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A Unified and Generalized Approach to Quantum Error Correction

David Kribs·Raymond Laflamme·David Poulin
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Abstract

We present a unified approach to quantum error correction, called operator quantum error correction. This scheme relies on a generalized notion of noiseless subsystems that is not restricted to the commutant of the interaction algebra. We arrive at the unified approach, which incorporates the known techniques -- i.e. the standard error correction model, the method of decoherence-free subspaces, and the noiseless subsystem method -- as special cases, by combining active error correction with this generalized noiseless subsystem method. Moreover, we demonstrate that the quantum error correction condition from the standard model is a necessary condition for all known methods of quantum error correction.

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David Kribs, Raymond Laflamme, David Poulin. 2004-12-14. A Unified and Generalized Approach to Quantum Error Correction. https://doi.org/10.1103/physrevlett.94.180501

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