\([[2^r, 2^r-r-2, 3]]\) quantum Hamming code[1]

Description

A family of stabilizer codes of distance \(3\) that asymptotically saturate quantum Hamming bound.

Protection

Protects against any single qubit error.

Parent

Cousins

Zoo code information

Internal code ID: quantum_hamming

Your contribution is welcome!

on github.com (edit & pull request)

edit on this site

Zoo Code ID: quantum_hamming

Cite as:
“\([[2^r, 2^r-r-2, 3]]\) quantum Hamming code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/quantum_hamming
BibTeX:
@incollection{eczoo_quantum_hamming, title={\([[2^r, 2^r-r-2, 3]]\) quantum Hamming code}, booktitle={The Error Correction Zoo}, year={2022}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/quantum_hamming} }
Permanent link:
https://errorcorrectionzoo.org/c/quantum_hamming

References

[1]
D. Gottesman, “Class of quantum error-correcting codes saturating the quantum Hamming bound”, Physical Review A 54, 1862 (1996). DOI; quant-ph/9604038

Cite as:

“\([[2^r, 2^r-r-2, 3]]\) quantum Hamming code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/quantum_hamming

Github: https://github.com/errorcorrectionzoo/eczoo_data/tree/main/codes/quantum/qubits/quantum_hamming.yml.