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arXiv:2604.19874

Measurement and feedback-driven adaptive dynamics in the classical and quantum kicked top

Mahaveer Prasad, Ahana Chakraborty, Thomas Iadecola, Manas Kulkarni, J. H. Pixley, Sriram Ganeshan, Justin H. Wilson

quant-phcond-mat.dis-nncond-mat.stat-mechnlin.CDSubmitted Apr 21, 2026• Announced Apr 23, 2026• 0 citations
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Abstract

In classical dynamical systems, stochastic feedback can stabilize otherwise unstable periodic orbits, giving rise to distinct controlled and uncontrolled phases as the rate of control application is varied. In this work, we apply these control protocols in classical, semiclassical, and quantum regimes to the kicked top, a paradigmatic model of quantum chaos. The quantum kicked top, modeled as the dynamics of a spin-S object, naturally interpolates between these regimes with the spin size S acting as an effective Planck constant. We show that the dynamics of the kicked top in classical, semiclassical, and fully quantum limits can all be controlled using stochastic feedback protocols. Comparing the full quantum dynamics to a truncated Wigner approximation that captures quantum noise but neglects interference beyond the Ehrenfest time, we find that low-moment observables are largely accounted for semiclassically, while the remaining discrepancy in higher moments is consistent with contributions from interference and possibly nonlinearities in rare trajectories that explore the compact phase space. We also find rapid purification in the numerics studied for all rates of control considered, suggesting that control quenches the top's ability to encode a qubit of quantum information even in the uncontrolled phase.

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22 pages, 9+3 figures

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In classical dynamical systems, stochastic feedback can stabilize otherwise unstable periodic orbits, giving rise to distinct controlled and uncontrolled phases as the rate of control application is varied. In this work, we apply these control protocols in classical, semiclassical, and quantum regimes to the kicked top, a paradigmatic model of quantum chaos. The quantum kicked top, modeled as the dynamics of a spin-S object, naturally interpolates between these regimes with the spin size S acting as an effective Planck constant. We show that the dynamics of the kicked top in classical, semiclassical, and fully quantum limits can all be controlled using stochastic feedback protocols. Comparing the full quantum dynamics to a truncated Wigner approximation that captures quantum noise but neglects interference beyond the Ehrenfest time, we find that low-moment observables are largely accounted for semiclassically, while the remaining discrepancy in higher moments is consistent with contributions from interference and possibly nonlinearities in rare trajectories that explore the compact phase space. We also find rapid purification in the numerics studied for all rates of control considered, suggesting that control quenches the top's ability to encode a qubit of quantum information even in the uncontrolled phase.
The quantum kicked top (QKT) is one of the most widely studied models in quantum chaos, providing a minimal yet powerful framework for exploring the relationship between classical nonlinear dynamics and quantum behavior. Unlike many chaotic systems with infinite-dimensional Hilbert spaces, the QKT possesses a finite-dimensional Hilbert space, making it analytically and numerically controllable while still showing a rich dynamical phenomena. In this chapter, we present a comprehensive introduction to the QKT as a paradigmatic model of quantum chaos. Starting from the classical kicked top, we derive the discrete nonlinear map governing the dynamics on the unit sphere and analyze its phase space structure through fixed points, stability analysis, bifurcations and Lyapunov exponents. We then discuss the role of symmetries, including rotational and time-reversal symmetry, and how their breaking modifies the dynamics. The quantum description is developed using Floquet theory, where the periodically driven spin system is represented by a unitary Floquet operator acting on a (2j+1)(2j+1)(2j+1)-dimensional Hilbert space. Within this framework, signatures of quantum chaos such as spectral statistics, entanglement generation and recurrences are discussed. The model also admits an interpretation as a system of interacting qubits, enabling explicit few-qubit realizations and direct connections with quantum information measures through reduced density matrices and entanglement entropy. By linking classical phase space structures with quantum dynamical indicators, the QKT provides a clear setting to investigate the emergence of chaotic behavior in the semiclassical limit. The chapter, therefore, highlights the quantum kicked top as a bridge between nonlinear classical dynamics, quantum chaos and modern quantum information science.
We investigate universal features of measurement-and-feedback control of quantum chaotic dynamics by examining the quantum Arnold cat map, a paradigmatic model of quantum chaos. Inspired by probabilistic control of classical chaos, our protocol stochastically alternates between intrinsic instability and engineered control operations that steer trajectories toward a target point. Simulation of exact quantum dynamics and a semiclassical truncated Wigner approximation reveal universal properties of the cat map's control transition. To further characterize this universality, we introduce the inverted harmonic oscillator as an analytically tractable effective model of instability. By integrating numerical simulations, a semiclassical Fokker-Planck description, and a direct spectral analysis of the stochastic quantum channel, we identify quantum signatures absent in classical limits. The close agreement between quantum simulation, truncated Wigner approximation, and inverted oscillator analysis shows that universal features of the transition are set by uncertainty-limited quantum fluctuations and are insensitive to genuine quantum interference.
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We study a method to simulate quantum many-body dynamics of spin ensembles using measurement-based feedback. By performing a weak collective measurement on a large ensemble of two-level quantum systems and applying global rotations conditioned on the measurement outcome, one can simulate the dynamics of a mean-field quantum kicked top, a standard paradigm of quantum chaos. We analytically show that there exists a regime in which individual quantum trajectories adequately recover the classical limit, and show the transition between noisy quantum dynamics to full deterministic chaos described by classical Lyapunov exponents. We also analyze the effects of decoherence, and show that the proposed scheme represents a robust method to explore the emergence of chaos from complex quantum dynamics in a realistic experimental platform based on an atom-light interface.
We uncover a dynamical entanglement transition in a monitored quantum system that is heralded by a local order parameter. Classically, chaotic systems can be stochastically controlled onto unstable periodic orbits and exhibit controlled and uncontrolled phases as a function of the rate at which the control is applied. We show that such control transitions persist in open quantum systems where control is implemented with local measurements and unitary feedback. Starting from a simple classical model with a known control transition, we define a quantum model that exhibits a diffusive transition between a chaotic volume-law entangled phase and a disentangled controlled phase. Unlike other entanglement transitions in monitored quantum circuits, this transition can also be probed by correlation functions without resolving individual quantum trajectories.
Quantum sensors driven into the quantum chaotic regime can have dramatically enhanced sensitivity, which, however, depends intricately on the details of the underlying classical phase space. Here, we develop an accurate semiclassical approach that provides direct and efficient access to the phase-space-resolved quantum Fisher information (QFI), the central quantity that quantifies the ultimate achievable sensitivity. This approximation reveals, in very concrete terms, that the QFI is large whenever a specific dynamical quantity tied to the sensing parameter displays a large variance over the course of the corresponding classical time evolution. Applied to a paradigmatic system of quantum chaos, the kicked top, we show that the semiclassical description is accurate already for modest quantum numbers, i.e., deep in the quantum regime, and it extends seamlessly to very high quantum numbers that are beyond the reach of other methods.