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arXiv · 2405.12890

Block Encodings of Discrete Subgroups on Quantum Computer

Henry Lamm·Ying-Ying Li·Jing Shu·Yi-Lin Wang·Bin Xu
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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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Henry Lamm, Ying-Ying Li, Jing Shu, Yi-Lin Wang, Bin Xu. 2024-05-21. Block Encodings of Discrete Subgroups on Quantum Computer. https://arxiv.org/abs/2405.12890

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