Steane code

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The Steane code is a tool in quantum error correction introduced by Andrew Steane in 1996. It is a perfect 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 [7,3,3] 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