Shor code

The Shor Code is an error correction technique used to protect a quantum computer against single qubit errors. Published in 1995 by Peter Shor, it is the first example of a quantum error correcting code. Classical error correction techniques, which rely on redundancy, are not applicable to quantum information due to the No-cloning theorem. This limitation was overcome with the Shor code.

The code

We map the basis states $|0\rangle$, $|1\rangle$ as follows

$|0\rangle \rightarrow {\frac {1}{2{\sqrt {2}}}}(|000\rangle +|111\rangle )(|000\rangle +|111\rangle )(|000\rangle +|111\rangle )$

$|1\rangle \rightarrow {\frac {1}{2{\sqrt {2}}}}(|000\rangle -|111\rangle )(|000\rangle -|111\rangle )(|000\rangle -|111\rangle )$