\((5,1,2)\)-convolutional code[1] 

Description

Quantum convolutional code with the stabilizer generators \begin{align} \begin{array}{cccccccc} X & Z & I & I & I & I & I & \cdots\\ Z & X & X & Z & I & I & I & \cdots\\ I & Z & X & X & Z & I & I & \cdots\\ I & I & Z & X & X & Z & I & \cdots\\ \vdots & \vdots & \vdots & \vdots & \vdots & \vdots & \vdots & \ddots \end{array} \tag*{(1)}\end{align}

Parent

Cousin

  • Five-qubit perfect code — The \((5,1,2)\)-convolutional code is an infinite-qubit version of the five-qubit perfect code, with the former's lattice-translation symmetry being the extension of the latter's cyclic permutation symmetry.

References

[1]
H. Ollivier and J.-P. Tillich, “Description of a Quantum Convolutional Code”, Physical Review Letters 91, (2003) arXiv:quant-ph/0304189 DOI
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Zoo Code ID: stab_5_1_2_convolutional

Cite as:
“\((5,1,2)\)-convolutional code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023. https://errorcorrectionzoo.org/c/stab_5_1_2_convolutional
BibTeX:
@incollection{eczoo_stab_5_1_2_convolutional,
  title={\((5,1,2)\)-convolutional code},
  booktitle={The Error Correction Zoo},
  year={2023},
  editor={Albert, Victor V. and Faist, Philippe},
  url={https://errorcorrectionzoo.org/c/stab_5_1_2_convolutional}
}
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Permanent link:
https://errorcorrectionzoo.org/c/stab_5_1_2_convolutional

Cite as:

“\((5,1,2)\)-convolutional code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023. https://errorcorrectionzoo.org/c/stab_5_1_2_convolutional

Github: https://github.com/errorcorrectionzoo/eczoo_data/tree/main/codes/quantum/qubits/stabilizer/topological/convolutional/stab_5_1_2_convolutional.yml.