Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Probing Quantum Scrambling via OTOCs in Digital Circuits: Finite-Size Recurrences, System-Size Scaling, and Validation on IBM Quantum Hardware

Erick Francisco Perez Eugenio

Published Feb 24, 2026• 0 citations
Publisher

Abstract

Code, data, and manuscript for a study of quantum scrambling via out-of-time-ordered correlators (OTOCs) in the Kicked Ising model across system sizes N = 4, 8, 12, 20, combining exact statevector simulation with experiments on IBM Quantum hardware (ibm_marrakesh, 156-qubit Heron processor). Introduces the scrambling residual Ω as a fit-free diagnostic that correctly classifies dynamical regimes on both simulated and hardware data.

DOI
10.5281/zenodo.18752607

Related papers

Out of Time Order Correlators as Measures of Quantum Information Scrambling with Spectral Diagnostic

Bannishikha Banerjee

Abstract Out-of-time-order correlators (OTOCs) have emerged as the preeminent theoretical and experimental probe of quantum information scrambling — the delocalization of quantum information across many-body degrees of freedom. Here we present a comprehensive computational study of OTOCs across three paradigmatic models: the Sachdev-Ye-Kitaev (SYK) model, the non-integrable transverse-field Ising chain, and random unitary circuits. Through exact diagonalization and large-N analytics, we extract Lyapunov exponents, scrambling times, and butterfly velocities, demonstrating that all chaotic systems studied approach, but do not saturate, the Maldacena-Shenker-Stanford (MSS) bound λ_L ≤ 2π/β. Crucially, we introduce the Spectral Out-of-Time-Order Correlator (SOTOC), a novel frequency-domain diagnostic that decomposes information scrambling into its constituent spectral modes. The SOTOC achieves a 32% improvement in Lyapunov exponent extraction precision over conventional log-linear fitting and maintains robust performance at noise levels σ > 0.30, where traditional methods fail. Our phase diagram reveals a sharp transition in scrambling dynamics at h/J ≈ 1.0 in the TFIM, coinciding with the onset of quantum chaos as measured by level-spacing statistics. These results establish SOTOC as a practical and theoretically grounded tool for probing scrambling in near-term quantum devices and holographic systems.

•May 6, 2026•0 citations

Quantum information scrambling in molecules

Chenghao Zhang, Peter Guy Wolynes, Martin Gruebele

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.

arXiv:2202.09949•Physical Review A•Mar 29, 2022•11 citations

OTOC-Based Quantum Feature Engineering; A Framework and Empirical Study

Amol Yadav

Conventional quantum machine learning feature maps primarily employ static encoding strategies that fail to capture the dynamical evolution of quantum systems. We propose leveraging Out-of-Time-Order Correlators (OTOCs)—a diagnostic tool for quantum information scrambling—as a dynamical feature extraction mechanism for classification tasks. Our framework extracts physically meaningful features including scrambling rates (Lyapunov-like exponents), saturation values, and temporal variance from OTOC trajectories. We benchmark this approach against classical kernels and standard quantum baselines across three classification problems: distinguishing chaotic from integrable regimes, detecting quantum phase transitions, and classifying a standard tabular dataset. While OTOC-derived features encode interpretable physical dynamics, our results reveal accuracy and scalability challenges compared to optimized classical baselines, suggesting that system size and encoding strategy require further optimization for practical advantage.

•Nov 28, 2025•0 citations

Analyzing Information Scrambling in Simulated Quantum Systems Using Out-of-Time-Ordered Correlators

Bibiana Firmin R, M. Sathishkumar

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.

International Journal For Multidisciplinary Research•Nov 15, 2025•0 citations

Detecting scrambling via statistical correlations between randomized measurements on an NMR quantum simulator

Xinfang Nie, Ze Zhang, Xiuzhu Zhao +3 more

Out-of-time-order correlator (OTOC), been suggested as a measure of quantum information scrambling in quantum many-body systems, has received enormous attention recently. The experimental measurement of OTOC is quite challenging. The existing theoretical protocols consist in implementing time-reversal operations or using ancillary quantum systems, therefore only a few experiments have been reported. Recently, a new protocol to detect OTOC using statistical correlations between randomized measurements was put forward. In this work, we detect the OTOCs of a kicked-Ising model using this new measurement method on a 4-qubit nuclear magnetic resonance quantum simulator. In experiment, we use random Hamiltonian evolutions to generate the random operations that are required by the randomized OTOC detection protocol. Our experimental results are in good agreement with the theoretical predictions, thus confirming the feasibility of the protocols. Therefore, our work represents a step in exploring realistic quantum chaotic dynamics in complicated quantum systems.

arXiv:1903.12237•Mar 28, 2019•15 citations

Application of quantum scrambling in Rydberg atom on IBM quantum computer

Daattavya Aggarwal, Shivam Raj, Bikash K. Behera +1 more

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.

arXiv:1806.00781•Jun 3, 2018•7 citations
Code, data, and manuscript for a study of quantum scrambling via out-of-time-ordered correlators (OTOCs) in the Kicked Ising model across system sizes N = 4, 8, 12, 20, combining exact statevector simulation with experiments on IBM Quantum hardware (ibm_marrakesh, 156-qubit Heron processor). Introduces the scrambling residual Ω as a fit-free diagnostic that correctly classifies dynamical regimes on both simulated and hardware data.
Abstract Out-of-time-order correlators (OTOCs) have emerged as the preeminent theoretical and experimental probe of quantum information scrambling — the delocalization of quantum information across many-body degrees of freedom. Here we present a comprehensive computational study of OTOCs across three paradigmatic models: the Sachdev-Ye-Kitaev (SYK) model, the non-integrable transverse-field Ising chain, and random unitary circuits. Through exact diagonalization and large-N analytics, we extract Lyapunov exponents, scrambling times, and butterfly velocities, demonstrating that all chaotic systems studied approach, but do not saturate, the Maldacena-Shenker-Stanford (MSS) bound λ_L ≤ 2π/β. Crucially, we introduce the Spectral Out-of-Time-Order Correlator (SOTOC), a novel frequency-domain diagnostic that decomposes information scrambling into its constituent spectral modes. The SOTOC achieves a 32% improvement in Lyapunov exponent extraction precision over conventional log-linear fitting and maintains robust performance at noise levels σ > 0.30, where traditional methods fail. Our phase diagram reveals a sharp transition in scrambling dynamics at h/J ≈ 1.0 in the TFIM, coinciding with the onset of quantum chaos as measured by level-spacing statistics. These results establish SOTOC as a practical and theoretically grounded tool for probing scrambling in near-term quantum devices and holographic systems.
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.
Conventional quantum machine learning feature maps primarily employ static encoding strategies that fail to capture the dynamical evolution of quantum systems. We propose leveraging Out-of-Time-Order Correlators (OTOCs)—a diagnostic tool for quantum information scrambling—as a dynamical feature extraction mechanism for classification tasks. Our framework extracts physically meaningful features including scrambling rates (Lyapunov-like exponents), saturation values, and temporal variance from OTOC trajectories. We benchmark this approach against classical kernels and standard quantum baselines across three classification problems: distinguishing chaotic from integrable regimes, detecting quantum phase transitions, and classifying a standard tabular dataset. While OTOC-derived features encode interpretable physical dynamics, our results reveal accuracy and scalability challenges compared to optimized classical baselines, suggesting that system size and encoding strategy require further optimization for practical advantage.
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.
Out-of-time-order correlator (OTOC), been suggested as a measure of quantum information scrambling in quantum many-body systems, has received enormous attention recently. The experimental measurement of OTOC is quite challenging. The existing theoretical protocols consist in implementing time-reversal operations or using ancillary quantum systems, therefore only a few experiments have been reported. Recently, a new protocol to detect OTOC using statistical correlations between randomized measurements was put forward. In this work, we detect the OTOCs of a kicked-Ising model using this new measurement method on a 4-qubit nuclear magnetic resonance quantum simulator. In experiment, we use random Hamiltonian evolutions to generate the random operations that are required by the randomized OTOC detection protocol. Our experimental results are in good agreement with the theoretical predictions, thus confirming the feasibility of the protocols. Therefore, our work represents a step in exploring realistic quantum chaotic dynamics in complicated quantum systems.
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.