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

• URL: http://arxiv.org/abs/2511.17437v1
• Date: Fri, 21 Nov 2025 17:35:23 GMT
• Title: Primitive Quantum Gates for an $SU(3)$ Discrete Subgroup: $Σ(72\times3)$
• Authors: Sebastian Osorio Perez, Edison M. Murairi, Erik J. Gustafson, Henry Lamm,
• Abstract summary: We construct a primitive gate set for the digital quantum simulation of a subgroup of 216-element $(72times3)$.<n>The resulting fault-tolerant T gate costs for a fiducial calculation of shear viscosity would require about $1012$ T gates.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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