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arXiv · 2208.12309

Primitive Quantum Gates for an SU(2) Discrete Subgroup: BT

Erik J. Gustafson·Henry Lamm·Felicity Lovelace·Damian Musk
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Abstract

We construct a primitive gate set for the digital quantum simulation of the binary tetrahedral ($\mathbb{BT}$) group on two quantum architectures. This nonabelian 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.

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Erik J. Gustafson, Henry Lamm, Felicity Lovelace, Damian Musk. 2022-09-01. Primitive Quantum Gates for an SU(2) Discrete Subgroup: BT. https://doi.org/10.1103/physrevd.106.114501

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