\(((5,6,2))\) qubit code[1] 

Description

Six-qubit cyclic CWS code detecting a single-qubit error.

This code is the smallest nontrivial member of the \(((5+2r,3\times 2^{2r+1},2))\) qubit code family [2] (see also [4][3; Ex. 8]). This code is also a qubit member of the \(((n, 1+n(q-1),2))_q\) Galois-qudit code family [5].

Its codeword stabilizer consists of all cyclic shifts of \(ZXZII\). It's automorphism group is of size 3840 and given in Ref. [1] (see also [2; Corr. 18]).

Parents

References

[1]
E. M. Rains et al., “A Nonadditive Quantum Code”, Physical Review Letters 79, 953 (1997) arXiv:quant-ph/9703002 DOI
[2]
E. M. Rains, “Quantum codes of minimum distance two”, (1997) arXiv:quant-ph/9704043
[3]
V. Aggarwal and A. R. Calderbank, “Boolean Functions, Projection Operators, and Quantum Error Correcting Codes”, IEEE Transactions on Information Theory 54, 1700 (2008) arXiv:cs/0610159 DOI
[4]
D. Hu et al., “Graphical nonbinary quantum error-correcting codes”, Physical Review A 78, (2008) arXiv:0801.0831 DOI
[5]
V. Arvind, P. P. Kurur, and K. R. Parthasarathy, “Nonstabilizer Quantum Codes from Abelian Subgroups of the Error Group”, (2002) arXiv:quant-ph/0210097
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Zoo Code ID: qubit_5_6_2

Cite as:
\(((5,6,2))\) qubit code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023. https://errorcorrectionzoo.org/c/qubit_5_6_2
BibTeX:
@incollection{eczoo_qubit_5_6_2, title={\(((5,6,2))\) qubit code}, booktitle={The Error Correction Zoo}, year={2023}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/qubit_5_6_2} }
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Cite as:

\(((5,6,2))\) qubit code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023. https://errorcorrectionzoo.org/c/qubit_5_6_2

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/quantum/qubits/small_distance/small/qubit_5_6_2.yml.