Quantum Computing and Error Correction

Details Quantum Computing and Error Correction Quantum Computing and Error Correction

2003-04-02

arxiv.org/abs/quant-ph/0304016v2

A. Steane in "Decoherence and its implications in quantum computation and information transfer", Gonis and Turchi, eds, pp.284

Physics

Quantum Physics

12 pages, a very simple tutorial introduction to error correction, with emphasis on avoiding misconceptions regarding the trea

Scientific paper

The main ideas of quantum error correction are introduced. These are encoding, extraction of syndromes, error operators, and code construction. It is shown that general noise and relaxation of a set of 2-state quantum systems can always be understood as a combination of Pauli operators acting on the system. Each quantum error correcting code allows a subset of these errors to be corrected. In many situations the noise is such that the remaining uncorrectable errors are unlikely to arise, and hence quantum error correction has a high probability of success. In order to achieve the best noise tolerance in the presence of noise and imprecision throughout the computer, a hierarchical construction of a quantum computer is proposed.

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