\(((5,3,2))_3\) qutrit code[1] 

Description

Smallest qutrit block code realizing the \(\Sigma(360\phi)\) subgroup of \(SU(3)\) transversally. The next smallest code is \(((7,3,2))_3\).

Transversal Gates

\(\Sigma(360\phi)\) group gates can be realized transversally.

Parent

  • Twisted \(1\)-group code — The \(((5,3,2))_3\) qutrit code admits a transversal representation of the twisted \(1\)-group \(\Sigma(360\phi)\) [1].

Cousin

  • \(SU(3)\) spin code — The \(((5,3,2))_3\) qutrit code can be interpreted as a \(SU(3)\) single-spin code.

References

[1]
E. Kubischta and I. Teixeira, “Free Quantum Codes from Twisted Unitary \(t\)-groups”, (2024) arXiv:2402.01638
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Zoo Code ID: su3_sigma360

Cite as:
“\(((5,3,2))_3\) qutrit code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/su3_sigma360
BibTeX:
@incollection{eczoo_su3_sigma360, title={\(((5,3,2))_3\) qutrit code}, booktitle={The Error Correction Zoo}, year={2024}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/su3_sigma360} }
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Permanent link:
https://errorcorrectionzoo.org/c/su3_sigma360

Cite as:

“\(((5,3,2))_3\) qutrit code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/su3_sigma360

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/quantum/spins/many_spin/su3_sigma360.yml.