CAREER: Applications of Quantum Information Theory and Symmetry Principles in Quantum Physics

在过去的几十年里，量子信息科学（QIS）的研究人员已经发现，自然界的量子特性，如纠缠和量子相干性，可以用来增强计算机、传感器和其他信息处理设备的能力。量子信息系统的快速发展也对物理学的其他领域产生了深远的影响。从高能物理到凝聚态理论，在这一领域发展起来的思想、技术和概念框架产生了革命性的影响。在这个项目中，首席研究员将解决一系列对理论物理和量子计算至关重要的相关QIS问题。从广义上讲，本项目旨在研究存在对称性和守恒律的复合量子力学系统的行为和性质。除了在量子信息系统中的应用外，该项目还探讨了这项研究在物理学其他领域的意义。具体来说，该项目研究了量子现象如何增强或影响热机的性能。该项目还为物理、工程和其他计算科学领域的学生提供了教育机会。该项目包括两个主要部分：第一部分全面研究局部对称量子电路（LSQC）的性质和应用，特别是随机LSQC。刻画LSQC的问题等价于确定局部对称哈密顿量产生的幺正时间演化的一般特征。这对于理解具有守恒电荷的多体系统的混沌和热化是有用的。尽管LSQC的某些方面已经在量子混沌和对称保护拓扑（SPT）秩序的背景下进行了研究，但对这类电路的性质仍然缺乏广泛而精确的理解。初步的研究揭示了这个框架的意想不到的特征和丰富的数学结构。预期的结果在量子控制、量子热力学、SPT秩序和量子引力等领域具有应用和意义。本项目第二部分从量子信息论的角度研究量子热力学，更具体地说，从近十年来蓬勃发展的热力学资源理论的角度研究量子热力学。该项目旨在解决现有框架的一些重要缺陷，即在量子热力学的资源理论框架中建立统一的功和相干蒸馏理论，并提出探索该理论真正量子特征的实验建议。该奖项反映了美国国家科学基金会的法定使命，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。

Over the last few decades, researchers in Quantum Information Science (QIS) have discovered that quantum properties of nature, such as entanglement and quantum coherence, can be used to enhance the power of computers, sensors, and other information-processing devices. The rapid progress of QIS has also had profound impacts on the rest of physics. From high-energy physics to condensed matter theory, ideas, techniques, and conceptual frameworks developed in this field have had revolutionary effects. In this project, the Principal Investigator will address a series of related QIS questions of critical importance to both theoretical physics and quantum computing. Broadly speaking, this project aims to investigate the behavior and properties of composite quantum-mechanical systems in the presence of symmetries and conservation laws. Besides applications in QIS, the project also explores the implications of this study in other areas of Physics. Specifically, the project investigates how quantum phenomena can enhance or affect the performance of thermal machines. This project also provides educational opportunities for a range of students in physics, engineering, and other computational sciences. The project consists of two main parts: The first part fully investigates the properties and applications of Local Symmetric Quantum Circuits (LSQC) and, specifically, random LSQC. The problem of characterizing LSQC is equivalent to determining the general features of the unitary time evolutions generated by local symmetric Hamiltonians. This is useful, e.g., for understanding chaos and thermalization of many-body systems with conserved charges. Although certain aspects of LSQC have been previously studied in the context of quantum chaos and Symmetry-Protected Topological (SPT) order, a broad and precise understanding of the properties of this family of circuits is still missing. A preliminary study has revealed unexpected features and the rich mathematical structure of this framework. The anticipated results have applications and implications in areas such as quantum control, quantum thermodynamics, SPT order, and quantum gravity. The second part of this project investigates quantum thermodynamics from the point of view of quantum information theory, and more specifically, the resource-theoretic approach to thermodynamics, which has been flourishing in the last ten years. The project aims to address some important shortcomings of the existing framework, namely to develop a unified theory of work and coherence distillation in the resource-theoretic framework of quantum thermodynamics, as well as experimental proposals for probing genuine quantum features of this theory.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.