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The '''Shor Code''' is an ] technique used to protect a ] against single ] errors. The '''Shor Code''' is an ] technique used to protect a ] against single ] errors. Published in by ] it is the first example of a quantum error correcting code.<ref name="Sh95">
{{cite journal
| author = ]
| title = Scheme for reducing decoherence in quantum computer memory
| journal = Physical Review A
| volume = 52
| pages = 493-496
| date = 1995
⚫ | url = http://www.theory.caltech.edu/people/preskill/ph229/shor_error.ps
| format = PS}}}
</ref> Due to the ] classical error correction, which relies on duplicating classical information, could not be applied. This limitation was overcome with the Shor code.


== The code == == The code ==
We map the ] <math>\alpha |0\rangle + \beta|1\rangle</math> to the nine ] state We map the basis states <math>|0\rangle</math>, <math>|1\rangle</math> as follows
:<math>\frac{\alpha}{2\sqrt{2}} (|000\rangle + |111\rangle) (|000\rangle + |111\rangle) (|000\rangle + |111\rangle)</math> :<math>|0\rangle\rightarrow\frac{1}{2\sqrt{2}} (|000\rangle + |111\rangle) (|000\rangle + |111\rangle) (|000\rangle + |111\rangle)</math>
:<math> + \frac{\beta}{2\sqrt{2}} (|000\rangle - |111\rangle) (|000\rangle - |111\rangle) (|000\rangle - |111\rangle) </math> :<math>|1\rangle\rightarrow\frac{1}{2\sqrt{2}} (|000\rangle - |111\rangle) (|000\rangle - |111\rangle) (|000\rangle - |111\rangle) </math>


==External links== ==References==
{{reflist}}
⚫ ]]


] ]

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The Shor Code is an error correction technique used to protect a quantum computer against single qubit errors. Published in by Peter Shor it is the first example of a quantum error correcting code. Due to the No-cloning theorem classical error correction, which relies on duplicating classical information, could not be applied. 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: 493–496.}
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