Chaotic Quantum Systems Become Stable with Feedback Control Techniques

Scientists Mahaveer Prasad and colleagues at the International Centre for Theoretical Sciences (ICTS-TIFR), in collaboration with Louisiana State University, Ames National Laboratory, Rutgers University, City College, The Pennsylvania State University, City University of New York, Tata Institute of Fundamental Research, CUNY Graduate Centre, National University of Singapore 117543, Singapore University of Technology and Design, Flatiron Institute, USA and 10 Materials Research Institute, Centre for Computational Quantum Physics, demonstrate control of chaotic systems using stochastic feedback, a technique with implications for stabilising unstable orbits in classical dynamics. The findings reveal that lower-order dynamics are well-described by semiclassical approximations. However, discrepancies in higher-order moments highlight the importance of quantum interference effects. Importantly, this control sharply diminishes the kicked top’s potential as a qubit for quantum information storage.

Rapid Stochastic Purification Eliminates Quantum Information Storage in Kicked Tops

A 99.9% reduction in the kicked top’s ability to encode a qubit of quantum information demonstrates that stochastic feedback rapidly diminishes its potential for quantum information storage. This significant purification was observed consistently across all control rates studied, representing a key departure from previous quantized models which often exhibit extended phases suitable for qubit encoding; the kicked top does not exhibit this behaviour under stochastic control. The finding establishes stochastic control of chaos across classical, semiclassical, and fully quantum regimes, revealing a crossover from extensive to subextensive entanglement as spin size ‘S’ increases, effectively acting as a Planck constant in this system. Low-moment observables align with semiclassical predictions, while discrepancies in higher moments suggest contributions from quantum interference and rare trajectories exploring the system’s phase space. A moment-threshold diagram was constructed, indicating the range of observables governed by fixed-point linear stability, and entanglement diagnostics showed a crossover from extensive to subextensive entanglement scaling with log2 S. The kicked top, a model system for quantum chaos, consists of a rigid body rotated impulsively about two orthogonal axes. Its quantum analogue is particularly sensitive to chaotic behaviour, making it an ideal testbed for control protocols.

The concept of stochastic feedback control involves making small, random corrections to a system’s parameters based on its current state. These corrections, when applied appropriately, can counteract the natural tendency of chaotic systems to diverge from predictable trajectories. In this study, the researchers applied this technique to the kicked top, meticulously adjusting the control rate to observe its effect on the system’s dynamics. The observed 99.9% reduction in qubit encoding capability is a substantial result, indicating that while the system can be stabilised, its quantum properties are severely compromised. This is because the stochastic corrections effectively destroy the delicate quantum coherence necessary for maintaining quantum information. The implications extend beyond the kicked top itself, suggesting a fundamental trade-off between controlling chaos and preserving quantum information in more complex systems. Previous attempts at controlling quantum chaos often focused on suppressing the chaotic behaviour entirely, which can be difficult to achieve without also suppressing the desired quantum properties. This work demonstrates a different approach, stabilisation through stochastic feedback, but highlights its detrimental effect on quantum information storage.

Stabilising quantum chaos via stochastic feedback compromises qubit coherence

Controlling chaos has long been a goal, offering potential to stabilise systems ranging from satellite orbits to fusion reactors. This work successfully extends that control into the quantum realm, a feat previously elusive despite progress in classical dynamical systems. However, this approach, while effective at stabilisation, appears to rapidly destroy the kicked top’s potential as a quantum bit, or qubit. The technique employs continuous corrections, successfully governing the behaviour of the kicked top model across classical, semiclassical, and fully quantum states, representing a major advancement in controlling chaotic systems, a longstanding goal across multiple scientific fields. The classical kicked top is a well-studied example of a chaotic system, exhibiting sensitive dependence on initial conditions. The quantum kicked top introduces the complexities of quantum mechanics, including wave-particle duality and the uncertainty principle, leading to a richer and more nuanced dynamical behaviour.

Previous investigations focused on classical systems, but this work demonstrates a unified control mechanism applicable across classical, semiclassical, and quantum regimes. Stochastic feedback protocols applied to the kicked top, a model of quantum chaos, allow control of the dynamics regardless of the limit. Comparing quantum dynamics with a Wigner approximation reveals that low-moment observables are well described semiclassically, while discrepancies in higher moments relate to interference and rare trajectories. The Wigner function provides a quasi-probability distribution in phase space, allowing for a direct comparison between classical and quantum dynamics. This observation suggests the system’s behaviour is relatively simple at low energies. However, the deviations observed in higher moments indicate the importance of quantum effects, such as interference and tunnelling, which become more pronounced at higher energies. Rapid purification was also indicated by the analysis, suggesting control limits the system’s ability to encode quantum information. This purification process effectively suppresses the chaotic fluctuations, but at the cost of destroying the quantum coherence required for qubit operation. The researchers characterised the entanglement properties of the system using entanglement diagnostics, revealing a crossover from extensive to subextensive entanglement scaling with log2 S. This indicates that the amount of entanglement in the system grows more slowly than linearly with the spin size, suggesting a fundamental limit to the system’s ability to store quantum information. The value of ‘S’ effectively acts as a Planck constant, governing the scale at which quantum effects become significant.

The implications of this research are significant for the field of quantum information processing. While the kicked top itself is unlikely to be used as a practical qubit, the findings provide valuable insights into the challenges of controlling and preserving quantum coherence in chaotic systems. Understanding these challenges is crucial for developing more robust and reliable quantum technologies. Further research will focus on exploring alternative control strategies that can stabilise chaotic systems without sacrificing quantum information storage capabilities, potentially opening new avenues for quantum computation and communication.

The researchers demonstrated that stochastic feedback control can stabilise the dynamics of a kicked top across classical, semiclassical, and fully quantum regimes. This control maintains stability regardless of the system’s complexity, as evidenced by the analysis of spin-S objects where ‘S’ represents an effective Planck constant. Comparison with a Wigner approximation revealed that low-moment observables are well-described by semiclassical methods, while discrepancies in higher moments suggest the influence of quantum interference. The study also found that this control rapidly suppresses the system’s ability to store quantum information, indicating a trade-off between control and quantum coherence.