Small-distance block quantum code 

Description

A block code on \(n\) subsystems that either detects or corrects errors on only a single subsystem. These two cases correspond to distance \(d=2\) or \(d=3\) block quantum codes, respectively.

All single error-correcting qubit stabilizer codes have been classified [1]. See Ref. [2] for single error-detecting qubit stabilizer codes.

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References

[1]
S. Yu et al., “All the stabilizer codes of distance 3”, (2011) arXiv:0901.1968
[2]
E. M. Rains, “Quantum codes of minimum distance two”, (1997) arXiv:quant-ph/9704043
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Zoo Code ID: small_distance

Cite as:
“Small-distance block quantum code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023. https://errorcorrectionzoo.org/c/small_distance
BibTeX:
@incollection{eczoo_small_distance,
  title={Small-distance block quantum code},
  booktitle={The Error Correction Zoo},
  year={2023},
  editor={Albert, Victor V. and Faist, Philippe},
  url={https://errorcorrectionzoo.org/c/small_distance}
}
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Cite as:

“Small-distance block quantum code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023. https://errorcorrectionzoo.org/c/small_distance

Github: https://github.com/errorcorrectionzoo/eczoo_data/tree/main/codes/quantum/properties/block/small_distance.yml.