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PreprintCC BY 4.0arXiv

Primitive Quantum Gates for an SU(3) Discrete Subgroup: Σ(216×3)

  • Erik J. Gustafson
  • Henry Lamm
  • Edison Murairi
  • Sebastian Osorio Perez
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Abstract

We construct a primitive gate set for the digital quantum simulation of the $648$-element discrete subgroup of SU(3), dsb. The five algorithmic primitives are the inversion, group multiplication, trace, group Fourier transform, and kinetic-phase gates, for which we provide qubit and qutrit--qubit decompositions. For a fiducial shear-viscosity calculation on a 103 spatial lattice with $50$ time steps and a total synthesis-error budget of 10−8, the estimated fault-tolerant costs are $2.3−−6.8\times10^{10}$ T gates in the qubit architecture and $1.3−−5.9\times10^{12}$ R gates in the qutrit--qubit architecture.

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Cite

BibTeXRIS
BibTeX
@misc{gustafson2026primitive,
  title = {{Primitive Quantum Gates for an $SU(3)$ Discrete Subgroup: $Σ(216\times3)$}},
  author = {Erik J. Gustafson and Henry Lamm and Edison Murairi and Sebastian Osorio Perez},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.08161},
  eprint = {2611.08161},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.08161},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Primitive Quantum Gates for an SU(3) Discrete Subgroup: Σ(216×3)
AU  - Erik J. Gustafson
AU  - Henry Lamm
AU  - Edison Murairi
AU  - Sebastian Osorio Perez
PY  - 2026
DA  - 2026/11/05
PB  - arXiv
DO  - 10.48550/arxiv.2611.08161
UR  - https://arxiv.org/abs/2611.08161
AB  - We construct a primitive gate set for the digital quantum simulation of the $648$-element discrete subgroup of SU(3), dsb. The five algorithmic primitives are the inversion, group multiplication, trace, group Fourier transform, and kinetic-phase gates, for which we provide qubit and qutrit--qubit decompositions. For a fiducial shear-viscosity calculation on a 10^3 spatial lattice with $50$ time steps and a total synthesis-error budget of 10^−8, the estimated fault-tolerant costs are $2.3−−6.8\times10^{10}$ T gates in the qubit architecture and $1.3−−5.9\times10^{12}$ R gates in the qutrit--qubit architecture.
ER  -