Small-distance block quantum code 

Description

A block quantum code on \(n\) subsystems that either detects or corrects errors on at most two subsystems, i.e., have distance \(\leq 5\).

All single error-correcting qubit stabilizer codes have been classified [1]. See Refs. [2,3] for other small-distance 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
[3]
D. Hu et al., “Graphical nonbinary quantum error-correcting codes”, Physical Review A 78, (2008) arXiv:0801.0831 DOI
[4]
S. Bravyi and J. Haah, “Magic-state distillation with low overhead”, Physical Review A 86, (2012) arXiv:1209.2426 DOI
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Zoo Code ID: small_distance_quantum

Cite as:
“Small-distance block quantum code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023. https://errorcorrectionzoo.org/c/small_distance_quantum
BibTeX:
@incollection{eczoo_small_distance_quantum, 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_quantum} }
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“Small-distance block quantum code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023. https://errorcorrectionzoo.org/c/small_distance_quantum

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