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.

Parent

Children

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
Page edit log

Your contribution is welcome!

on github.com (edit & pull request)

edit on this site

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} }
Share via:
Twitter | Mastodon |  | E-mail
Permanent link:
https://errorcorrectionzoo.org/c/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

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