Steane code: Difference between revisions
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The '''Steane code''' is a tool in [[quantum error correction]] introduced by [[Andrew Steane]] in 1996. It is a [[ |
The '''Steane code''' is a tool in [[quantum error correction]] introduced by [[Andrew Steane]] in 1996. It is a [[Hamming_bound#Perfect_codes|perfect]] [[CSS code]], using the classical binary [[self-dual]] [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. |
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In the [[stabilizer formalism]], the Steane code has 6 generators, and the [[check matrix]] in [[standard form]] is |
In the [[stabilizer formalism]], the Steane code has 6 generators, and the [[check matrix]] in [[standard form]] is |
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Revision as of 21:00, 3 January 2010
The Steane code is a tool in quantum error correction introduced by Andrew Steane in 1996. It is a perfect CSS code, using the classical binary self-dual [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
References
- Steane, Andrew (1996). "Multiple-Particle Interference and Quantum Error Correction". Proc. Roy. Soc. Lond. A. 452: 2551–2577. doi:10.1098/rspa.1996.0136.
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