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.
Highlights
The out-of-time-order correlator (OTOC), given byFðtÞ 1⁄4 hB †ðtÞA †ð0ÞBðtÞAð0Þiβ; ð1Þ is proposed as a quantum generalization of a classical measure of chaotic behaviors [1,2]
One experimental approach closely related to time reversal of quantum systems is the echo technique [16], and the echo has been studied extensively for both noninteracting particle systems and many-body systems to characterize the stability of quantum evolution in the presence of perturbations [17,18,19], and the physics is already quite close to OTOC
We report measurements of OTOCs on a nuclear magnetic resonance (NMR) quantum simulator
Summary
FðtÞ 1⁄4 hB †ðtÞA †ð0ÞBðtÞAð0Þiβ; ð1Þ is proposed as a quantum generalization of a classical measure of chaotic behaviors [1,2]. A concrete quantum mechanics model, known as the Sachdev-Ye-Kitaev model, has been shown to fulfill this conjecture [2,7,8] This establishes a profound connection between the existence of holographic duality and the chaotic behavior in many-body quantum systems [9]. One experimental approach closely related to time reversal of quantum systems is the echo technique [16], and the echo has been studied extensively for both noninteracting particle systems and many-body systems to characterize the stability of quantum evolution in the presence of perturbations [17,18,19], and the physics is already quite close to OTOC. On one hand, our approach is universal and can be applied to any system that has full local quantum control, including a superconducting qubit and trapped ion; on the other hand, this experiment is currently limited to a small size not because of our scheme but because of the scalability issue of the quantum computer
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