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This research establishes universal principles for controlling quantum chaotic systems, such as the Arnold cat map, using measurement-and-feedback protocols that rely on uncertainty-limited fluctuations rather than genuine quantum interference. By bridging exact quantum simulations with semiclassical Fokker-Planck descriptions, the study clarifies how engineered operations can steer unstable trajectories toward specific targets without being hindered by decoherence effects typical in classical chaos control. These findings advance the theoretical framework for stabilizing complex quantum dynamics through stochastic intervention.
Universality of Stochastic Control of Quantum Chaos with Measurement and Feedback
arXiv:2506.10067v3 Announce Type: replace Abstract: 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.
Abstract: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.
Quantum Physics (quant-ph); Disordered Systems and Neural Networks (cond-mat.dis-nn); Statistical Mechanics (cond-mat.stat-mech); Chaotic Dynamics (nlin.CD)
arXiv:2506.10067 [quant-ph]
(or arXiv:2506.10067v3 [quant-ph] for this version)
Phys. Rev. Lett. 136, 210401 (2026)
https://doi.org/10.1103/xgfv-p42g DOI(s) linking to related resources
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