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

Description

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

Transversal and Permutation-Based Gates

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

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Primary Hierarchy

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

References

[1]
C. Zhang, Z. Wu, S. Huang, and B. Zeng, “Transversal Gates in Nonadditive Quantum Codes”, (2025) arXiv:2504.20847
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Zoo Code ID: qubit_6_2_3

Cite as:
“\(((6,2,3))\) transversal-\(\mathbb{Z}_{10}\) code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2026. https://errorcorrectionzoo.org/c/qubit_6_2_3, arXiv:2606.11484
BibTeX:
@incollection{eczoo_qubit_6_2_3,
title={\(((6,2,3))\) transversal-\(\mathbb{Z}_{10}\) code},
booktitle={The Error Correction Zoo},
year={2026},
editor={Albert, Victor V. and Faist, Philippe},
eprint={2606.11484},
doi={10.48550/arXiv.2606.11484},
url={https://errorcorrectionzoo.org/c/qubit_6_2_3}
}
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Permanent link:
https://errorcorrectionzoo.org/c/qubit_6_2_3

Cite as:

“\(((6,2,3))\) transversal-\(\mathbb{Z}_{10}\) code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2026. https://errorcorrectionzoo.org/c/qubit_6_2_3, arXiv:2606.11484

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