\([[8, 3, 3]]\) code[13] 

Description

Eight-qubit code that can be obtained from a modified CSS construction using a first-order \([8,4,4]\) RM code and a \([8,7,2]\) even-weight code [3]. The modification introduces signs between the codewords.

See [4; Table 3.3] for its stabilizer generator matrix. The code's automorphism group is \(\text{A}\Gamma\text{L}(1,8)\) [5].

Parent

References

[1]
D. Gottesman, “Class of quantum error-correcting codes saturating the quantum Hamming bound”, Physical Review A 54, 1862 (1996) arXiv:quant-ph/9604038 DOI
[2]
A. R. Calderbank et al., “Quantum Error Correction and Orthogonal Geometry”, Physical Review Letters 78, 405 (1997) arXiv:quant-ph/9605005 DOI
[3]
A. M. Steane, “Simple quantum error-correcting codes”, Physical Review A 54, 4741 (1996) arXiv:quant-ph/9605021 DOI
[4]
D. Gottesman, “Stabilizer Codes and Quantum Error Correction”, (1997) arXiv:quant-ph/9705052
[5]
H. Hao, “Investigations on Automorphism Groups of Quantum Stabilizer Codes”, (2021) arXiv:2109.12735
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Zoo Code ID: stab_8_3_3

Cite as:
\([[8, 3, 3]]\) code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023. https://errorcorrectionzoo.org/c/stab_8_3_3
BibTeX:
@incollection{eczoo_stab_8_3_3, title={\([[8, 3, 3]]\) code}, booktitle={The Error Correction Zoo}, year={2023}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/stab_8_3_3} }
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Permanent link:
https://errorcorrectionzoo.org/c/stab_8_3_3

Cite as:

\([[8, 3, 3]]\) code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023. https://errorcorrectionzoo.org/c/stab_8_3_3

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/quantum/qubits/small_distance/small/stab_8_3_3.yml.