Shor code

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.cite journal
author = Peter Shor
title = Scheme for reducing decoherence in quantum computer memory
journal = Physical Review A: Atomic. Molecular, and Optical Physics
volume = 52
pages = R2493–R2496
date = 1995
url = http://www.theory.caltech.edu/people/preskill/ph229/shor_error.ps
format = PS}] 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 $|0\; angle$, $|1\; angle$ as follows:$|0\; angle\; ightarrowfrac\{1\}\{2sqrt\{2\; (|000\; angle\; +\; |111\; angle)\; (|000\; angle\; +\; |111\; angle)\; (|000\; angle\; +\; |111\; angle)$:$|1\; angle\; ightarrowfrac\{1\}\{2sqrt\{2\; (|000\; angle\; -\; |111\; angle)\; (|000\; angle\; -\; |111\; angle)\; (|000\; angle\; -\; |111\; angle)$

References