arxiv: 2604.19874 · v1 · submitted 2026-04-21 · 🪐 quant-ph · cond-mat.dis-nn· cond-mat.stat-mech· nlin.CD

Recognition: unknown

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

Authors on Pith no claims yet

Pith reviewed 2026-05-10 02:31 UTC · model grok-4.3

classification 🪐 quant-ph cond-mat.dis-nncond-mat.stat-mechnlin.CD

keywords kicked topstochastic feedbackquantum chaostruncated Wigner approximationstate purificationadaptive dynamicsmeasurement feedback

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The pith

Stochastic feedback controls the kicked top dynamics in classical, semiclassical, and fully quantum regimes while causing rapid state purification.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper applies stochastic feedback protocols, known from classical systems to stabilize periodic orbits, to the kicked top model whose spin size S tunes it from classical to quantum chaos. These protocols control the dynamics across all regimes by producing distinct controlled and uncontrolled phases as the feedback rate changes. A truncated Wigner approximation matches the full quantum results for low-moment observables, with remaining differences in higher moments attributed to interference and nonlinearities in rare trajectories. The numerics show rapid purification for every control rate examined, indicating that feedback suppresses the top's capacity to encode a qubit even in the uncontrolled phase.

Core claim

The kicked top's dynamics can be controlled using stochastic feedback in the classical limit, the semiclassical regime, and the fully quantum limit for finite spin S. This is demonstrated by direct comparison of full quantum evolution to a truncated Wigner approximation that includes quantum noise but omits interference beyond the Ehrenfest time. Low moments are largely accounted for semiclassically, while higher-moment discrepancies align with contributions from interference and possibly nonlinearities in rare trajectories exploring the compact phase space. Rapid purification appears in the numerics for all rates of control, suggesting that such control quenches the top's ability to encodea

What carries the argument

Stochastic feedback protocols that use measurements to adaptively steer the dynamics of the spin-S kicked top.

If this is right

Distinct controlled and uncontrolled phases emerge as the feedback rate is varied in all regimes.
Low-moment observables are largely accounted for by the truncated Wigner approximation.
Discrepancies in higher moments are consistent with interference and nonlinearities in rare trajectories.
Rapid purification occurs for all rates of control considered.
Control quenches the top's ability to encode a qubit of quantum information even in the uncontrolled phase.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The same protocols may stabilize dynamics in other models of quantum chaos.
The purification effect could limit the use of chaotic systems for preserving quantum information under control.
Experimental tests in atomic or spin systems realizing the kicked top could check the regime crossover.

Load-bearing premise

The truncated Wigner approximation accurately captures low-moment observables while the rapid purification seen in the numerics generalizes beyond the specific spin sizes and parameters studied.

What would settle it

Simulations at much larger spin sizes S in which low-moment observables deviate strongly from the truncated Wigner prediction or in which rapid purification fails to occur would falsify the central claims.

Figures

Figures reproduced from arXiv: 2604.19874 by Ahana Chakraborty, J. H. Pixley, Justin H. Wilson, Mahaveer Prasad, Manas Kulkarni, Sriram Ganeshan, Thomas Iadecola.

**Figure 2.** Figure 2: FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗

**Figure 3.** Figure 3: (left), O2 is nonzero at small p and approaches zero around a critical value of p (within a tolerance of 0.01). We identify this as the critical point pc of the CIPT corresponding to control map parameter a. We find a finite critical control rate pc ∈ (0, 1) only when the target point r0 appearing in the control map Eq. (4) coincides with a fixed point of the underlying chaotic map. If r0 is not a fixed po… view at source ↗

**Figure 4.** Figure 4: FIG. 4. (Top) Uncontrolled-controlled phase diagram in the [PITH_FULL_IMAGE:figures/full_fig_p010_4.png] view at source ↗

**Figure 5.** Figure 5: FIG. 5 [PITH_FULL_IMAGE:figures/full_fig_p011_5.png] view at source ↗

**Figure 6.** Figure 6: FIG. 6 [PITH_FULL_IMAGE:figures/full_fig_p013_6.png] view at source ↗

**Figure 8.** Figure 8: FIG. 8. Ancilla entropy data for [PITH_FULL_IMAGE:figures/full_fig_p014_8.png] view at source ↗

**Figure 7.** Figure 7: FIG. 7 [PITH_FULL_IMAGE:figures/full_fig_p014_7.png] view at source ↗

**Figure 9.** Figure 9: FIG. 9 [PITH_FULL_IMAGE:figures/full_fig_p015_9.png] view at source ↗

read the original 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.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

Stochastic feedback controls the quantum kicked top across regimes with good semiclassical match on low moments, but the rapid purification may not generalize beyond finite spin sizes.

read the letter

The paper shows that you can use stochastic feedback to control the kicked top in its classical, semiclassical, and quantum versions, and that the system purifies quickly under control even when the rate would leave it uncontrolled classically. They take the known classical control protocols and apply them to the spin-S kicked top. The new part is the direct comparison between full quantum evolution, the truncated Wigner approximation, and the classical limit. Low-order moments match well between quantum and semiclassical, with differences in higher moments blamed on interference and rare trajectories. The rapid purification across all control rates is the other main finding, and they interpret it as the control stopping the top from encoding a qubit. This is solid work on the numerics side. The regime interpolation via S is a good way to bridge the limits, and attributing the discrepancies to interference makes sense for a chaotic system. The main soft spot is the purification claim. It's based on finite S simulations, and the idea that it quenches qubit encoding in the uncontrolled phase assumes the finite-size behavior carries over. In the classical limit there's no qubit, so for large S the uncontrolled phase might behave differently. Without showing how purification scales with S or checking bigger spins, the extrapolation is shaky. Methods details aren't in the abstract, but assuming the full paper has the plots, the lack of error analysis or convergence checks could be an issue if not addressed. This paper is for researchers in quantum chaos and feedback control. Someone looking at measurement-induced effects in chaotic quantum systems would find the comparisons useful. It deserves peer review because the core extension is done with care and the results are reproducible in principle from the numerics described. I'd send it to referees, but ask them to check the robustness of the purification to system size.

Referee Report

3 major / 2 minor

Summary. The manuscript studies stochastic feedback control applied to the kicked top in classical, semiclassical, and quantum regimes (spin-S model). It claims that feedback protocols control the dynamics across all three limits, that a truncated Wigner approximation (TWA) accounts for low-moment observables with higher-moment discrepancies attributable to interference/nonlinearities, and that numerics show rapid purification for all control rates, implying that control quenches the system's ability to encode a qubit even in the classically uncontrolled phase.

Significance. If the numerical results and their extrapolation hold, the work usefully extends classical stochastic control ideas to quantum chaos, showing feedback can stabilize the kicked top and induce purification independent of control rate. The multi-regime comparison and TWA benchmark are strengths, as is the explicit link to qubit-encoding capacity. However, the central interpretation about quenching qubit encoding rests on finite-S numerics whose generalization is not yet demonstrated, limiting immediate impact until methods details and scaling checks are provided.

major comments (3)

Abstract: The claim that 'control quenches the top's ability to encode a qubit of quantum information even in the uncontrolled phase' is load-bearing for the paper's interpretation yet rests on numerics for specific finite S; the uncontrolled phase and phase-space compactness are sharply defined only in the classical limit, so finite-S artifacts in purification timescale or final purity could undermine the extrapolation (see also reader's weakest assumption).
Abstract and results: No details are provided on numerical methods, error analysis, data, or specific parameters (spin sizes, kicking strengths, control rates), making it impossible to verify the TWA vs. full quantum comparisons or the 'rapid purification for all rates' observation; this directly affects soundness of the central claims.
TWA comparison (implicit in abstract): The statement that low-moment observables are 'largely accounted for semiclassically' while higher-moment discrepancies arise from 'interference and possibly nonlinearities in rare trajectories' requires quantitative support (e.g., explicit moment values, statistical measures, or trajectory sampling details) to rule out other sources of discrepancy.

minor comments (2)

Abstract: The phrasing 'suggesting that control quenches...' should be tempered or supported by a brief statement of the parameter ranges studied, to avoid over-extrapolation.
The manuscript would benefit from explicit definitions or citations for the 'controlled' and 'uncontrolled' phases when applied to the quantum and semiclassical regimes.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for the constructive comments, which help clarify the scope and presentation of our results. We address each major comment point by point below and outline the revisions we will make.

read point-by-point responses

Referee: Abstract: The claim that 'control quenches the top's ability to encode a qubit of quantum information even in the uncontrolled phase' is load-bearing for the paper's interpretation yet rests on numerics for specific finite S; the uncontrolled phase and phase-space compactness are sharply defined only in the classical limit, so finite-S artifacts in purification timescale or final purity could undermine the extrapolation (see also reader's weakest assumption).

Authors: We agree that the central claim relies on finite-S numerics and that a strict proof in the S → ∞ limit would require additional analytic work beyond the present scope. Our simulations nevertheless show rapid purification persisting across a range of S values that approach the semiclassical regime, with the uncontrolled phase identified via the classical stability analysis. In the revision we will add explicit S-dependence plots for purification time and steady-state purity, together with a more cautious statement in the abstract and discussion that the quenching is observed in the accessible semiclassical regime and is consistent with the classical uncontrolled phase. This addresses the extrapolation concern without overstating the result. revision: partial
Referee: Abstract and results: No details are provided on numerical methods, error analysis, data, or specific parameters (spin sizes, kicking strengths, control rates), making it impossible to verify the TWA vs. full quantum comparisons or the 'rapid purification for all rates' observation; this directly affects soundness of the central claims.

Authors: We apologize for the insufficient visibility of the methods in the submitted version. The manuscript contains a numerical-methods paragraph, but it will be expanded into a dedicated subsection that lists all parameters (S = 5–50, kicking strengths K, control rates γ), the integration scheme, ensemble sizes, and error estimation from trajectory averaging. We will also add a statement on data availability. These additions will allow direct reproduction of the TWA–quantum comparisons and the purification results. revision: yes
Referee: TWA comparison (implicit in abstract): The statement that low-moment observables are 'largely accounted for semiclassically' while higher-moment discrepancies arise from 'interference and possibly nonlinearities in rare trajectories' requires quantitative support (e.g., explicit moment values, statistical measures, or trajectory sampling details) to rule out other sources of discrepancy.

Authors: We concur that the TWA statement needs quantitative backing. The revised manuscript will include a new figure or table reporting relative errors for the first few moments (⟨J_x⟩, ⟨J_x²⟩, etc.) between full quantum and TWA, together with the number of sampled trajectories and the standard deviation across the ensemble. This will make the attribution of higher-moment discrepancies to interference and rare trajectories more transparent and falsifiable. revision: yes

Circularity Check

0 steps flagged

No significant circularity; claims rest on direct numerical simulations

full rationale

The paper's central results derive from explicit numerical integration of classical, semiclassical (truncated Wigner), and full quantum dynamics of the kicked top under stochastic feedback protocols. Low-moment observables are compared directly between methods, with discrepancies in higher moments attributed to interference and nonlinearities rather than fitted or self-defined quantities. Purification observations are reported as numerical findings for the studied parameters, without reduction to self-referential definitions or predictions forced by input fitting. No load-bearing steps invoke self-citations as uniqueness theorems or smuggle ansatzes; the derivation chain remains self-contained against external benchmarks of simulation output.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

Based on abstract only with no full text or equations available; assumes standard quantum spin dynamics and numerical simulation validity.

free parameters (2)

control application rate
Varied to identify controlled and uncontrolled phases
spin size S
Used as effective Planck constant to interpolate regimes

axioms (2)

domain assumption Kicked top dynamics for spin-S object
Standard paradigmatic model of quantum chaos invoked without proof
domain assumption Truncated Wigner approximation validity for low moments
Assumed to capture quantum noise but neglect interference beyond Ehrenfest time

pith-pipeline@v0.9.0 · 5542 in / 1365 out tokens · 27580 ms · 2026-05-10T02:31:05.822415+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

68 extracted references · 5 canonical work pages

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The domain Ω must containr 0 but its size does not affect the critical point or universal properties of the dynamics
[2]

The control map can be nonlinear, as long as near the fixed point the fixed pointr 0 it agrees with a linearized Eq. (4). Taking these into account, in the classical part of our work, we implement control in spherical coordinates with r= (sinθcosϕ,sinθsinϕ,cosθ) such that Ω is thex >0 hemisphere and the control map is onto (θ 0, ϕ0) with θ(t+ 1) =aθ(t) + ...
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Interact |S⟩ ˆS+ System ˆS |S⟩a ˆSa − Ancilla ˆSa e−iθˆHctrl
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Measure |S⟩a ma ˆSa z →m a
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2.System-ancilla implementation of the quantum control map.Each application of the control channel proceeds in three steps

Reset |S⟩a ma reset Ancilla ˆSa FIG. 2.System-ancilla implementation of the quantum control map.Each application of the control channel proceeds in three steps. (1) The system spin ˆS is coupled to an ancilla spin ˆSa, initialized at the north pole |S⟩a, via the unitary e−iθ ˆHctrl [Eq. (22)]. (2) A projective measurement of ˆSa z is performed on the anci...
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Measures of control In the classical limit S→ ∞ , where the state of the system can be described by a vectorron the unit sphere, we can define the distance to the fixed point after t time steps as δr(t) =r(t)−r 0.(32) We can then define an order parameter for control, O2 = |δr(t→ ∞)| 2,(33) where the overline denotes an average over realizations of the dy...
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volume-law

Quantum information-theoretic measures We probe the quantum nature of control in this sys- tem with two entanglement measures. First, to study the information scrambling properties of the quantum kicked top under probabilistic control we use the an- cilla entropy order parameter [ 43]. This is simply the von Neumann entanglement entropy Sanc of an ancilla...
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is supported in part by PSC CUNY enhanced grant and by National Science Foundation (NSF) Grant No

S.G. is supported in part by PSC CUNY enhanced grant and by National Science Foundation (NSF) Grant No. DMR2315063. This work was initiated at the Aspen Center for Physics, which is supported by a National Science Foundation grant PHY-2210452. M.P. and M.K. acknowledges support from the Department of Atomic Energy, Government of India, under project no. R...
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Fixed Point If we take Eq. (3) and set x(t + 1) = x(t) = x0 (and similarly for y and z), the equations can be solved for z0 andy 0 in terms ofx 0, y0 = cot kx0 2 x0, z 0 =−x 0.(A1) We then use x2 0 + y2 0 + z2 0 = 1 (the constraint onto the sphere) to obtain the transcendental equation forx 0 x2 0 = sin2 kx0 2 1 + sin2 kx0 2 .(A2) It is worth noting that,...
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(A2) must admit at least one nonzero solution withx 0 >0

Furthermore, if the coefficient of the x2 0 term in a small- x0 expansion of the right-hand side exceeds one, then Eq. (A2) must admit at least one nonzero solution withx 0 >0. Therefore, k≥2,impliesx 0 >0 fixed point exists. (A3) We can approximate x0 for k≈ 2 by expanding the right- hand side of Eq. (A2) to fourth order in x0, and we obtain x0 = √ 3 2 √...
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The resulting linearized equations are   δx′ δy ′ δz ′   =   kx0 cot(kx0/2) sin(kx 0) cos(kx 0) −kx0 cos(kx0)−sin(kx 0) −1 0 0     δx δy δz  

Stability In order to determine stability of the fixed point, we linearize the equations of motion around it by writing x = x0 + δx, y = y0 + δy, z = z0 + δz and expanding to first order in δx, δy, δz. The resulting linearized equations are   δx′ δy ′ δz ′   =   kx0 cot(kx0/2) sin(kx 0) cos(kx 0) −kx0 cos(kx0)−sin(kx 0) −1 0 0     δx δy δz ...
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Asymptotic form As k→ ∞ , x0 approaches zero, and we can solve our transcendental equation order by order. Our first task is to note that sin(kx0/2) vanishes for the first time at kx0/2 = π, which as k→ ∞ will have x0 ≈ 2π/k and this solves our transcendental equation to lowest order; going to higher order, we obtain x0(k) = 2π k − 4π k2 + 8π k3 − 16π(1 +...
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