Optimal Control of Open Quantum Systems

在技术方面，有几个新兴的和令人兴奋的发展来理解和利用表现出独特量子特性的系统。例子包括量子传输，其中纳米材料和分子是电子设备的核心部分，以及量子计算，其中量子门的操作被执行以解决经典计算机难以解决的科学计算问题。这种量子特性通常由与周围环境隔离的封闭量子系统来描述。但实际上，所有量子系统都是开放的，与环境的相互作用是不可避免的。这些相互作用往往是连续发生的，它们导致了复杂的不可逆量子动力学，这也对控制量子系统执行特定任务提出了巨大的挑战。 该项目将支持2名研究生和1名本科生的3年的项目。该项目将开发开放的量子模型，其中环境的影响是隐含的。 几个一致性条件的实施，以确保模型的准确性，使减少的模型具有的准确性，是完全的动态。该模型将与最优控制框架相结合，以实现外部控制，从而使量子系统能够保持其量子特性并执行特定任务。将构造鲁棒和有效的数值算法来解决最优控制问题。总体目标是开发可靠的计算工具，更好地理解开放量子系统的动力学特性，并提供利用量子特性的策略。该奖项反映了NSF的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

On the technological front, there have been several emerging and exciting developments to understand and utilize systems that exhibit unique quantum properties. Examples include quantum transport, where nano-materials and molecules are central parts of electronic devices, and quantum computing, where the operations of quantum gates are carried out to solve scientific computing problems that are difficult for classical computers. Such quantum properties are often described by a closed quantum system that is isolated from its surrounding environment. But in practice, all quantum systems are open, and the interactions with their environments are inevitable. The interactions often occur continuously and they lead to complicated irreversible quantum dynamics, which also poses a great challenge for the control of the quantum system to carry out specific tasks. This project will support 2 graduate students and 1 undergraduate student each of the 3 years of the project. This project will develop open quantum models, where the influence of the environment is incorporated implicitly. Several consistency conditions are enforced to ensure the model accuracy so that the reduced model has an accuracy that is comparable to the full dynamics. The model will be combined with an optimal control framework to enable an external control so that the quantum system can retain its quantum properties and perform specific tasks. Robust and efficient numerical algorithms will be constructed to solve the optimal control problem. The overall objective is to develop reliable computational tools, better understand the dynamic properties of open quantum systems, and provide strategies to utilize quantum properties.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.