An Introduction to Quantum Error Correction

Details An Introduction to Quantum Error Correction An Introduction to Quantum Error Correction

2000-04-18

arxiv.org/abs/quant-ph/0004072v1

in Quantum Computation: A Grand Mathematical Challenge for the Twenty-First Century and the Millennium, ed. S. J. Lomonaco, Jr

Physics

Quantum Physics

15 pages, AMSLaTeX, talk given at AMS Short Course on Quantum Computation

Scientific paper

Quantum states are very delicate, so it is likely some sort of quantum error correction will be necessary to build reliable quantum computers. The theory of quantum error-correcting codes has some close ties to and some striking differences from the theory of classical error-correcting codes. Many quantum codes can be described in terms of the stabilizer of the codewords. The stabilizer is a finite Abelian group, and allows a straightforward characterization of the error-correcting properties of the code. The stabilizer formalism for quantum codes also illustrates the relationships to classical coding theory, particularly classical codes over GF(4), the finite field with four elements.

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