Shawn Xingshan Cui

Shawn Xingshan Cui is Associate Professor in the Departments of Mathematics and Physics & Astronomy at Purdue University. His research bridges low-dimensional topology, quantum field theory, and quantum information science, with focus on topological quantum computation and tensor category applications.

His work develops mathematical frameworks for topological quantum computing using knot theory, Hopf algebras, and modular tensor categories. Recent publications explore quantum error correction in topological codes (Kitaev model, toric code), non-semisimple invariants of 3-/4-manifolds, and quantum circuit implementations. He leads research on constructing fault-tolerant quantum gates using topological phases and anyonic braiding.

Current projects investigate Floquet codes, fracton models, and the application of neural networks to quantum state representation. His SIAM News article 'Fighting Errors with Space' highlights spatial approaches to quantum error correction.

He supervises graduate students working on quantum algorithms, topological phases of matter, and mathematical foundations of quantum computation. Teaching includes MA 261: Multivariate Calculus and specialized topics in topological quantum computation.