Block encodings of discrete subgroups on a quantum computer

Journal Article · 08 September 2024 · Physical Review. D.

DOI: https://doi.org/10.1103/PhysRevD.110.054505 · OSTI ID:2440062

Lamm, Henry ; Li, Ying-Ying ; Shu, Jing; Wang, Yi-Lin ; Xu, Bin

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 $SU\left(2\right)$ and $\mathbb{V}$ of $SU\left(3\right)$ . 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 quantum computer with estimated fidelities of ${40}_{-4}^{+5}\%$ and $4_{-3}^{+5}\%$ , respectively. Published by the American Physical Society 2024

• Research Organization: BIMSA, Beijing; Fermi National Accelerator Laboratory (FNAL), Batavia, IL (United States); Hefei, CUST; PCFT, Hefei; Peking U., CHEP; Peking U., SKLNPT
• Sponsoring Organization: US Department of Energy; USDOE
• Grant/Contract Number: 89243024CSC000002; AC02-07CH11359
• OSTI ID: 2440062
• Report Number(s): FERMILAB-PUB-24-0242-T; USTC-ICTS/PCFT-24-15; 054505
• Journal Information: Physical Review. D., Journal Name: Physical Review. D. Journal Issue: 5 Vol. 110; ISSN PRVDAQ; ISSN 2470-0010
• Publisher: American Physical SocietyCopyright Statement
• Country of Publication: United States
• Language: English