Primitive quantum gates for an $SU(2)$ discrete subgroup: Binary tetrahedral

We construct a primitive gate set for the digital quantum simulation of the binary tetrahedral ($\mathbb{BT}$ ) group on two quantum architectures. This non-Abelian discrete group serves as a crude approximation to SU⁡(2) lattice gauge theory while requiring five qubits or one quicosotetrit per gaug...

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Bibliographic Details
Published in:Physical review. D 2022-12, Vol.106 (11)
Main Authors: Gustafson, Erik J., Lamm, Henry, Lovelace, Felicity, Musk, Damian
Format: Article
Language:English
Subjects:
lattice gauge theory
PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
quantum algorithms
quantum simulation
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Summary:We construct a primitive gate set for the digital quantum simulation of the binary tetrahedral ($\mathbb{BT}$ ) group on two quantum architectures. This non-Abelian discrete group serves as a crude approximation to SU⁡(2) lattice gauge theory while requiring five qubits or one quicosotetrit per gauge link. The necessary basic primitives are the inversion gate, the group multiplication gate, the trace gate, and the $\mathbb{BT}$ Fourier transform over $\mathbb{BT}$ . We experimentally benchmark the inversion and trace gates on ibm_nairobi, with estimated fidelities between 14%–55%, depending on the input state.
ISSN:2470-0010
2470-0029
DOI:10.1103/PhysRevD.106.114501