EMt/QIS New Designs and Algorithms for Quantum Error Correction

EMT/QIT--量子纠错的新设计和译码算法摘要李静(蒂芙尼)量子计算机可能会为爆炸性增长的信息数据和日益迫切的解决复杂和综合问题(如因式分解和离散问题)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，这是一种数学-物理机制，可以防止不必要的演化导致脆弱的量子态，从而使量子处理设备的健壮实现和在嘈杂的量子通道上的可靠传输成为可能。概念验证和第一个建设性的量子纠错码直到1995年才出现，这项研究仍处于初级阶段。这项研究需要认真的理论和算法研究，以提高量子纠错的状态。新的方法将为系统地构造更好的量子稳定器码，特别是无限制的低密度奇偶校验(LDPC)稳定器码提供一个刷新的角度。将设计新的高效译码算法来恢复几个现有的稳定子码。将开发新的概念和工具来分析和评估量子码。研究中使用的工具是高度数学-物理的，涉及到量子力学、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.