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Operator Quantum Error Correction. (English) Zbl 1152.81760
Summary: This paper is an expanded and more detailed version of a recent work in which the Operator Quantum Error Correction formalism was introduced. This is a new scheme for the error correction of quantum operations that 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, and relies on a generalized mathematical framework for noiseless subsystems that applies to arbitrary quantum operations. We also discuss a number of examples and introduce the notion of “unitarily noiseless subsystems”.

81P68 Quantum computation
14D06 Fibrations, degenerations in algebraic geometry