[Jump to code hierarchy]

\(((6,2,3))\) \(\mathbb{Z}_{10}\) code[1]

Description

Six-qubit code that realizes gates from the group \(\mathbb{Z}_{10}\) transversally. This is the smallest distance-three code supporting a transversal gate outside of the Clifford group. See Ref. [1] for the codewords.

Transversal Gates

The \(\mathbb{Z}_{10}\) group can be realized transversally [1]. This is the smallest distance-three code supporting a transversal gate outside of the Clifford group.

Member of code lists

Primary Hierarchy

Quantum Domain
Qubit Kingdom
Qubit codeQECC Quantum
Parents
Qubit code
Small-distance block quantum codeQECC Quantum
\(((6,2,3))\) \(\mathbb{Z}_{10}\) code

References

[1]
C. Zhang, Z. Wu, S. Huang, and B. Zeng, “Transversal Gates in Nonadditive Quantum Codes”, (2025) arXiv:2504.20847
Page edit log

Your contribution is welcome!

on github.com (edit & pull request)— see instructions

edit on this site

Zoo Code ID: qubit_6_2_3

Cite as:
“\(((6,2,3))\) \(\mathbb{Z}_{10}\) code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2025. https://errorcorrectionzoo.org/c/qubit_6_2_3
BibTeX:
@incollection{eczoo_qubit_6_2_3, title={\(((6,2,3))\) \(\mathbb{Z}_{10}\) code}, booktitle={The Error Correction Zoo}, year={2025}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/qubit_6_2_3} }
Share via:
Twitter | Mastodon |  | E-mail
Permanent link:
https://errorcorrectionzoo.org/c/qubit_6_2_3

Cite as:

“\(((6,2,3))\) \(\mathbb{Z}_{10}\) code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2025. https://errorcorrectionzoo.org/c/qubit_6_2_3

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/quantum/qubits/small_distance/small/6/qubit_6_2_3.yml.