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.[1] 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.

[edit] The code

We map the basis states |0\rangle, |1\rangle as follows

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

[edit] 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. }