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| 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. | |||
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| == The code == | |||
| {{R with history}} | |||
| We map the basis states <math>|0\rangle</math>, <math>|1\rangle</math> as follows | |||
| :<math>|0\rangle\rightarrow\frac{1}{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> | |||
| ==References== | |||
| {{reflist}} | |||
| ] | |||
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