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| year = 1995 | year = 1995
| url = http://www.theory.caltech.edu/people/preskill/ph229/shor_error.ps | url = http://www.theory.caltech.edu/people/preskill/ph229/shor_error.ps
| format = 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. </ref> Classical error correction techniques, which rely on redundancy, are not applicable to ] due to the ]. This limitation was overcome with the Shor code.


Revision as of 19:50, 14 May 2009

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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: Atomic. Molecular, and Optical Physics. 52: R2493 – R2496. doi:10.1103/PhysRevA.52.R2493.
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