Knots, quantum computing and AI: $6m grant supports exploration of the surprising connections - USC Dornsife

USC Dornsife News MENU Sub-atomic “anyons,” first observed in in 2020, could be the key to quantum computers, according to research by a USC Dornsife-led international collaboration. (Image source: iStock.) Knots, quantum computing and AI: $6m grant supports exploration of the surprising connections Renewed support from the Simons Foundation will help a USC Dornsife-led international collaboration build on discoveries in mathematics that could reshape how computers solve complex problems. ByUSC Dornsife News November 13, 2026 Share Copy Link Facebook X LinkedIn Bluesky Email For most people, a tangled cord is just a nuisance. But for mathematician Aaron Lauda, knots hold clues to the future of quantum computing and artificial intelligence. Now, a $6 million grant renewal from the Simons Foundation will allow an international research collaboration led by Lauda, divisional dean of math and physical sciences at the USC Dornsife College of Letters, Arts and Sciences, to pursue those connections for another three years. Established in 2023, the Simons Collaboration on New Structures in Low-Dimensional Topology brings together 11 institutions worldwide. The new award increases the foundation’s total investment in the project to $14 million. USC will receive more than $2 million of the new funding. “We began with fundamental questions about knots and the possible shapes of three- and four-dimensional spaces, including those used to describe spacetime,” says Lauda, professor of mathematics and physics and astronomy. “Following those questions has led us to new ways of thinking about quantum computation and machine learning.” Giving quantum computers a new twist One of quantum computing’s biggest challenges is preventing errors. The mathematics of knots could help. One promising approach involves anyons, bizarre particle-like phenomena that can emerge in certain two-dimensional quantum systems. In a quantum computer, moving anyons around one another would change the information they hold, allowing calculations to take place. Their paths form “braids,” and the structure of those braids could help keep information nearly error-free. There’s a catch, though. In one promising model, which uses “Ising” anyons, those movements can perform only a limited set of calculations. Researchers need a way to expand that set so the model can handle the full range of quantum computing tasks. In a 2025 Nature Communications paper, Lauda and collaborators Filippo Iulianelli, Sung Kim and Joshua Sussan showed how to do just that. By adding a new type of anyon, dubbed a “neglecton,” to an expanded mathematical model, they demonstrated how the full range of quantum computations could be performed through braiding alone. For now, the breakthrough remains theoretical. Researchers still need to find a physical system that can put it into practice. As anyons interact they form braids. (Images source: Wikimedia Commons.) And the benefits could run both ways: Just as knot mathematics might improve quantum computing, quantum computers could help mathematicians investigate knots. Simons Collaboration researchers developed instructions for a quantum computer to estimate properties of a mathematical tool called Khovanov homology, which helps distinguish one knot from another. Under certain conditions, the method could perform those calculations with high efficiency. At USC Dornsife, Associate Professor of Mathematics Cris Negron develops mathematical frameworks connecting quantum physics, algebra and topology, the study of properties of shapes that remain unchanged when they are stretched or bent. “We want to take the insights coming from physics and turn them into precise mathematical tools,” Negron says. “These tools provide new methods for analyzing and distinguishing knots and spaces that we may not have discovered otherwise.” Putting AI through its paces The team’s mathematical puzzles are also helping researchers explore how AI tackles problems when solutions are exceptionally hard to find. Caltech collaborator Sergei Gukov and colleagues studied a type of AI that learns through trial and error, testing different moves and earning rewards for success. But what happens when the right moves are so difficult to find that the AI rarely earns a reward? To study that question, the researchers turned to the Andrews–Curtis conjecture, a mathematical puzzle that has stymied researchers for more than 60 years. The hypothesis proposes that certain complicated descriptions of a simple mathematical structure can always be simplified using a small, fixed set of moves. Combining computer searches with mathematical reasoning, they showed that several suspected exceptions to the conjecture were not exceptions after all. Whether any true exceptions exist remains an open question. But the research also points toward ways to improve AI’s search methods, helping it find solutions when successful paths are few and far between. Exploring the next dimension While we’re accustomed to navigating a world of three dimensions, the collaboration also explores mathematical spaces with four. In physics, that fourth dimension can be time, giving us spacetime, as Albert Einstein famously described. But the team also studies four-dimensional spaces beyond spacetime, developing ways to determine when two such spaces are mathematically distinct. Supported by a Simons Collaboration workshop, researchers Qiuyu Ren of Stanford University and Michael Willis of Texas A&M University used tools from knot mathematics to distinguish some of these spaces, giving mathematicians a new way to explore their differences. The collaboration is also helping cultivate the next generation of mathematicians. In June, Negron co-organized a workshop at the American Institute of Mathematics in Pasadena, Calif., introducing graduate students and recent PhD recipients to the team’s ideas. “Working with people who approach similar problems in a different way can help young researchers refine the questions they ask in the future,” Negron says. “And building these relationships can have a strong positive impact on their work that persists deep into their career.” With the renewed funding, Lauda hopes to build on the team’s early discoveries and expand its reach. “We can now take ideas that emerged during the first phase and develop them together,” he says. “That means giving the mathematics time to mature, while pursuing the connections to quantum computing and AI that are already taking shape.” Related Articles Pulitzer Prize-winning author Jhumpa Lahiri receives USC Dornsife’s 2026 Chowdhury Prize in Literature If you want Americans to pay attention to climate change, just call it climate change Quantum physicist aims to make tomorrow’s technology ultra-fast and ultra-efficient Categories: Science and Technology Topics: math and physical sciences mathematics physics