FET: Small: An Integrated Framework for the Optimal Control of Open Quantum Systems --- Theory, Quantum Algorithms, and Applications

在计算机科学、材料科学、化学工程和量子生物学领域的许多新兴应用广泛依赖于利用底层物理系统表现出的量子属性。这些属性可以通过控制变量进行微调和优化，通常通过操纵外部场来实现。然而，由于量子系统的高维性及其与环境的持续相互作用，通过直接的计算机模拟来确定最优控制变量是一个重大的且尚未解决的挑战。这个项目的主要目标是建立一个全面的数学框架，有效地描述在存在环境噪声的情况下量子系统的动力学。通过开发这种数学描述，研究人员的目标是为构建能够获得此类系统的最优控制参数的高效量子算法铺平道路。除了进行严格的理论分析以确保模型精度和评估算法的复杂性外，该项目还非常重视开发专门为模拟非马尔科夫区域的开放量子系统而定制的高效量子算法。在这样的体制下，量子系统与其环境之间的相互作用发生在可比较的时间尺度上，导致了复杂的动力学，需要新的数学描述。通过关注这一方面，研究人员的目标是解决现实情景带来的挑战，在现实情景中，环境对量子系统的影响不能被视为简单的马尔可夫过程。此外，该项目的一个关键方面是围绕能够准确估计目标函数的梯度的量子算法的设计和实现。这是通过仔细校准测量噪声的统计来实现的，测量噪声的统计在优化过程的复杂性中起着关键作用。该项目包括积极指导本科生从事科学和研究事业。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。

Numerous emerging applications in the fields of computer science, material science, chemical engineering, and quantum biology rely extensively on harnessing the quantum properties exhibited by underlying physical systems. These properties can be fine-tuned and optimized through control variables, typically achieved by manipulating external fields. However, due to the substantial dimensionality of quantum systems and their continuous interactions with the environment, determining the optimal control variables through direct computer simulations has posed a significant and unresolved challenge. The primary objective of this project is to establish a comprehensive mathematical framework that effectively characterizes the dynamics of quantum systems in the presence of environmental noise. By developing this mathematical description, the investigators aim to pave the way for the construction of efficient quantum algorithms capable of obtaining the optimal control parameters for such systems.In addition to conducting rigorous theoretical analyses to ensure model accuracy and evaluate the complexity of algorithms, this project places a significant emphasis on the development of efficient quantum algorithms specifically tailored for simulating open quantum systems in non-Markovian regimes. In such regimes, the interactions between the quantum system and its environment occur on comparable time scales, resulting in intricate dynamics that necessitate novel mathematical descriptions. By focusing on this aspect, the investigators aim to address the challenges posed by realistic scenarios where the influence of the environment on the quantum system cannot be treated as a simple Markovian process. Furthermore, a crucial aspect of this project centers around the design and implementation of quantum algorithms capable of accurately estimating the gradient of objective functions. This is achieved by carefully calibrating the statistics of the measurement noise, which plays a pivotal role in the complexity of the optimization procedure. The project involves active undergraduate student mentoring to pursue careers in science and research.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.