Adam Nahum, École Normale Supérieure, Paris, France

Out of Equilibrium Dynamics and Quantum Circuits (10.5h)

Lectures on many-body dynamics in quantum circuits

I will discuss out-of-equilibrium dynamics in chaotic quantum many-body systems, emphasising that some basic dynamical questions about correlations and entanglement can be reduced to effective classical stat mech problems (involving random walks, domain walls, percolation, traveling waves, etc.).

1. Many-body dynamics far from the ground state

Quantum many-body dynamics far from the ground state: the search for universality. (Quantum chaos and complexity; entanglement entropy; decoherence and the emergence of hydrodynamics.) Many-body dynamics in the NISQ era. Random quantum circuits as simple models.

2. Quantum correlation functions and classical Markov processes

Lieb-Robinson and causality. Correlations in quantum circuits: mapping to a classical Markov process. Two-point functions and spacetime trajectories. “Unbinding” phase transition for spacetime trajectories. Questions about efficient simulation of quantum systems.

3. Mapping between quantum circuits and classical lattice models

Entanglement entropy as free energy of a membrane in an effective classical model. Coarse-grained evolution equation for the entanglement entropy.

4. Decoherence

Motivations: quantum trajectories of continually measured systems. Entanglement transitions: schematic picture. Replica picture (overview)

5. Entanglement transitions in random (tree) tensor networks

The simplest example of an entanglement phase transition and reduction to a recursion relation on a tree.

Outlook and other topics