Block Encodings of Discrete Subgroups on Quantum Computer
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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_ | 1866914804040466432 |
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| author | Lamm, Henry Li, Ying-Ying Shu, Jing Wang, Yi-Lin Xu, Bin |
| author_facet | Lamm, Henry Li, Ying-Ying Shu, Jing Wang, Yi-Lin Xu, Bin |
| contents | We introduce a block encoding method for mapping discrete subgroups to qubits on a quantum computer. This method is applicable to general discrete groups, including crystal-like subgroups such as $\mathbb{BI}$ of $SU(2)$ and $\mathbb{V}$ of $SU(3)$. We detail the construction of primitive gates -- the inversion gate, the group multiplication gate, the trace gate, and the group Fourier gate -- utilizing this encoding method for $\mathbb{BT}$ and for the first time $\mathbb{BI}$ group. We also provide resource estimations to extract the gluon viscosity. The inversion gates for $\mathbb{BT}$ and $\mathbb{BI}$ are benchmarked on the $\texttt{Baiwang}$ quantum computer with estimated fidelities of $40^{+5}_{-4}\%$ and $4^{+5}_{-3}\%$ respectively. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2405_12890 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Block Encodings of Discrete Subgroups on Quantum Computer Lamm, Henry Li, Ying-Ying Shu, Jing Wang, Yi-Lin Xu, Bin High Energy Physics - Lattice Quantum Physics We introduce a block encoding method for mapping discrete subgroups to qubits on a quantum computer. This method is applicable to general discrete groups, including crystal-like subgroups such as $\mathbb{BI}$ of $SU(2)$ and $\mathbb{V}$ of $SU(3)$. We detail the construction of primitive gates -- the inversion gate, the group multiplication gate, the trace gate, and the group Fourier gate -- utilizing this encoding method for $\mathbb{BT}$ and for the first time $\mathbb{BI}$ group. We also provide resource estimations to extract the gluon viscosity. The inversion gates for $\mathbb{BT}$ and $\mathbb{BI}$ are benchmarked on the $\texttt{Baiwang}$ quantum computer with estimated fidelities of $40^{+5}_{-4}\%$ and $4^{+5}_{-3}\%$ respectively. |
| title | Block Encodings of Discrete Subgroups on Quantum Computer |
| topic | High Energy Physics - Lattice Quantum Physics |
| url | https://arxiv.org/abs/2405.12890 |