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Shor code

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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 ⟩ {\displaystyle |0\rangle } , | 1 ⟩ {\displaystyle |1\rangle } as follows

| 0 ⟩ → 1 2 2 ( | 000 ⟩ + | 111 ⟩ ) ( | 000 ⟩ + | 111 ⟩ ) ( | 000 ⟩ + | 111 ⟩ ) {\displaystyle |0\rangle \rightarrow {\frac {1}{2{\sqrt {2}}}}(|000\rangle +|111\rangle )(|000\rangle +|111\rangle )(|000\rangle +|111\rangle )}
| 1 ⟩ → 1 2 2 ( | 000 ⟩ − | 111 ⟩ ) ( | 000 ⟩ − | 111 ⟩ ) ( | 000 ⟩ − | 111 ⟩ ) {\displaystyle |1\rangle \rightarrow {\frac {1}{2{\sqrt {2}}}}(|000\rangle -|111\rangle )(|000\rangle -|111\rangle )(|000\rangle -|111\rangle )}

References

  1. Peter Shor (1995). "Scheme for reducing decoherence in quantum computer memory" (PS). Physical Review A. 52: R2493 – R2496.}
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