Mario Flory (Jagiellonian University, Krakow)

In this talk, I will explain the concept of complexity of states and operations, an idea originating in quantum information theory which has recently found its way to (quantum-) gravity research and the study of black holes via the AdS/CFT correspondence. As a particularly relevant and tractable case, I will study complexity in the universal setting of 1+1-dimensional conformal field theory with a holographic dual. As the operators generating conformal transformations can be explicitly constructed in CFT terms, this setting allows for a quantitative comparison between holographic conjectures of computing computational complexity and purely field-theoretic calculations. Furthermore, I will present a proposal for assigning a cost to circuits based on the Fubini-Study metric, and discuss the geometric properties of the underlying geometry.