PIRSA:26040081 Scientific Series Other

DOI10.48660/26040081

Series: Colloquium

(2026). Quantum chaos and the complexity of time evolution. Perimeter Institute. https://pirsa.org/26040081

Quantum chaos and the complexity of time evolution. Perimeter Institute, Apr. 01, 2026, https://pirsa.org/26040081 

@misc{ pirsa_PIRSA:26040081,
  doi = {10.48660/26040081},
  url = {https://pirsa.org/26040081},
  author = {},
  keywords = {Other},
  language = {en},
  title = {Quantum chaos and the complexity of time evolution},
  publisher = {Perimeter Institute},
  year = {2026},
  month = {apr},
  note = {PIRSA:26040081 see, \url{https://pirsa.org}}
}

Abstract

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.

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