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Block Encodings of Discrete Subgroups on Quantum Computer
- Publication Year :
- 2024
-
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.<br />Comment: 12 pages, 10 figures
- Subjects :
- High Energy Physics - Lattice
Quantum Physics
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2405.12890
- Document Type :
- Working Paper