Henry Murairi, Edison M. Perez, Sebastian Osorio Zhu, Shuchen |
| author_facet | Gustafson, Erik J. Ji, Yao Lamm, Henry Murairi, Edison M. Perez, Sebastian Osorio Zhu, Shuchen |
| contents | We construct the primitive gate set for the digital quantum simulation of the 108-element $Σ(36\times3)$ 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 $Σ(36\times3)$ 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2405_05973 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Primitive Quantum Gates for an SU(3) Discrete Subgroup: $Σ(36\times3)$ Gustafson, Erik J. Ji, Yao Lamm, Henry Murairi, Edison M. Perez, Sebastian Osorio Zhu, Shuchen High Energy Physics - Lattice Quantum Physics We construct the primitive gate set for the digital quantum simulation of the 108-element $Σ(36\times3)$ 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 $Σ(36\times3)$ 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. |
| title | Primitive Quantum Gates for an SU(3) Discrete Subgroup: $Σ(36\times3)$ |
| topic | High Energy Physics - Lattice Quantum Physics |
| url | https://arxiv.org/abs/2405.05973 |