论文标题
量子误差校正代码及其几何形状
Quantum error-correcting codes and their geometries
论文作者
论文摘要
这是一篇说明性文章，旨在向读者介绍量子误差校正的基本数学和几何形状。存储在量子粒子上的信息受环境的噪声和干扰。量子误差校正代码允许否定这些效果，以便成功恢复原始量子信息。我们简要描述了必要的量子机械背景，以便能够了解量子误差校正的工作原理。我们继续构建量子代码：首先是Qubit稳定器代码，然后是Qubit非稳定器代码，最后具有更高的局部维度代码。我们将深入研究这些代码的几何形状。这样一来，人们就可以有效地推导代码的参数，推断具有相同参数的代码之间的不等值，并为推论某些参数的可行性提供了有用的工具。我们还包括有关量子最大距离可分离代码和量子MacWilliams身份的部分。
This is an expository article aiming to introduce the reader to the underlying mathematics and geometry of quantum error correction. Information stored on quantum particles is subject to noise and interference from the environment. Quantum error-correcting codes allow the negation of these effects in order to successfully restore the original quantum information. We briefly describe the necessary quantum mechanical background to be able to understand how quantum error-correction works. We go on to construct quantum codes: firstly qubit stabilizer codes, then qubit non-stabilizer codes, and finally codes with a higher local dimension. We will delve into the geometry of these codes. This allows one to deduce the parameters of the code efficiently, deduce the inequivalence between codes that have the same parameters, and presents a useful tool in deducing the feasibility of certain parameters. We also include sections on quantum maximum distance separable codes and the quantum MacWilliams identities.
