EMt/QIS New Designs and Algorithms for Quantum Error Correction

摘要李静（Tiffany）量子计算机将可能为信息数据的爆炸式增长以及解决复杂和综合问题（如因式分解和离散问题）日益紧迫的需求提供最终的解决方案。对量子计算和通信至关重要的是量子纠错，这是一种数学-物理机制，可以防止脆弱的量子态发生不必要的演变，从而实现量子处理设备的健壮实现和在有噪声的量子信道上的可靠传输。概念验证和第一个建设性的量子纠错码直到1995年才出现，研究仍处于起步阶段。这项研究需要认真的理论和算法研究，以推进量子纠错的状态。研究新的方法，为更好的量子稳定码族，特别是无限制低密度奇偶校验（LDPC）稳定码的系统构建提供一个新的角度。新的和有效的解码算法将被设计来恢复几个现有的稳定码。将开发新的概念和工具来分析和评估量子代码。研究中使用的工具是高度数学物理的，涉及量子力学、量子信息论、线性代数、欧几里得/射影几何、矩阵理论、图论和凸优化。

EMT/QIT -- New Designs and Decoding Algorithms for Quantum Error CorrectionAbstractJing Li (Tiffany)Quantum computers will likely provide the ultimate cure for the explosive growth of information data and the increasingly pressing demand to solve complex and comprehensive problems (such as factoring and discrete problems). Of critical importance to quantum computation and communication is quantum error correction, the mathematical-physical mechanism that protests the fragile quantum states from unwanted evolutions, thus enabling robust implementation of quantum processing devices and reliable transmission over noisy quantum channels. Proof-of-concept and the first constructive quantum error correction code did not appear until 1995, and the research is still at its infancy. This research entails serious theoretic and algorithmic study to advance the state of quantum error correction. New methods will be investigated to provide a refreshing angle to the systematic construction of better families of quantum stabilizer codes and especially unrestricted low-density parity-check (LDPC) stabilizer codes. New and efficient decoding algorithms will be designed to revive several existing stabilizer codes. New concepts and tools will be developed to analyze and evaluate quantum codes. The tools used in the research is highly mathematical-physical, and involve quantum mechanics, quantum information theory, linear algebra, Euclidean/projective geometry, matrix theory, graph theory and convex optimization.