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arxiv: 2606.26870 · v1 · pith:UBMZXP2Unew · submitted 2026-06-25 · 🪐 quant-ph · cond-mat.stat-mech· cond-mat.str-el

Dissipation-Induced Deviations from Kibble-Zurek Scaling in Non-Hermitian Quantum Annealing

H. Najafzadeh , S. Sadeghizade , R. Jafari , A. Langari This is my paper

Pith reviewed 2026-06-26 04:57 UTC · model grok-4.3

classification 🪐 quant-ph cond-mat.stat-mechcond-mat.str-el
keywords quantum annealingKibble-Zurek scalingnon-Hermitian Ising modeldefect densitydissipationexcitation probabilitiesmomentum sectorstransverse field
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The pith

Dissipation strength in non-Hermitian quantum annealing determines whether defect density follows standard Kibble-Zurek scaling, anti-Kibble-Zurek behavior, or faster suppression.

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

The paper establishes that quantum annealing in the non-Hermitian transverse-field Ising model produces defect densities whose scaling with annealing time depends on dissipation strength. Unlike the Hermitian case, where defects arise mainly from modes near the gap-closing point, here broad momentum sectors contribute substantially to the excitation probabilities. These probabilities directly explain the three observed regimes: standard scaling at weak dissipation, extra excitations causing anti-Kibble-Zurek growth at intermediate strength, and vanishing probabilities causing faster suppression at stronger dissipation. A sympathetic reader would care because the result shows how openness alters the reliability of ground-state preparation in quantum annealing protocols.

Core claim

In the non-Hermitian transverse-field Ising model the intrinsic transition probabilities involve significant contributions from broad momentum sectors rather than only near the gap-closing point. Depending on dissipation strength the resulting defect density exhibits standard Kibble-Zurek scaling, anti-Kibble-Zurek behavior, or suppression faster than the Kibble-Zurek prediction. The fast decay originates from a vanishing excitation probability that spans a range of annealing times across all allowed modes, while the anti-Kibble-Zurek behavior arises from supplementary excitations facilitated by dissipation over a broad range of modes away from the gap-closing region.

What carries the argument

The excitation probabilities across all momentum modes, which determine the defect density through the non-Hermitian dynamics.

If this is right

  • Defect density can exhibit anti-Kibble-Zurek scaling when dissipation adds excitations over a wide momentum range.
  • Faster-than-Kibble-Zurek suppression occurs when excitation probability vanishes across all modes for a range of annealing times.
  • The deviations are tied directly to the momentum dependence of the intrinsic transition probabilities rather than to the gap-closing region alone.
  • Standard Kibble-Zurek scaling is recovered only in the limit of weak dissipation where broad-sector contributions remain small.

Where Pith is reading between the lines

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

  • The same broad-momentum mechanism could be tested in other non-Hermitian models by varying the dissipation operator while keeping the annealing schedule fixed.
  • If confirmed, the result would imply that open-system annealing protocols can deliberately tune defect production by choosing dissipation strength to enter the faster-suppression regime.
  • The analysis suggests checking whether similar deviations appear when the annealing path passes near other types of critical points in non-Hermitian systems.
  • Numerical checks for finite-size chains could quantify how the width of the momentum sectors that contribute changes with system size.

Load-bearing premise

The non-Hermitian transverse-field Ising model together with the chosen form of dissipation correctly captures the physical system and that the derived transition probabilities accurately reflect the broad momentum contributions driving the scaling deviations.

What would settle it

A plot of defect density versus annealing time for several fixed values of dissipation strength that shows the three distinct regimes, including anti-Kibble-Zurek growth and faster-than-Kibble-Zurek suppression.

Figures

Figures reproduced from arXiv: 2606.26870 by A. Langari, H. Najafzadeh, R. Jafari, S. Sadeghizade.

Figure 1
Figure 1. Figure 1: FIG. 1. (Color online) Phase diagram of the dissipative [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. (Color online) The density plot of excitation probabil [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. (Color online) The defect density versus annealing [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. (Color online) The density plot of excitation proba [PITH_FULL_IMAGE:figures/full_fig_p005_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. (Color online) Density of excitation versus annealing [PITH_FULL_IMAGE:figures/full_fig_p006_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. (Color online) The density of excitations versus the [PITH_FULL_IMAGE:figures/full_fig_p011_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9. (Color online) Density of excitations versus annealing [PITH_FULL_IMAGE:figures/full_fig_p012_9.png] view at source ↗
read the original abstract

We revisit the quantum annealing problem in the non-Hermitian transverse-field Ising model. We determine, both analytically and numerically, the intrinsic transition probabilities and the resulting defect density. Our results reveal that, unlike the Hermitian case where defect production is dominated by modes near the gap-closing point, the non-Hermitian dynamics involve significant contributions from broad momentum sectors. We find that, depending on the dissipation strength, the defect density exhibits standard Kibble-Zurek scaling, anti-Kibble-Zurek behavior, and a suppression faster than the Kibble-Zurek prediction. We demonstrate that these deviations from the standard Kibble-Zurek scaling can be understood in terms of the underlying excitation probabilities. Specifically, the fast decay of the defect density originates from a vanishing excitation probability spanning a range of annealing times across all allowed modes, even at the gap-closing points. In contrast, the anti-Kibble-Zurek behavior arises from supplementary excitations facilitated by dissipation over a broad range of allowed modes, particularly those situated away from the gap-closing region.

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

0 major / 2 minor

Summary. The paper studies quantum annealing in the non-Hermitian transverse-field Ising model. It determines transition probabilities and defect density both analytically and numerically, showing that non-Hermitian dynamics allow significant contributions from broad momentum sectors (unlike the Hermitian case, which is dominated by modes near the gap-closing point). Depending on dissipation strength, the defect density exhibits standard Kibble-Zurek scaling, anti-Kibble-Zurek behavior, or suppression faster than the KZ prediction; these regimes are tied to the functional form of the excitation probabilities, including vanishing probabilities across modes for fast suppression and supplementary excitations away from the gap-closing region for anti-KZ scaling.

Significance. If the analytical derivations and numerical results hold, the work provides a concrete mechanism by which dissipation modifies the Kibble-Zurek scaling in non-Hermitian systems, identifying three distinct regimes directly linked to excitation probabilities. The explicit contrast with the Hermitian case and the focus on broad-momentum contributions constitute a clear advance in understanding defect production in open quantum annealing protocols.

minor comments (2)
  1. The abstract states that results are obtained 'both analytically and numerically,' but the main text should include explicit error bars, convergence checks, and system-size scaling for the numerical data to substantiate the reported scaling exponents.
  2. Notation for the dissipation strength and the momentum sectors should be defined once at first use and used consistently; occasional redefinition of symbols can obscure the connection between the excitation probability expressions and the three scaling regimes.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their positive summary and recommendation of minor revision. The report identifies no specific major comments requiring point-by-point response.

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The paper derives transition probabilities and defect densities analytically and numerically from the non-Hermitian transverse-field Ising model dynamics. The reported scalings (standard KZ, anti-KZ, faster suppression) are presented as direct consequences of the functional form of excitation probabilities across momentum sectors, with no reduction to fitted parameters, self-definitions, or load-bearing self-citations. The central claims rest on explicit model calculations rather than renaming or circular invocation of prior results by the same authors.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

No information is available from the abstract to populate free parameters, axioms, or invented entities.

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