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arXiv:2511.17437

Primitive Quantum Gates for an $SU(3)$ Discrete Subgroup: $Σ(72\times3)$

Sebastian Osorio Perez, Edison M. Murairi, Erik J. Gustafson, Henry Lamm

hep-latquant-phSubmitted Nov 21, 2025• Announced Nov 24, 2025• 0 citations
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Abstract

We construct a primitive gate set for the digital quantum simulation of a discrete subgroup of $SU(3)$: the 216-element $Σ(72\times3)$. The necessary primitives are the inversion gate, the group multiplication gate, the trace gate, and the group Fourier transform, for which we provide qubit decompositions. The resulting fault-tolerant T gate costs for a fiducial calculation of shear viscosity would require about $10^{12}$ T gates which compares favorably to other modern estimates.

Comments
13 pages, 17 figures

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