Les Houches lectures on random quantum circuits and monitored quantum dynamics

TL;DR

This paper discusses the application of statistical mechanics principles to understand the complex dynamics of quantum information in random quantum circuits, including monitored systems, where exact solutions are generally difficult to obtain.

Contribution

It introduces a framework for analyzing the dynamics of quantum information in random circuits using statistical mechanics, highlighting approaches for systems with monitoring.

Findings

Provides a theoretical foundation for studying monitored quantum circuits

Connects quantum information dynamics with statistical mechanics principles

Highlights challenges in obtaining exact descriptions of individual circuit realizations

Abstract

These lecture notes are based on lectures given by the author at the Les Houches 2025 summer school on "Exact Solvability and Quantum Information". The central theme of these notes is to apply the philosophy of statistical mechanics to study the dynamics of quantum information in ideal and monitored random quantum circuits -- for which an exact description of individual realizations is expected to be generically intractable.