Lecture Notes: Introduction to random unitary circuits and the measurement-induced entanglement phase transition

TL;DR

These lecture notes introduce the core concepts of entanglement dynamics in random unitary circuits and the measurement-induced phase transition, emphasizing the minimal cut and statistical mechanics mappings.

Contribution

They provide an accessible, conversational overview of the key ideas and theoretical frameworks underlying measurement-induced entanglement phase transitions.

Findings

Explanation of the minimal cut concept

Introduction to statistical mechanics mappings

Overview of entanglement phase transition mechanisms

Abstract

These are lecture notes compiled for a short lecture series at the 2023 Condensed Matter Summer School at the University of Minnesota. They are designed to be conversational and fun, and not to take the place of review articles that do a serious job of stating things precisely and citing literature thoroughly. The goal of the notes is to introduce some central ideas underlying the study of entanglement dynamics in random unitary circuits and the measurement-induced entanglement phase transition. A particular focus is the concept of the "minimal cut" and its associated stat mech mappings.