ICTS

I will describe new ideas relating quantum chaos to the complexity of time evolution.  One approach treats physical time evolution as a quantum computation, and bounds the smallest quantum circuit that can simulate this evolution.  The second approach quantifies how ergodically and rapidly a quantum state explores the accessible part of the system's Hilbert space.  I will illustrate how these measures separate integrable and chaotic quantum systems by considering examples including spin chains, quantum billiards, quantum many body systems, and Random Matrix Theory.  I will end by describing an application of these methods to a conjecture that geometrizes complexity in quantum gravity, and will comment on the relevance of these ideas for the break down of effective field theory near spacelike singularities.