Quantum scrambling measured by out-of-time-ordered correlator (OTOC) has an important role in understanding the physics of black holes and evaluating quantum chaos. It is known that Rydberg atom has been a general interest due to its extremely favourable properties for building a quantum simulator. Fast and efficient quantum simulators can be developed by studying quantum scrambling in related systems. Here we present a general quantum circuit to theoretically implement an interferometric protocol which is a technique proposed to measure OTOC functions. We apply this circuit to measure OTOC and hence the quantum scrambling in a simulation of two spin Ising spin model for Rydberg atom. We apply this method to both initial product and entangled states to compare the scrambling of quantum information in both cases. Finally we discuss other constructions where this technique can be applied.
Quantum scrambling measured by out-of-time-ordered correlator (OTOC) has an important role in understanding the physics of black holes and evaluating quantum chaos. It is known that Rydberg atom has been a general interest due to its extremely favourable properties for building a quantum simulator. Fast and efficient quantum simulators can be developed by studying quantum scrambling in related systems. Here we present a general quantum circuit to theoretically implement an interferometric protocol which is a technique proposed to measure OTOC functions. We apply this circuit to measure OTOC and hence the quantum scrambling in a simulation of two spin Ising spin model for Rydberg atom. We apply this method to both initial product and entangled states to compare the scrambling of quantum information in both cases. Finally we discuss other constructions where this technique can be applied.
Out-of-time-order correlators (OTOCs) are the main tool for probing quantum chaos and scrambling, and have become crucial probes in many areas of quantum computing. However, the measurement of OTOCs is difficult to implement on analog quantum computers due to the requirement of backward time evolution. In this paper, we develop and implement a randomized measurement protocol to compute OTOCs on Aquila by QuEra Computing. Unlike traditional methods that require backward time evolution, our approach utilizes a sequence of global randomized quenches that approximates the unitary 2-design properties necessary for extracting infinite-temperature OTOCs from statistical correlations. We demonstrate the protocol's success by explicitly observing the lightcone of information propagation in 1D Rydberg chains, and compare hardware results to both state-vector simulations and matrix product state (MPS) tensor network calculations. This work establishes the first demonstration of fully analog randomized OTOC measurements in neutral-atom simulators, providing a scalable pathway to probe quantum chaos in complex many-body systems.
The recent advancements in out-of-time-ordered correlator (OTOC) measurements have provided a promising pathway to explore quantum chaos and information scrambling. However, despite recent advancements, their experimental realization remains challenging due to the complexity of implementing backward time evolution. Here, we present a scalable quantum circuit combined with the interferometric protocol, offering a more efficient framework for OTOC measurement. Using this method, we simulate commutator growth in integrable and chaotic regimes of a 9-qubit Ising chain. Our Trotterized circuit achieves errors below 10−11 with 4th-order Trotterization and performs well even with lower-order Trotterization approximations. We believe, this approach paves the way for studying information dynamics, highly entangled quantum systems, and complex observables efficiently.
Out-of-time-order correlators (OTOCs) can be used to probe how quickly a quantum system scrambles information when the initial conditions of the dynamics are changed. In sufficiently large quantum systems, one can extract from the OTOC the quantum analog of the Lyapunov coefficient that describes the timescale on which a classical chaotic system becomes scrambled. OTOCs have been applied only to a very limited number of toy models, such as the Sachdev-Ye-Kitaev model connected with black hole information scrambling, but they could find much wider applicability for information scrambling in quantum systems that allow comparison with experiments. The vibrations of polyatomic molecules are known to undergo a transition from regular dynamics at low energy to facile energy flow at sufficiently high energy. Molecules therefore represent ideal quantum systems to study scrambling in many-body systems of moderate size (here 6 to 36 degrees of freedoms). By computing quantum OTOCs and their classical counterparts we quantify how information becomes ``scrambled'' quantum mechanically in molecular systems. Between early ``ballistic'' dynamics, and late ``saturation'' of the OTOC when the full density of states is explored, there is indeed a regime where a quantum Lyapunov coefficient can be defined for all molecules in this study. Comparison with experimental rate data shows that slow scrambling as measured by the OTOC can reach the timescale of molecular reaction dynamics. Even for the smallest molecules we discuss, the Maldacena bound remains satisfied by regularized OTOCs, but not by unregularized OTOCs, highlighting that the former are more useful for discussing information scrambling in this type of moderate-size quantum system.
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, it also diagnoses the chaotic behavior of many-body quantum systems and characterizes information scrambling.Based on OTOCs, three different concepts-quantum chaos, holographic duality, and information scrambling-are found to be intimately related to each other.Despite its theoretical importance, the experimental measurement of the OTOC is quite challenging, and thus 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 nonintegrable 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 nonintgrable 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.
Out-of-time-ordered correlation functions (OTOCs) play a crucial role in the study of thermalization, entanglement, and quantum chaos, as they quantify the scrambling of quantum information due to complex interactions. As a consequence of their out-of-time-ordered nature, OTOCs are difficult to measure experimentally. Here we propose an OTOC measurement protocol that does not rely on the reversal of time evolution and is easy to implement in a range of experimental settings. The protocol accounts for both pure and mixed initial states, and is applicable to systems that interact with environmental degrees of freedom. We demonstrate the application of our protocol by the characterization of scrambling in a periodically driven spin that exhibits quantum chaos.
Quantum computing has introduced new paradigms in how information is stored, processed, and transmitted. Unlike classical computation, where data follows deterministic pathways, quantum systems display complex interactions driven by superposition and entanglement. One of the most powerful tools for studying these interactions is the Out-of-Time-Ordered Correlator (OTOC), a mathematical framework used to quantify how information disperses and becomes scrambled in quantum systems. This paper explores information scrambling dynamics in simulated quantum environments using OTOC-based analysis. Rather than relying on a specific quantum processor, this study uses computational simulations to emulate noisy and noise-mitigated conditions, analyzing how OTOC behavior varies across these regimes. Through numerical modeling and circuit-level quantum simulations, the study demonstrates how information spreads, how chaos develops, and how error mitigation influences the stability of information propagation. The findings provide theoretical foundations for designing stable, error-tolerant quantum algorithms and highlight the intersection between quantum physics, computer science, and information theory.