Quantum chaos and the complexity of time evolution

Vijay Balasubramanian connects quantum chaos with the complexity of time evolution. One approach bounds the smallest circuit needed to simulate physical dynamics; another measures how quickly and ergodically a state explores its accessible Hilbert space. Examples from spin chains, billiards, many-body systems and random matrices distinguish chaotic and integrable behaviour. Applications address geometric conjectures for complexity in quantum gravity and possible failure of effective field theory near spacelike singularities.