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Algebraic Quantum Error Correction Codes
Abstract:A systematic and exhaustive method based on the group structure of a unitary Lie algebra is proposed to generate an enormous number of quantum codes. With respect to the algebraic structure, the orthogonality condition, which is the central rule of generating quantum codes, is proved to be fully equivalent to the distinguishability of the elements in this structure. In addition, four types of quantum codes are classified according to the relation of the codeword operators and some initial quantum state. By linking the unitary Lie algebra with the additive group, the classical correspondences of some of these quantum codes can be rendered.
Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1060485Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF
 Z.-Y. Su (2006), quant-ph/0603190.
 I. L. Chuang, et al. (2008), quant-ph/0803.3232.
 M.-C. Tsai, K.-P. Chen, W.-C. Su and Z.-Y. Su., "Additive and Nonadditive Quantum Codes", to appear.