Circuit complexity and (some of) its applications

Motivated by recent interesting holographic results, several attempts have been made to study complexity (rather "Circuit Complexity") for quantum field theories using Nielsen's geometric method. Since then, it has found many interesting applications. We discuss some of its applications. In particular, we discuss whether circuit complexity can be used as a diagnostics of quantum chaos. We use a simple toy model, namely the Inverted Harmonic Oscillator (IHO), to establish our claim and discuss further applications in the context of quantum cosmology.