RTG: The Mathematics of Quantum Information Science

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.