Project Grant 1664359

This $599,159 federal Project Grant award from the National Science Foundation's (NSF) Computer and Information Science and Engineering (CISE) program supports research at the University of California, Davis (UC Davis) focused on the intersection of quantum mathematics, computational complexity, and geometry. The project aims to explore the existence or non-existence of quantum algorithms, fast algorithms for geometric and topological problems, and the geometric properties of quantum physics...

This National Science Foundation (NSF) Project Grant, awarded under the Mathematical and Physical Sciences program (CFDA 47.049), provides $172,247 to support collaborative research on small quantum groups, their categorifications, and topological applications. The research aims to bridge the gap between 3D topological quantum field theories and our 4D universe, with a focus on developing homological invariants of 3D and 4D manifolds. The project will involve students and postdocs,...

This Project Grant from the National Science Foundation Division of Mathematical Sciences provides $194,902 to Texas A&M University under the Mathematical and Physical Sciences program (CFDA 47.049) to study the quantum symmetries of topological phases of matter. The investigator will classify and distinguish topological phases through their mathematical symmetries, probe their properties, and understand relationships between phases through transitions. Some emphasis will be placed on...

This federal Project Grant award, funded by the National Science Foundation (NSF) under the Computer and Information Science and Engineering (CISE) program (CFDA 47.070), provides $590,886 to Purdue University to conduct research on quantum algorithms and complexity for quantum algebra and topology. The project aims to make progress on two key challenges in the development of quantum computers: fault tolerance and identifying problems where quantum computers can outperform non-quantum computers....

This two-year project grant from the National Science Foundation's Division of Computing and Communication Foundations, under the Computer and Information Science and Engineering program (CFDA 47.070), provides $175,000 to the Missouri University of Science and Technology to develop new theoretical foundations for quantum walks and their applications. The university will investigate the power and limitations of quantum walks, which are a quantum analogue of classical random walks, in order to...

The National Science Foundation awarded a $385,878 project grant to The Regents of the University of Colorado for research titled "Topological and C*-Algebraic Quantum Matter" under the Mathematical and Physical Sciences program (CFDA 47.049). The three-year award beginning July 1, 2021 will support research into topological and operator algebraic structures in quantum many-body systems and quantum field theories. The University of Colorado will leverage its expertise in operator...

This $330,000 Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences (CFDA 47.049) program supports research into quantum groups, W-algebras, and Brauer-Kauffmann categories, with a focus on understanding the underlying mathematical symmetries that govern natural phenomena. The principal investigator will develop emerging theories and applications of I-quantum groups, including exploring braid group actions, Drinfeld presentations, and...

This Project Grant award from the National Science Foundation's Mathematical and Physical Sciences program (CFDA 47.049) provides $279,013 to support research on using quantum computers to investigate the fractional quantum Hall effect, a quantum state of matter with unusual properties. The key products and services to be delivered under this award include: Designing quantum circuits to simulate the braiding and verify the quasihole statistics of non-Abelian fractional quantum Hall states....

This Project Grant from the National Science Foundation's Division of Mathematical Sciences will support research into operator algebra and quantum information theory at the University of Illinois from August 2023 through July 2026. The $288,684 award will fund the development of tools from functional analysis, operator algebras, and quantum probability to explore connections to quantum information theory. Specifically, the grantee will analyze how information is encoded in the state of a...

This Project Grant award of $307,887 from the National Science Foundation (NSF) Division of Physics, under the Mathematical and Physical Sciences program (CFDA 47.049), will enable the University of California, Merced to advance the scientific understanding and technological applications of topological quantum matter at finite temperatures. The research project aims to utilize the power of quantum computers to systematically characterize the properties of topological quantum systems at finite...