Eric Samperton
My research focuses on interactions between topology and computer science. I am most interested in interactions between 3-dimensional geometric topology, topological quantum field theories, and quantum computation. My motivations are to understand both quantum advantage (the kinds of things quantum computers can do better than non-quantum computers) and fault tolerance (i.e., grappling with the fact that building real world quantum computers will require t… ↓More
Joined department: Fall 2022
Research Areas
Education
Ph.D., University of California, Davis, Mathematics (2018)
B.S., California Institute of Technology, Mathematics with a minor in English (2012)
My research focuses on interactions between topology and computer science. I am most interested in interactions between 3-dimensional geometric topology, topological quantum field theories, and quantum computation. My motivations are to understand both quantum advantage (the kinds of things quantum computers can do better than non-quantum computers) and fault tolerance (i.e., grappling with the fact that building real world quantum computers will require the use of quantum error correcting codes in order to make them scale). Topology studies the properties of mathematical spaces that are invariant under small perturbations. As such, this branch of math is used as a source of inspiration and techniques for dealing with the kinds of errors that can perturb a quantum computation away from yielding a correct answer.
Selected Publications
Topological quantum computation is hyperbolic. Communications in Mathematical Physics (2023), Volume 402, pp. 79-96. arXiv
Coloring invariants of knots are often intractable. With Greg Kuperberg. Algebraic & Geometry Topology (2021), Volume 21, Issue 3, pp. 1479-1510. arXiv
Haah codes on general three manifolds. With Kevin Tian and Zhenghan Wang. Annals of Physics (2020), Volume 412, 168014. arXiv
Computational complexity and 3-manifolds and zombies. With Greg Kuperberg. Geometry & Topology (2018), Volume 22, Issue 6, pp. 3623-3670. arXiv, YouTube
Towards a complexity-theoretic dichotomy for (2+1)-dimensional TQFT invariants. With Nicolas Bridges. 20th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 350, pp. 5:1-5:21. arXiv, video