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

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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.