RTG: The Mathematics of Quantum Information Science

量子信息科学（QIS）旨在利用物质在原子水平上的独特特性，开发新的计算和通信方法。这包括密码学的进步、更快的计算速度以及对原子水平上发生的自然过程的更好理解。由于其广泛的影响，QIS涉及国家利益的许多领域，包括网络安全、制药、金融服务、医疗保健等。量子信息系统涉及与经典信息科学根本不同的逻辑，该领域（如量子算法和量子密码学等领域）的进步往往依赖于创造性的数学突破。此外，对于各种背景和技能水平的学生和导师来说，数学是QIS的一个可访问的切入点。考虑到这些原则，该项目通过培训数学家进入量子研究领域来加强数学和QIS。一个全面的课程指导项目参与者从学习量子原理到应用复杂的数学工具来推进QIS，同时也探索他们研究的社会影响。该项目将支持数学科学的本科生、研究生和博士后的参与，由数学和量子科学相关领域的领导者指导。通过将QIS培训扩展到数学，该项目将有助于建立一支更强大、更多样化的QIS队伍。该项目将通过在量子算法、量子密码学和量子系统这三个成熟的研究主题中解决前沿理论问题来推进数学，这些研究主题足以允许数学处理和创新。这些主题中的每一个都有严格的数学模型（社区一致认为是有用的），这些模型产生了大量尚未探索的数学问题，其解决方案可能对科学计算、网络安全和纳米技术产生重大影响。15名教师将指导本科生、研究生和博士后研究人员进行QIS项目，这些项目涉及代数/表示理论、非线性分析、偏微分方程、科学计算和随机分析。研究目标将包括：开发新的和增强现有的量子算法，利用数学的力量来扩大量子密码学的范围和有用性，并通过量子系统理论的进步来改进量子信息科学，反之亦然。该项目预计将刺激数学家的研究和事业，使他们能够在马里兰大学帕克学院和国家层面上从事量子信息科学的研究。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。

Quantum Information Science (QIS) aims to develop new ways to compute and communicate by taking advantage of the unique properties of matter at the atomic level. This includes advances in cryptography, faster calculations, and better understanding of natural processes taking place at the atomic level. Because of its spanning impact, QIS addresses many areas of national interest, including cybersecurity, pharmaceuticals, financial services, health care, among others. QIS involves a fundamentally different logic than classical information science, and advances in the field (in areas such as quantum algorithms and quantum cryptography) have often depended on creative mathematical breakthroughs. Furthermore, mathematics is an accessible entry point to QIS for students and mentors from a wide range of backgrounds and skill levels. With these principles in mind, this project strengthens both mathematics and QIS by training mathematicians to enter the world of quantum research. A holistic curriculum guides program participants from learning quantum principles to applying sophisticated mathematical tools to advance QIS, while also exploring the societal impact of their research. This project will support the involvement of undergraduate and graduate students, and postdoc fellows from the Mathematical Sciences, to be mentored by faculty who are leaders in fields relevant to mathematics and quantum science. By expanding QIS training to Mathematics, this project will contribute to a more robust and diverse QIS workforce.This project will advance mathematics by tackling cutting-edge theoretical questions within three research themes that are mature enough to allow for mathematical treatment and innovation: Quantum Algorithms, Quantum Cryptography, and Quantum Systems. Each of these themes has rigorous mathematical models (that the community agrees are useful) and these models rise to an abundance of mathematical problems that are yet to be explored and whose solution is likely to have high impact on scientific computing, cybersecurity, and nanotechnology. Fifteen faculty will mentor undergraduate, graduate, and postdoctoral researchers in QIS projects that draw from algebra/representation theory, nonlinear analysis, partial differential equations, scientific computing, and stochastic analysis. Research goals will include: to develop new and enhance existing quantum algorithms, to use the power of mathematics to expand the range and usefulness of quantum cryptography, and to improve Quantum Information Science through advances in quantum systems theory and vice versa. The project is expected to stimulate the research and careers of mathematicians by equipping them to pursue research in Quantum Information Science, both at the University of Maryland, College Park level and at the national level.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.