Primitive Quantum Gates for an $SU(2)$ Discrete Subgroup: Binary Octahedral

Published 16 Dec 2023 in hep-lat and quant-ph | (2312.10285v1)

Abstract: We construct a primitive gate set for the digital quantum simulation of the 48-element binary octahedral ($\mathbb{BO}$) group. This nonabelian discrete group better approximates $SU(2)$ lattice gauge theory than previous work on the binary tetrahedral group at the cost of one additional qubit -- for a total of six -- per gauge link. The necessary primitives are the inversion gate, the group multiplication gate, the trace gate, and the $\mathbb{BO}$ Fourier transform.

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