High Accuracy, Broadband Simulation of Complex Structures with Quantum Effects, Parallel Fast Algorithm, and Integral Equation Domain Decomposition

尽管经典电磁理论已经存在了150多年，但它的不朽遗产并没有减少。事实上，它融入了如此多的现代技术，以至于在无线通信、计算机技术、生物医学工程和大数据传输等现代世界中不可或缺。最近在电磁学中出现了两个概念。首先是使用20世纪出现的计算机和数学方法来求解高度复杂的电磁学，从而产生了计算电磁学(CEM)领域。第二是研究电磁系统中的量子效应和量子理论(也出现在20世纪)，产生了量子光学等领域，这些领域可能会潜在地影响信息、通信和计算技术，如量子信息、通信、加密和计算。这个项目将结合使用计算电磁学知识来理解与电磁场相互作用的量子系统。这将催生未来量子技术的发展，为以前尚未开发的可能性打开新的大门。该项目将开发计算工具，以满足纳米芯片、纳米光学和量子光学等新兴技术的需求。由于晶体管、光学结构和量子信息系统的小型化，纳米结构中的电磁和量子效应的建模变得越来越重要。但到目前为止，对此类问题进行建模的过高复杂性和计算成本阻碍了它们的精确解决。该方案的目的是开发能够捕捉电路物理、波物理和量子效应的快速计算算法，以便有效地模拟电路-量子电动力学(C-QED)系统。这将需要开发多尺度、多物理的解算器，同时通过使用并矢格林S函数来结合量子效应。生成的代码将根据实验结果进行验证。如果成功，这项研究将为如何使用快速、稳定和准确的计算算法分析C-QED系统开辟新的前沿。这反过来将使C-QED的新发现成为可能，这可能会影响量子计算和量子信息处理。计划开展广泛的教育宣传活动，包括让K-12和本科生参与，开发可视化工具和视频讲座，向公众传播成果。

Even though classical electromagnetic theory has been around for over 150 years, its enduring legacy has not diminished. In fact, it finds its way into so many modern day technologies that it is indispensable in the modern world such as in wireless communications, computer technologies, bio-medical engineering, and big data transfer. Two concepts in electromagnetics have emerged in recent past. First is the use of computers and mathematical methods that have appeared in the 20th century to solve highly complex electromagnetics, giving rise to the field of computational electromagnetics (CEM). Second is the study of quantum effects and quantum theory (that also appeared in the 20th century) in electromagnetic systems giving rise to fields like quantum optics that can potentially impact information, communications, and computation technologies such as quantum information, communication, encryption, and computation. This project will combine the use of computational electromagnetics knowledge to understand quantum systems that interact with electromagnetic fields. This will engender the development of future quantum technologies that open new gateways to previously untapped possibilities.This project will develop computational tools to meet the demands of emerging technologies in nano chip, nano optics, and quantum optics. The modeling of electromagnetic and quantum effects in nanostructures has become increasingly important due to the miniaturization of transistors, optical structures, and quantum information systems. But the exorbitant complexity and computational cost of modeling such problems have precluded their precise solution so far. The objective of this proposal is to develop fast computational algorithms that can capture circuit physics, wave physics and quantum effects in order to effectively simulate circuit-quantum electrodynamics (C-QED) systems. This will entail the development of multi-scale, multi-physics solvers while incorporating quantum effects through the use of the dyadic Green?s function. The resulting codes will be validated against experimental results. If successful, this research will open up a new frontier on how C-QED systems can be analyzed using fast, stable and accurate computational algorithms. This in turn would enable new discoveries in C-QED that could impact quantum computing and quantum information processing. Extensive educational outreach activities are planned including the involvement of K-12 and undergraduate students, and the development of visualization tools and video lectures to disseminate results to the public.