Block Encodings of Discrete Subgroups on Quantum Computer

• URL: http://arxiv.org/abs/2405.12890v1
• Date: Tue, 21 May 2024 16:00:04 GMT
• Title: Block Encodings of Discrete Subgroups on Quantum Computer
• Authors: Henry Lamm, Ying-Ying Li, Jing Shu, Yi-Lin Wang, Bin Xu,
• Abstract summary: We introduce a block encoding method for mapping discrete subgroups to qubits on a quantum computer. We detail the construction of primitive gates -- the inversion gate, the group multiplication gate, the trace gate, and the group Fourier gate. The inversion gates for $mathbbBT$ and $mathbbBI$ are benchmarked on the $textttwang$ quantum computer with estimated fidelities of $40+5_-4%$ and $4+5_-3%$ respectively.
• Score: 23.493000556496376
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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