Approaches to Quantum Error Correction
arXiv:quant-ph/0612185
Abstract
The purpose of this little survey is to give a simple description of the main approaches to quantum error correction and quantum fault-tolerance. Our goal is to convey the necessary intuitions both for the problems and their solutions in this area. After characterising quantum errors we present several error-correction schemes and outline the elements of a full fledged fault-tolerant computation, which works error-free even though all of its components can be faulty. We also mention alternative approaches to error-correction, so called error-avoiding or decoherence-free schemes. Technical details and generalisations are kept to a minimum.
29 pages, 5 figures, survey written for Poincare seminar lecture 19 Nov. 2005. Bookchapter in "Quantum Decoherence", Poincare seminar 2005, Progress in Mathematical Physics series, Birhaeuser, p. 85--123, 2006