Circuit Complexity in Topological Quantum Field Theory

Quantum circuit complexity has played a central role in recent advances holography and many-body physics. Within quantum field theory, it typically been studied Lorentzian (real-time) framework. In departure from standard treatments, we aim to quantify the of Euclidean path integral. this setting, there is no clear separation between space time, notion unitary evolution on fixed Hilbert longer applies. As proof concept, argue that pants decomposition provides natural within category 2-dimensional bordisms use formulate states operators topological theory. We comment analogies our formalism others mechanics, such as tensor networks second quantization.