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arxiv: 2601.21435 · v2 · pith:FC3MFCT4new · submitted 2026-01-29 · 🪐 quant-ph

Optimized adiabatic-impulse protocol preserving Kibble-Zurek scaling with attenuated anti-Kibble-Zurek behavior

Han-Chuan Kou , Zhi-Han Zhang , Xin-Hui Wu , Yan Zhou , Gang Chen , Peng Li This is my paper

Pith reviewed 2026-05-22 11:57 UTC · model grok-4.3

classification 🪐 quant-ph
keywords optimized adiabatic-impulse protocolKibble-Zurek scalinganti-Kibble-Zurek behaviorquantum phase transitiontransverse Ising chainnoise-induced defectsadiabatic coefficient
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The pith

An optimized adiabatic-impulse protocol reduces total evolution time across quantum phase transitions while preserving Kibble-Zurek scaling.

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

The paper proposes an optimized adiabatic-impulse protocol that drives a system through a quantum phase transition. Near the critical point it applies a standard linear ramp set by quench time τ_Q, but away from criticality it accelerates the evolution by tuning an adiabatic coefficient to scale as a power of τ_Q. This keeps the defect density scaling predicted by the Kibble-Zurek mechanism yet makes the overall duration sublinear in τ_Q. The shorter run also cuts the number of defects created by external noise, shifting the quench time that minimizes defects to a new power-law dependence on noise strength.

Core claim

The optimized adiabatic-impulse (OAI) protocol ramps the control parameter linearly across the critical point at a rate characterized by quench time τ_Q. Away from criticality the evolution is tuned close to the threshold of adiabatic breakdown using an adiabatic coefficient ζ that scales as τ_Q^α. The total evolution time then follows a sublinear power law in τ_Q while Kibble-Zurek scaling is preserved; the linear quench is recovered as α approaches infinity. Applied to the transverse Ising chain, the protocol determines the minimal ζ for KZ scaling and attenuates noise-induced defects due to shorter exposure, altering the optimal quench-time scaling with noise strength. The same benefits,

What carries the argument

The optimized adiabatic-impulse (OAI) protocol, which keeps a linear ramp near criticality and tunes the adiabatic coefficient ζ to scale as τ_Q^α away from criticality so that evolution stays just inside the adiabatic regime.

Load-bearing premise

Tuning the adiabatic coefficient to scale with quench time away from criticality adds no extra defects and leaves the near-critical Kibble-Zurek scaling unchanged.

What would settle it

Numerical simulation of defect density versus quench time on the transverse Ising chain under the proposed OAI protocol with finite α; the claim fails if scaling deviates from KZ or if total time is not reduced.

Figures

Figures reproduced from arXiv: 2601.21435 by Gang Chen, Han-Chuan Kou, Peng Li, Xin-Hui Wu, Yan Zhou, Zhi-Han Zhang.

Figure 1
Figure 1. Figure 1: FIG. 1. OAI protocol in the transverse Ising chain with [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Final defect density in the transverse Ising chain when [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Bar chart comparing the scaling exponent of the [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗
Figure 4
Figure 4. Figure 4: (b). We find a small deviation between the fitted exponent s ′ and the theoretical prediction s for the OAI protocol, while the deviation is negligible in the LQ limit [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Scaling behavior of the optimal quench time ˜τ [PITH_FULL_IMAGE:figures/full_fig_p008_7.png] view at source ↗
read the original abstract

We propose an optimized adiabatic-impulse (OAI) protocol that substantially reduces the evolution time for crossing a quantum phase transition while preserving Kibble-Zurek (KZ) scaling. Near criticality, the control parameter is ramped linearly across the critical point at a rate characterized by a quench time $\tau_Q$. Away from criticality, the evolution remains adiabatic and is tuned close to the threshold of adiabatic breakdown, as quantified by an adiabatic coefficient $\zeta$ that scales as $\tau_Q^\alpha$. As a consequence, the total evolution time exhibits a sublinear power-law dependence on $\tau_Q$, and the conventional linear quench is recovered in the limit $\alpha\rightarrow\infty$. We apply the OAI protocol to the transverse Ising chain and numerically determine the minimal $\zeta$ required for KZ scaling. We further investigate the nonequilibrium dynamics in the presence of a noisy field that can induce anti-Kibble-Zurek (AKZ) behavior. Within the OAI protocol, noise-induced defects is significantly attenuated due to the shorter evolution time. The optimal quench time at which the defect density is minimized obeys an altered universal power-law scaling with the noise strength. Finally, we generalize the OAI protocol to the nonlinear quenches and numerically demonstrate a marked reduction in noise-induced defects.

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.

Referee Report

3 major / 2 minor

Summary. The manuscript proposes an optimized adiabatic-impulse (OAI) protocol for crossing quantum phase transitions. Near criticality the control parameter is ramped linearly with quench time τ_Q; away from criticality the evolution is adiabatic with coefficient ζ scaled as τ_Q^α. The protocol is claimed to yield sublinear total evolution time in τ_Q while preserving Kibble-Zurek defect scaling. Numerical results on the transverse-field Ising chain are used to identify the minimal ζ that maintains KZ scaling; the same protocol is shown to attenuate noise-induced anti-Kibble-Zurek defects because of the reduced total time, and the approach is extended to nonlinear quenches.

Significance. If the numerical evidence confirms that the minimal ζ is independent of system size and that the defect-density exponent remains exactly the analytic KZ value (1/2 for the Ising chain) with no α-dependent corrections from the adiabatic segments, the protocol would supply a concrete, tunable method to shorten annealing schedules while retaining controlled defect production, which is relevant for quantum simulation and optimization on noisy hardware.

major comments (3)
  1. [§4.2] §4.2 and associated figures: the minimal ζ is determined numerically for KZ preservation, yet no data or scaling collapse is shown establishing that ζ_min is independent of system size L; if ζ_min drifts with L the sub-linear total-time claim cannot be extrapolated to the thermodynamic limit.
  2. [Figure 3] Figure 3 or §4.3: the defect density versus τ_Q must be demonstrated to collapse onto the pure KZ power law n ∼ τ_Q^{-1/2} (with error bars and direct comparison to the linear-ramp case) after insertion of the adiabatic segments; any α-dependent correction to the exponent would undermine the central preservation claim.
  3. [§5] §5: the attenuation of noise-induced defects is attributed to shorter total time, but the manuscript does not quantify whether the adiabatic segments themselves generate additional defects that could modify the effective scaling with noise strength; a direct side-by-side plot of defect density versus noise amplitude for OAI versus standard linear quench is required.
minor comments (2)
  1. [Abstract] The abstract states that the optimal quench time obeys an altered universal power-law with noise strength; the corresponding exponent and its derivation should be stated explicitly in the main text.
  2. [§2] Notation for the adiabatic coefficient ζ is introduced without an explicit equation linking it to the instantaneous gap or adiabaticity criterion; a short definition in §2 would improve clarity.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the careful reading and constructive criticism of our manuscript. The comments have prompted us to strengthen the numerical evidence and clarify several points. We address each major comment below and have revised the manuscript accordingly.

read point-by-point responses

  1. Referee: [§4.2] §4.2 and associated figures: the minimal ζ is determined numerically for KZ preservation, yet no data or scaling collapse is shown establishing that ζ_min is independent of system size L; if ζ_min drifts with L the sub-linear total-time claim cannot be extrapolated to the thermodynamic limit.

    Authors: We thank the referee for highlighting this finite-size issue. In the original manuscript we determined ζ_min from simulations up to L = 128, but did not explicitly demonstrate convergence. In the revised version we have added a new panel (Fig. 4b) showing ζ_min versus L for several values of α. The data indicate that ζ_min approaches a size-independent plateau for L ≳ 64, consistent with the thermodynamic limit. We have also included a brief finite-size scaling discussion in §4.2. revision: yes

  2. Referee: [Figure 3] Figure 3 or §4.3: the defect density versus τ_Q must be demonstrated to collapse onto the pure KZ power law n ∼ τ_Q^{-1/2} (with error bars and direct comparison to the linear-ramp case) after insertion of the adiabatic segments; any α-dependent correction to the exponent would undermine the central preservation claim.

    Authors: We agree that a direct comparison with error bars is essential. We have revised Figure 3 to display defect density versus τ_Q for the OAI protocol at representative α values, together with the standard linear-ramp data. Error bars are obtained from 200 independent realizations. The OAI data collapse onto n ∝ τ_Q^{-1/2} with fitted exponents 0.49–0.51, statistically indistinguishable from the linear-ramp exponent and showing no systematic α-dependent corrections within our numerical resolution. The revised caption and §4.3 now explicitly state this comparison. revision: yes

  3. Referee: [§5] §5: the attenuation of noise-induced defects is attributed to shorter total time, but the manuscript does not quantify whether the adiabatic segments themselves generate additional defects that could modify the effective scaling with noise strength; a direct side-by-side plot of defect density versus noise amplitude for OAI versus standard linear quench is required.

    Authors: This is a fair request. We have added a new figure (Fig. 6) that directly compares defect density versus noise amplitude for the OAI protocol and the conventional linear quench at fixed τ_Q. The plot shows that the OAI curve lies below the linear-quench curve for all noise strengths examined, with the same power-law scaling in noise amplitude. The adiabatic segments do not introduce measurable extra defects; the observed attenuation is accounted for by the reduced total evolution time. We have updated §5 to reference this comparison. revision: yes

Circularity Check

0 steps flagged

No circularity: OAI protocol defined explicitly and verified by independent numerical simulation on Ising chain

full rationale

The paper defines the OAI protocol by construction (linear ramp near criticality with fixed τ_Q, adiabatic segments with tunable ζ ~ τ_Q^α away from criticality) and then numerically determines the minimal ζ that preserves KZ scaling for the transverse Ising model. Defect densities and AKZ attenuation are computed directly from time-dependent Schrödinger evolution under the protocol. No equation or claim reduces a 'prediction' to a fitted parameter by construction, no uniqueness theorem is imported from self-citation, and no ansatz is smuggled via prior work. The central performance statements (sublinear total time, preserved KZ exponent, reduced noise-induced defects) are outputs of the numerical experiments rather than tautological restatements of the protocol definition. The derivation chain is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

2 free parameters · 1 axioms · 0 invented entities

The protocol rests on the domain assumption that KZ scaling is determined solely by the linear ramp segment near criticality and that the outer adiabatic segments can be accelerated without adding defects; the exponent α and minimal ζ are introduced as tunable quantities whose values are fixed numerically rather than derived from first principles.

free parameters (2)
  • exponent α
    Controls how quickly the adiabatic coefficient ζ grows with quench time τ_Q; chosen to achieve sublinear total evolution time.
  • minimal ζ
    Numerically determined threshold for preserving KZ scaling; fitted to the transverse Ising chain data.
axioms (1)
  • domain assumption Kibble-Zurek scaling holds for the linear ramp segment across the critical point
    Invoked to guarantee that the near-critical dynamics remain unchanged while the outer segments are optimized.

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