Measuring out-of-time-order correlators on a nuclear magnetic resonance quantum simulator

TL;DR

This paper reports the first experimental measurement of out-of-time-order correlators (OTOCs) on a nuclear magnetic resonance quantum simulator, revealing differences between integrable and non-integrable systems and connecting OTOCs to entanglement entropy growth.

Contribution

It demonstrates the measurement of local OTOCs in a quantum simulator, linking OTOC behavior to quantum chaos, entanglement, and information scrambling.

Findings

OTOCs behave differently in integrable vs. non-integrable systems

Entanglement entropy oscillates or scrambles based on system integrability

Experimental butterfly velocity measured for correlation propagation

Abstract

The idea of the out-of-time-order correlator (OTOC) has recently emerged in the study of both condensed matter systems and gravitational systems. It not only plays a key role in investigating the holographic duality between a strongly interacting quantum system and a gravitational system, but also diagnoses the chaotic behavior of many-body quantum systems and characterizes the information scrambling. Based on the OTOCs, three different concepts -- quantum chaos, holographic duality, and information scrambling -- are found to be intimately related to each other. Despite of its theoretical importance, the experimental measurement of the OTOC is quite challenging and so far there is no experimental measurement of the OTOC for local operators. Here we report the measurement of OTOCs of local operators for an Ising spin chain on a nuclear magnetic resonance quantum simulator. We observe that the OTOC behaves differently in the integrable and non-integrable cases. Based on the recent discovered relationship between OTOCs and the growth of entanglement entropy in the many-body system, we extract the entanglement entropy from the measured OTOCs, which clearly shows that the information entropy oscillates in time for integrable models and scrambles for non-intgrable models. With the measured OTOCs, we also obtain the experimental result of the butterfly velocity, which measures the speed of correlation propagation. Our experiment paves a way for experimentally studying quantum chaos, holographic duality, and information scrambling in many-body quantum systems with quantum simulators.