Abstract

SALAS-PERALTA, P. J.. Introduction to error correcting codes in quantum computers. Rev. mex. fís. E [online]. 2006, vol.52, n.2, pp.218-243. ISSN 1870-3542.

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 shall relax this non-realistic assumption, introducing the quantum fault-tolerant concept. The existence of an error threshold permits us to conclude that there is no physical law preventing a quantum computer from being built. An error model based on the depolarising channel will be able to provide a simple estimate of the storage or memory computation error threshold: η_th < 5.2 10^-5. The encoding is made by means of the [[7,1,3]] Calderbank-Shor-Steane quantum code, and Shor's fault-tolerant method is used to measure the stabiliser's generators.

Keywords : Quantum error correcting codes; decoherence; quantum computation.

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