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

• URL: http://arxiv.org/abs/2208.12309v2
• Date: Thu, 1 Sep 2022 14:51:53 GMT
• Title: Primitive Quantum Gates for an SU(2) Discrete Subgroup: BT
• Authors: Erik J. Gustafson, Henry Lamm, Felicity Lovelace, Damian Musk
• Abstract summary: We construct a primitive gate set for the digital quantum simulation of the binary tetrahedral ($mathbbBT$) 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. We experimentally benchmark the inversion and trace gates on ibm nairobi, with estimated fidelities between $14-55%$, depending on the input state.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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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