[Paper Review] Scrambling Dynamics and Out-of-Time Ordered Correlators in Quantum Many-Body Systems: a Tutorial

Shenglong Xu, Brian Swingle|arXiv (Cornell University)|Feb 14, 2022

Quantum Computing Algorithms and ArchitectureComputer Science143 references44 citations

TL;DR

This tutorial introduces quantum information scrambling and explains how to quantify information spreading in many-body systems using out-of-time-ordered correlators (OTOC). It discusses toy models, numerical methods, and experimental schemes to measure OTOCs.

ABSTRACT

This tutorial article introduces the physics of quantum information scrambling in quantum many-body systems. The goals are to understand how to precisely quantify the spreading of quantum information and how causality emerges in complex quantum systems. We introduce a general framework to study the dynamics of quantum information, including detection and decoding. We show that the dynamics of quantum information is closely related to operator dynamics in the Heisenberg picture, and, under certain circumstances, can be precisely quantified by the so-called out-of-time ordered correlator~(OTOC). The general behavior of OTOC is discussed based on several toy models, including the Sachdev-Ye-Kitaev model, random circuit models, and Brownian models, in which OTOC is analytically tractable. We introduce numerical methods, including exact diagonalization and tensor network methods, to calculate OTOC for generic quantum many-body systems. We also survey current experimental schemes for measuring OTOC in various quantum simulators.

Motivation & Objective

• Motivate the study of quantum information scrambling as a framework to quantify information spreading in non-equilibrium quantum systems.
• Connect scrambling dynamics to operator growth and Heisenberg-picture evolution.
• Provide a general framework for detection and decoding of information flow in many-body dynamics.
• Illustrate the relationship between scrambling, entanglement, and thermalization across model classes.
• Survey practical numerical and experimental methods for accessing OTOCs.

Proposed method

• Present a general framework linking unitary dynamics to information scrambling via commutator growth.
• Use operator norms of commutators to bound information transfer between distant regions.
• Relate OTOCs to operator growth and Heisenberg evolution.
• Discuss toy models where OTOCs are analytically tractable (e.g., SYK, random circuits, Brownian models).
• Describe numerical approaches (exact diagonalization, Krylov methods, tensor networks) for computing OTOCs.
• Outline experimental schemes for measuring OTOCs in quantum simulators.

Experimental results

Research questions

• RQ1 How does information initially localized in a subsystem spread to non-local degrees of freedom under unitary dynamics?
• RQ2 What is the precise relationship between the growth of commutators, OTOCs, and operator spreading in various model classes?
• RQ3 How can Hayden-Preskill-type setups quantify scrambling and information recovery in many-body systems?
• RQ4 What numerical and experimental methods reliably access OTOCs in generic quantum many-body systems?

Key findings

• OTOCs offer a quantitative measure of information scrambling by tracking the growth of operator commutators in time.
• The emergent light-cone for information propagation can be studied via the growth of Heisenberg-evolved operators in locally interacting systems.
• Toy models such as SYK, random circuits, and Brownian models provide analytically tractable settings to understand OTOC behavior.
• Several numerical methods, including exact diagonalization and tensor-network techniques, enable OTOC computation in generic systems.
• Experimental schemes for measuring OTOCs across different quantum simulators are surveyed, highlighting practical measurement strategies.