Speaker
Description
In the holographic framework, the evolution of black hole interiors is supposed to be captured by computational complexity, which heuristically quantifies the difficulty of preparing the dual state from a reference one by implementing elementary transformations. Employing the differential geometry toolkit, complexity can be defined as the length of shortest paths on proper manifolds.
In this talk we consider a system of n qubits and, following the geometrical approach, we investigate the distinct but related notions of operator complexity and state complexity.
In particular, we discuss how a proper choice of penalty factors for the elementary computational gates is crucial for operator complexity to reproduce desired features of black holes physics. Then, by exploiting the formalism of Riemannian submersions, we describe what the geometry of operator complexity can teach us about state complexity, which is more relevant for the holographic application.
