多层级联量子码的稳定子理论研究

项目名称： 多层级联量子码的稳定子理论研究

项目编号： No.61301172

项目类型： 青年科学基金项目

立项/批准年度： 2014

项目学科： 无线电电子学、电信技术

项目作者： 王云江

作者单位： 西安电子科技大学

项目金额： 26万元

中文摘要： 量子纠错码是实现可信量子通信和可信量子计算的关键。而如何构造具有优良纠错能力，且具有较低编、译码复杂度的纠错码则一直是编码领域的核心问题。考虑到多层级联码在经典信息系统中的成功，本项目拟基于量子码的稳定子理论，深入研究码的多层级联架构在量子纠错码中的应用。具体包括: (1) 多层级联量子码的稳定子及其相应的逻辑操作算子的构建。(2) 多层级联量子码的参数推导（包括可达码率和最小码距）, 给出相应的理论证明。(3) 构造"好"的多层级联量子码，使其在码参数，以及编、译码复杂度方面取得良好平衡。言而总之，我们希望通过建立多层级联码的稳定子理论，提供一个新的视角来深入理解这种具有多层级联结构的量子码，给我们系统的设计和构造好的量子纠错码带来新的启示和思路，从而降低可信量子信息处理所需的时间和空间资源，为可信量子通信和量子计算提供保障。

中文关键词： 量子纠错码；稳定子；多层级联；；

英文摘要： Quantum error-correcting codes are necessary to reliable quantum communication and reliable quantum computation, but constructing powerful codes with low complexity in encoding and decoding is evidently the central question of coding theory. Considering the success of multilevel concatenated codes in classical information system, in this project, we are planing to introduce the multilevel concatenation into the quantum coding theory based on the stabilizer formalism. More precisely, we are going to explore: (1) The constitution of the generators and logical operators associated with the stabilizers for multilevel concatenated quantum codes (MCQCs). (2) Derive the parameters of the resultant MCQCs (such as the achievable rate and the minimal distance) and give corresponding poofs. (3) Construct MCQCs which have good trade-off among rate, distance, encoding and decoding costs. Summary, we are aiming to develop the stabilizer formalism for MCQCs, thereby offering a new perspective for the MCQC framework as well as a powerful and systematic technique for constructing good stabilizer codes to reduce requisite space and time resources for reliable quantum information processing, thus providing a strong support for the reliable quantum communication and reliable quantum computation.

英文关键词： Quantum error correction；Stabilizer；multi-level concatenation；；