  The goal of this paper is to review the theoretical basis for achieving a
faithful quantum information transmission and processing in the presence of
noise. Initially encoding and decoding, implementing gates and quantum error
correction will be considered error free. Finally we will relax this non
realistic assumption, introducing the quantum fault-tolerant concept. The
existence of an error threshold permits to conclude that there is no physical
law preventing a quantum computer from being built. An error model based on the
depolarizing channel will be able to provide a simple estimation of the storage
or memory computation error threshold: < 5.2 10-5. The encoding is made by
means of the [[7,1,3]] Calderbank-Shor-Steane quantum code and the Shor's
fault-tolerant method to measure the stabilizer's generators is used.
