Cyclic quantum code[1] 

Description

A block quantum code such that cyclic permutations of the subsystems leave the codespace invariant. In other words, the automorphism group of the code contains the cyclic group \(\mathbb{Z}_n\).

Protection

Cyclic symmetry guarantees that if a single subsystem is protected against some noise, then all other subsystems are also.

Decoding

Adapted from the Berlekamp decoding algorithm for classical BCH codes [1].

Notes

Many examples have been found by computer algebra programs. Ref. [1] give examples of \([[17,1,7]]\) and \([[17,9,3]]\) quantum cyclic codes.

Parent

Children

Cousin

References

[1]
S. Dutta and P. P. Kurur, “Quantum Cyclic Code”, (2010) arXiv:1007.1697
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Zoo Code ID: quantum_cyclic

Cite as:
“Cyclic quantum code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2021. https://errorcorrectionzoo.org/c/quantum_cyclic
BibTeX:
@incollection{eczoo_quantum_cyclic, title={Cyclic quantum code}, booktitle={The Error Correction Zoo}, year={2021}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/quantum_cyclic} }
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“Cyclic quantum code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2021. https://errorcorrectionzoo.org/c/quantum_cyclic

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/quantum/properties/block/symmetric/quantum_cyclic.yml.