One of the central tasks in quantum error-correction is to construct quantum codes that have good parameters. In this paper, we construct three new classes of quantum MDS codes from classical Hermitian self-orthogonal generalized Reed-Solomon codes. We also present some classes of quantum codes from matrix-product codes. It turns out that many of our quantum codes are new in the sense that the ...

In this paper we demonstrate how data encoded in a five-qubit quantum error correction code can be converted, fault-tolerantly, into a seven-qubit Steane code. This is achieved by progressing through a series of codes, each of which fault-tolerantly corrects at least one error. Throughout the conversion the encoded qubit remains protected. We found, through computational search, that the method...

Systems of forward-looking linear decision rules can be formulated as vector \rational" error correction models. The closed-form solution of the restricted error corrections is derived, and a full-information estimator is suggested. The error correction format indicates that the assumptions of convex adjustment costs and rational expectations impose di erent types of a priori restrictions on th...

The construction of optimal linear block errorcorrecting codes is not an easy problem, for this, many studies describe methods for generating good. That is, even when taking into account the multitude of errors possible for multilevel quantum systems, topological quantum error-correction codes employing. The point of error correcting codes is to control the error rate. Let's say you have a Sing...

We develop a mathematical foundation for operator quantum error correction. This is a new paradigm 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 notion of noiseless subsystems that is not ...