We construct a primitive gate set for the digital quantum simulation of the binary tetrahedral (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 BT Fourier transform over BT. We experimentally benchmark the inversion and trace gates on ibm nairobi, with estimated fidelities between 14−55%, depending on the input state.
Cite
@article{arxiv.2208.12309,
title = {Primitive Quantum Gates for an SU(2) Discrete Subgroup: BT},
author = {Erik J. Gustafson and Henry Lamm and Felicity Lovelace and Damian Musk},
journal= {arXiv preprint arXiv:2208.12309},
year = {2022}
}