| Revision as of 19:50, 14 May 2009 editCitation bot (talk | contribs)Bots5,457,890 editsm Citation maintenance. Formatted: doi. You can use this bot yourself! Please report any bugs.← Previous edit | Latest revision as of 23:18, 10 May 2021 edit undoCewbot (talk | contribs)Bots8,032,745 editsm Fix broken anchor: Fix broken anchor: 2021-02-28T19:02:47Z #The Shor code→Quantum error correction#Shor code, 2021-02-28T19:02:47Z #The_Shor_code→Quantum error correction#Shor codeTag: Redirect target changed | ||
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| The '''Shor Code''' is an ] technique used to protect a ] against single ] errors. Published in 1995 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: Atomic. Molecular, and Optical Physics | |||
| | volume = 52 | |||
| | pages = R2493–R2496 | |||
| | year = 1995 | |||
| | url = http://www.theory.caltech.edu/people/preskill/ph229/shor_error.ps | |||
| | format = PS | |||
| | doi = 10.1103/PhysRevA.52.R2493}} | |||
| </ref> Classical error correction techniques, which rely on redundancy, are not applicable to ] due to the ]. This limitation was overcome with the Shor code. | |||
| {{R to section}} | |||
| == 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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