Circuit Complexity in Topological Quantum Field Theory
Recent developments in holography have motivated the study of quantum circuit complexity within quantum field theory. I will describe a route toward extending the idea of complexity to the Euclidean path integral, using two-dimensional topological quantum field theory as a case study. In this setting, there is no clear separation between space and time, and the notion of unitary evolution on a fixed Hilbert space no longer applies. Hopefully, this talk will be a chance to explore some fun ideas at the interface of classical computation, quantum computation, and high-energy physics.