Algebraic Quantum Error Correction Codes

Authors: Ming-Chung Tsai, Kuan-Peng Chen, Zheng-Yao

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.

Keywords: Quotient-Algebra Partition, Codeword Spinors, Basis Codewords, Syndrome Spinors

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1060485

References:

[1] Z.-Y. Su (2006), quant-ph/0603190.
[2] I. L. Chuang, et al. (2008), quant-ph/0803.3232.
[3] M.-C. Tsai, K.-P. Chen, W.-C. Su and Z.-Y. Su., "Additive and Nonadditive Quantum Codes", to appear.