Statistical Theory of Quantum Controlled Dynamics

量子控制动力学统计理论

• 批准号: 2438034
• 金额: --
• 依托单位: University of Nottingham
• 依托单位国家: 英国
• 项目类别: Studentship
• 财政年份: 2020
• 资助国家: 英国
• 起止时间: 2020 至 无数据
• 项目状态: 未结题
• 来源: https://gtr.ukri.org/projects?ref=studentship-2438034
• 关键词: Statistical; Theory; Quantum; Controlled; Dynamics

The modelling, estimation and identification of quantum open systems are key enabling tools for a broad array of quantum engineering tasks such as state preparation and tomography, quantum feedback control, error correction, and high precision metrology. As quantum devices and measurement techniques become more sophisticated, experimenters have to interpret increasingly complex measurement datasets to obtain accurate information about the system's state and dynamics. Therefore, there is a need for expanding the mathematical foundations of quantum statistics beyond the traditional i.i.d. framework of state estimation, in order to tackle new inference problems involving correlated states of interacting systems, with realistic modelling of noise, and optimal experimental design. The goal of this PhD project is to build a statistical theory of quantum stochastic processes in the framework of quantum input-output (I-O) dynamics. The I-O formalism describes the system of interest (e.g. quantum device, or sensor) as a black-box interacting with the outside world via input and output channels. The central premise is that information about the dynamics is continuously encoded into the output state, and this resource can be exploited to perform tasks such as system identification, estimation and quantum enhanced metrology.

量子开放系统的建模、估计和识别是一系列量子工程任务的关键支持工具，如状态准备和断层扫描、量子反馈控制、误差校正和高精度计量。随着量子设备和测量技术变得越来越复杂，实验者必须解释越来越复杂的测量数据集，以获得有关系统状态和动态的准确信息。因此，有必要扩展量子统计的数学基础，超越传统的状态估计的i.i.d框架，以解决涉及相互作用系统相关状态的新推理问题，并具有现实的噪声建模和最佳实验设计。本博士项目的目标是在量子输入-输出（I-O）动力学框架下建立量子随机过程的统计理论。I-O形式主义将感兴趣的系统（例如量子设备或传感器）描述为通过输入和输出通道与外部世界交互的黑盒。中心前提是关于动态的信息被连续地编码到输出状态中，并且该资源可以被利用来执行诸如系统识别、估计和量子增强计量等任务。