Non-Equilibrium Quantum Many-Body Physics with Quantum Circuits

TL;DR

This paper introduces brickwork quantum circuits as a framework for studying non-equilibrium quantum many-body dynamics, demonstrating their similarity to local Hamiltonians and providing exact computations of dynamical properties.

Contribution

It pedagogically presents brickwork quantum circuits and shows they can be used to exactly compute dynamical and spectral properties in non-trivial interacting systems.

Findings

Brickwork quantum circuits evolve quantum correlations similarly to local Hamiltonians.

Exact computation of dynamical properties in interacting circuits is possible.

The framework aids understanding of non-equilibrium quantum many-body dynamics.

Abstract

These are the notes for the 4.5-hour course with the same title that I delivered in August 2025 at the Les Houches summer school ``Exact Solvability and Quantum Information''. In these notes I pedagogically introduce the setting of brickwork quantum circuits and show that it provides a useful framework to study non-equilibrium quantum many-body dynamics in the presence of local interactions. I first show that brickwork quantum circuits evolve quantum correlations in a way that is fundamentally similar to local Hamiltonians, and then present examples of brickwork quantum circuits where, surprisingly, one can compute exactly several relevant dynamical and spectral properties in the presence of non-trivial interactions.