# Complexity and entropy in quantum many-body systems

### APA

Faist, P. (2022). Complexity and entropy in quantum many-body systems. Perimeter Institute. https://pirsa.org/22010071

### MLA

Faist, Philippe. Complexity and entropy in quantum many-body systems. Perimeter Institute, Jan. 12, 2022, https://pirsa.org/22010071

### BibTex

@misc{ pirsa_22010071, doi = {10.48660/22010071}, url = {https://pirsa.org/22010071}, author = {Faist, Philippe}, keywords = {Quantum Information}, language = {en}, title = {Complexity and entropy in quantum many-body systems}, publisher = {Perimeter Institute}, year = {2022}, month = {jan}, note = {PIRSA:22010071 see, \url{https://pirsa.org}} }

Philippe Faist California Institute of Technology

## Abstract

Quantifying quantum states' complexity is a key problem in various subfields of science, from quantum computing to black-hole physics. Motivated by the expected behavior of wormholes in quantum gravity, Brown and Susskind conjectured that the quantum complexity of the state output by a random circuit on n qubits grows linearly as more and more random gates are applied, until saturating after a number of gates exponential in n. We prove this conjecture by studying the dimension of the set of all unitaries that can be accessed with a given arrangement of two-qubit gates. Our core technical contribution is a lower bound on this dimension, using techniques from algebraic geometry and considerations based on Clifford circuits. In the second part of my talk, I'll discuss some thermodynamic and effective information-theoretic aspects of the complexity of quantum states and its growth in quantum many-body systems, establishing a resource theory to capture a notion of quantum complexity and drawing a connection between the concepts of complexity and entropy.

Joint work with: Jonas Haferkamp, Teja Naga Bhavia Kothakonda, Anthony Munson, Jens Eisert, Nicole Yunger Halpern

Zoom Link: https://pitp.zoom.us/j/94288479163?pwd=Nm8wOUdReGhreDErdUpJTzFETlBUUT09