EMt/QIS New Designs and Algorithms for Quantum Error Correction

量子计算机将有可能为信息数据的爆炸性增长和日益迫切的解决复杂和综合问题（如因子分解和离散问题）的需求提供终极解决方案。对量子计算和通信至关重要的是量子纠错，这是一种物理机制，可以防止脆弱的量子态发生不必要的演化，从而实现量子处理设备的鲁棒实现和噪声量子信道上的可靠传输。直到1995年，概念证明和第一个构造性量子纠错码才出现，研究仍处于起步阶段。这一研究需要认真的理论和算法研究，以提高量子纠错的状态。新的方法将被研究，以提供一个新的角度，更好的家庭的量子稳定器码，特别是无限制的低密度奇偶校验（LDPC）稳定器码的系统建设。新的和有效的解码算法将被设计来恢复几个现有的稳定器码。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物理的，涉及量子力学，量子信息理论，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.