Entanglement dynamics in hybrid quantum circuits

TL;DR

This paper reviews recent advances in understanding entanglement, operator spreading, and thermalization in random quantum circuits, highlighting universal behaviors and measurement-induced phases through a statistical mechanics perspective.

Contribution

It synthesizes recent progress in applying statistical mechanics to analyze quantum information dynamics in random circuits, including new phases and critical phenomena.

Findings

Universal entanglement growth in random circuits

Operator spreading and chaos exhibit statistical mechanics analogies

Measurement-induced phases reveal new critical behaviors

Abstract

The central philosophy of statistical mechanics (stat-mech) and random-matrix theory of complex systems is that while individual instances are essentially intractable to simulate, the statistical properties of random ensembles obey simple universal "laws". This same philosophy promises powerful methods for studying the dynamics of quantum information in ideal and noisy quantum circuits -- for which classical description of individual circuits is expected to be generically intractable. Here, we review recent progress in understanding the dynamics of quantum information in ensembles of random quantum circuits, through a stat-mech lens. We begin by reviewing discoveries of universal features of entanglement growth, operator spreading, thermalization, and chaos in unitary random quantum circuits, and their relation to stat-mech problems of random surface growth and noisy hydrodynamics. We then explore the dynamics of monitored random circuits, which can loosely be thought of as noisy dynamics arising from an environment monitoring the system, and exhibit new types of measurement-induced phases and criticality. Throughout, we attempt to give a pedagogical introduction to various technical methods, and to highlight emerging connections between concepts in stat-mech, quantum information and quantum communication theory.