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Stabilizer Code

A stabilizer code on n qubits is a quantum error-correcting code that is the common +1 eigenspace of an abelian group S contained in the n-qubit Pauli group, with -I not in S. The group S is the quantum stabilizer group of the quantum error-correcting code.

If S has n-k independent generators, the code encodes k logical qubits and has dimension 2^k. Error detection and correction can be studied through commutation with the stabilizer generators and the Knill-Laflamme conditions.

See also

Abelian Group, Knill-Laflamme Conditions, Pauli Group, Quantum Error-Correcting Code, Qubit

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References

Gottesman, D. "Stabilizer Codes and Quantum Error Correction." PhD thesis. Pasadena, CA: California Institute of Technology, 28 May 1997. https://arxiv.org/abs/quant-ph/9705052.Nielsen, M. and Chuang, I. Quantum Computation and Quantum Information. Cambridge, England: Cambridge University Press, 2000.

Cite this as:

Weisstein, Eric W. "Stabilizer Code." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/StabilizerCode.html

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