Collaborative research: Problems in quantum error correction and quantum control

本项目是对量子纠错和量子控制的分析研究。其目的是发展理论和计算技术，以构造具有一般噪声的量子信道的纠错码，基于矩阵和李理论的考虑。量子计算是一个快速增长的多学科研究领域。如果能够建造大规模量子计算机，它们将能够解决超出当前经典计算机能力范围的重要问题。尽管量子计算机的发展带来了深远的影响，但仍有许多悬而未决的理论问题和实验挑战必须克服。例如，量子计算机必须采用一种方法来纠正数据错误，这些错误是由于量子系统与其环境之间不可避免的不可控相互作用造成的，这种现象被称为退相干。该项目的主要目标之一是进一步开发量子通道中的纠错算法。该项目还将研究量子控制理论中的其他数学问题。

This project is an analytical study of quantum error correction and quantum control. The aim is to develop theoretical and computational techniques to construct error correction codes for quantum channels with general noise, based on matrix- and Lie-theoretic considerations.Quantum computing is a rapidly-growing area of multidisciplinary research. If large-scale quantum computers can be built, they will be able to solve important problems that lie beyond the capabilities of current classical computers. While the development of quantum computers promises far-reaching implications, there are still many open theoretical questions and experimental challenges that must be overcome. For example, a quantum computer must employ a method to correct data errors that result from the inevitable uncontrollable interaction between a quantum system and its environment, a phenomenon known as decoherence. One of the main goals of this project is to further develop algorithms for error correction in a quantum channel. The project will also investigate other mathematical problems in quantum control theory.