Physics Group Meeting

Motivated by black hole physics, we study the relationship between quantum chaos, holographic complexity, and fined grained notions of randomness. First, we develop a diagnostic of quantum chaos by directly considering the time evolution of a simple local operator. This leads us to out-of-time-order correlation functions as natural probes of the butterfly effect. Next, we attempt to understand when random unitary operators can be used to approximate chaotic dynamics and how the quantum circuit complexity of such operators can grow. Quasi-periodically we will return to holography and connect these results to a recent conjecture that the complexity of a holographic state is related to the black hole interior.