Shor code

The Shor Code is a error correction technique used to protect a Quantum Computer against single qubit errors.

The code

We map the qubit $\alpha |0\rangle +\beta |1\rangle$ to the nine qubit state

${\frac {\alpha }{2{\sqrt {2}}}}(|000\rangle +|111\rangle )(|000\rangle +|111\rangle )(|000\rangle +|111\rangle )$

$+{\frac {\beta }{2{\sqrt {2}}}}(|000\rangle -|111\rangle )(|000\rangle -|111\rangle )(|000\rangle -|111\rangle )$