\(((5,6,2))\) qubit code[1] 

Description

Six-qubit cyclic CWS code detecting a single-qubit error. Smallest nontrivial member of the \(((5+2r,3\times 2^{2r+1},2))\) qubit code family [2]. Qubit member of the \(((n, 1+n(q-1),2))_q\) Galois-qudit code family [3].

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. 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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Permanent link:
https://errorcorrectionzoo.org/c/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

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