CHAOS, holography, and other science

Abstract

This thesis focuses on the relationship between black holes in holography, chaos in strongly-coupled quantum systems, and the computational complexity of holographic states. By directly considering the time evolution of local operators, I am led to a simple diagnostic of many-body chaos: a commutator of such operators separated in time and space. Using this diagnostic, I study the growth of operators-a manifestation of the butterfly effect-in a variety of quantum systems. By considering the butterfly effect in holography, I find evidence for a detailed correspondence between the tensor network (or quantum circuit) that builds the holographic state and the interior geometry (or Einstein-Rosen bridge) of the black hole. Ultimately, I try to understand these connections by considering entanglement across time: the entanglement between an output system following time evolution and a record or memory perfectly correlated with the initial system.