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

Description

A Hamming-based CSS code is a CCS code constructed with a classical Hamming code \([2^r-1,2^r-1-r,3]=C_X=C_Z\).

Protection

Protects against any single qubit error.

Fault Tolerance

Syndrome measurement can be done with two ancillary flag qubits [1].

Parent

Child

Cousins

Zoo code information

Internal code ID: quantum_hamming_css

Your contribution is welcome!

on github.com (edit & pull request)

edit on this site

Zoo Code ID: quantum_hamming_css

Cite as:
“\([[2^r-1, 2^r-2r-1, 3]]\) Hamming-based CSS code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/quantum_hamming_css
BibTeX:
@incollection{eczoo_quantum_hamming_css, title={\([[2^r-1, 2^r-2r-1, 3]]\) Hamming-based CSS code}, booktitle={The Error Correction Zoo}, year={2022}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/quantum_hamming_css} }
Permanent link:
https://errorcorrectionzoo.org/c/quantum_hamming_css

References

[1]
R. Chao and B. W. Reichardt, “Quantum Error Correction with Only Two Extra Qubits”, Physical Review Letters 121, (2018). DOI; 1705.02329

Cite as:

“\([[2^r-1, 2^r-2r-1, 3]]\) Hamming-based CSS code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/quantum_hamming_css

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