Steane code
The Steane code is a tool in quantum error correction introduced by Andrew Steane in 1996. It is a CSS code (Calderbank-Shor-Steane), using the classical binary [7,4,3] Hamming code to correct for qubit flip errors (X errors) and the dual of the Hamming code, the [7,3,4] code, to correct for phase flip errors (Z errors). The Steane code is able to correct arbitrary single qubit errors.
In the stabilizer formalism, the Steane code has 6 generators, and the check matrix in standard form is
where H is the parity-check matrix of the Hamming code and is given by
The Steane code is the first in the family of quantum Hamming codes, codes with parameters for integers . It is also a quantum color code.
![{\displaystyle [[7,1,3]]}](https://web.archive.org/web/20211226010443im_/https://wikimedia.org/api/rest_v1/media/math/render/svg/77ca97a28919d5c04a4ee9b5e77cbbb8190718f8)
![{\displaystyle [[2^{r}-1,2^{r}-1-2r,3]]}](https://web.archive.org/web/20211226010443im_/https://wikimedia.org/api/rest_v1/media/math/render/svg/fe00403028ec1dd96e3b8463f0adc09bfefb8b16)
References
- Steane, Andrew (1996). "Multiple-Particle Interference and Quantum Error Correction". Proc. Roy. Soc. Lond. A. 452 (1954): 2551–2577. arXiv:quant-ph/9601029. Bibcode:1996RSPSA.452.2551S. doi:10.1098/rspa.1996.0136.
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