Abstract:

There is an active paradigm shift within quantum topology from semisimple to non-semisimple phenomena. The primary mathematical instrument that catalyzed this shift is called the modified trace. Mathematicians have shown that non-semisimple topological quantum field theories (TQFTs) can distinguish certain topological features that their semisimple counterparts cannot.

One well-known application of quantum topology is topological quantum computation. Given this paradigm shift, it is natural to ask: what does it mean to do topological quantum computation via modified traces? In this talk, we explore this question through non-semisimple topological quantum computation accompanied with a concrete case study of the non-semisimple Ising anyon model.