CAREER: New Frontiers in Continuous-time Open Quantum Systems

连续时间量子系统的动力学在量子物理、量子化学、量子生物学和量子信息科学中普遍存在。在这些领域中，所有现实的量子系统都以不可忽视的方式耦合到一个不可控的环境中。这些系统被称为开放量子系统。然而，大多数对量子系统的研究都集中在一个理想化的模型上，在这个模型中，系统与环境隔离，称为闭合量子系统。从计算角度研究这些现实的开放量子系统仍然是一个重大挑战，因为现有的技术工具和模型主要是为封闭系统设计的。为了应对这一挑战，本项目将开发新的数学框架和量子计算技术来对开放量子系统的行为进行建模、分析和表征。该项目将在几个重要方向推进连续时间开放量子系统的研究，包括模拟其动力学、利用其计算能力和表征其计算能力。首要目标是建立这类系统的计算和数学处理方法，以推动量子计算的研究远远超出哈密尔顿制度，应用更广泛。该项目的具体目标包括：开发模拟开放量子系统的新技术；发现连续时间开放量子系统的进一步算法应用；确定不断发展的开放量子系统的物理含义；以及表征开放量子系统的计算能力。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

The dynamics of quantum systems in continuous time are ubiquitous in quantum physics, quantum chemistry, quantum biology, and quantum information science. In these fields, all realistic quantum systems are coupled to an uncontrollable environment in a non-negligible way. Thesesystems are known as open quantum systems. However, the majority of studies of quantum systems have focused on an idealized model where the systems are isolated from the environment, referred to as closed quantum systems. A significant challenge remains in studying these realistic open quantum systems from a computational perspective, as existing technical tools and models are primarily designed for closed systems. To address this challenge, this project will develop novel mathematical frameworks and quantum computing techniques to model, analyze, and characterize the behavior of open quantum systems.This project will advance the study of continuous-time open quantum systems in several important directions, including simulating their dynamics, harnessing their computational powers, and characterizing their computational capabilities. The overarching goal is to establish the computational and mathematical treatments of such systems to push the study of quantum computation far beyond the Hamiltonian regime for broader applications. Specific goals of this project include: developing novel techniques for simulating open quantum systems; discovering further algorithmic applications of continuous-time open quantum systems; identifying the physical implications of evolving open quantum systems; and characterizing the computational capabilities of open quantum systems.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.