The Steane code is a tool in quantum error correction

Quantum error correction

Quantum error correction is used in quantum computing to protect quantum information from errors due to decoherence and other quantum noise. Quantum error correction is essential if one is to achieve fault-tolerant quantum computation that can deal not only with noise on stored quantum...

 introduced by Andrew Steane

Andrew Steane

Andrew Martin Steane is Professor of physics at the University of Oxford. He is also a fellow of Exeter College, Oxford.He was a student at St Edmund Hall, Oxford where he obtained his MA and DPhil....

 in 1996. It is a perfect CSS code

CSS code

In quantum error correction, CSS codes, named after their inventors, A. R. Calderbank, Peter Shor and Andrew Steane, are a special type of Stabilizer codes constructed from classical codes with some special properties.- Construction :...

 (Calderbank-Shor-Steane), using the classical binary self-dual [7,4,3] Hamming code

Hamming code

In telecommunication, Hamming codes are a family of linear error-correcting codes that generalize the Hamming-code invented by Richard Hamming in 1950. Hamming codes can detect up to two and correct up to one bit errors. By contrast, the simple parity code cannot correct errors, and can detect only...

 to correct for qubit

Qubit

In quantum computing, a qubit or quantum bit is a unit of quantum information—the quantum analogue of the classical bit—with additional dimensions associated to the quantum properties of a physical atom....

 flip errors (X errors) and the dual

Dual

Dual may refer to:* Dual , a notion of paired concepts that mirror one another** Dual , a formalization of mathematical duality** . . ...

 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

Standard form

Standard form may refer to:*The more common name for scientific notation in British English*Standard form – a common form of a linear equation*Canonical form...

 is

where H is the parity-check matrix

Parity-check matrix

In coding theory, a parity-check matrix of a linear block code Cis a generator matrix of the dual code. As such, a codeword c is in C if and only if the matrix-vector product Hc=0....

of the Hamming code and is given by

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