Establishing the number of distinct stabilizer bases for a quantum qudit error-correcting code

3rd International Conference on Mathematical Modeling in Physical Sciences

物理学;数学

Wilmott, C.M.^1

Department of Mathematics and Physics, Nottingham Trent University, Nottingham

NG11 8NS, United Kingdom^1

关键词: Error correcting code;    Linear codes;    Parametrisation;    Quantum codes;    Stabilizer codes;    Stabilizer formalism;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/574/1/012096/pdf
DOI  :  10.1088/1742-6596/574/1/012096

来源: IOP

【 摘 要 】

The class of quantum codes called stabilizer codes is increasingly well-understood. The premise of the stabilizer formalism is that a quantum code can be efficiently described by a subgroup of its error group, and, interestingly, the stabilizer formalism permits correspondences with classical linear codes. In this paper, we examine one such correspondence, and we shall use this to establish the number of distinct stabilizer codes that exist for a fixed parametrisation.