Algebraic quantum codes: linking quantum mechanics and discrete mathematics

IF 0.9 Q3 COMPUTER SCIENCE, THEORY & METHODS
M. Grassl
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引用次数: 10

Abstract

We discuss the connection between quantum error-correcting codes (QECCS) and algebraic coding theory. We start with an introduction to the relevant concepts of quantum mechanics, including the general error model. A quantum error-correcting code is a subspace of a complex Hilbert space, and its error-correcting properties are characterized by the Knill-Laflamme conditions. Using the stabilizer formalism, we illustrate how QECCs for can be constructed using techniques from algebraic coding theory. We also sketch how the information obtained via a quantum measurement can be interpreted as syndrome of the related classical code. Additionally, we present secondary constructions for QECCs, leading to propagation rules for the parameters of QECCs. This includes the puncture code by Rains and construction X for quantum codes.
代数量子密码:连接量子力学和离散数学
讨论了量子纠错码与代数编码理论之间的联系。我们首先介绍量子力学的相关概念,包括一般误差模型。量子纠错码是复希尔伯特空间的一个子空间,其纠错性质由Knill-Laflamme条件表征。利用稳定器的形式,我们说明了如何使用代数编码理论的技术来构造qecc。我们还概述了通过量子测量获得的信息如何被解释为相关经典码的综合征。此外,我们提出了QECCs的二级结构,得到了QECCs参数的传播规则。这包括Rains的穿刺代码和用于量子代码的构造X。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
International Journal of Computer Mathematics: Computer Systems Theory
International Journal of Computer Mathematics: Computer Systems Theory Computer Science-Computational Theory and Mathematics
CiteScore
1.80
自引率
0.00%
发文量
11
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