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Magnetic Memory and Hysteresis from Quantum Transitions: Theory and Experiments on Quantum Annealers

T0 review · 5 major / 6 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read This paper claims that hysteresis on D-Wave quantum annealers in one-dimensional rings of up to 4,906 qubits is a genuine quantum memory effect, explained by interleaving Landau-Zener transitions with semiclassical domain-wall kinetics.

desk verdict A substantial experimental dataset and a novel hybrid LZ-semiclassical model, but the claim of genuine quantum memory is undercut by the absence of a classical stochastic control. read the letter →

arxiv 2507.18079 v1 pith:7FWFWYA4 submitted 2025-07-24 quant-ph cond-mat.stat-mech

Frank Barrows , Elijah Pelofske , Pratik Sathe , Francesco Caravelli , Cristiano Nisoli This is my paper · ORCID
classification quant-phcond-mat.stat-mech
keywords quantumannealingtransverse-fieldIsingmodelLandau-Zenertransitionshysteresisdomain-wallkineticsmemorykinkdensityscalingD-Waveannealer
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper argues that the hysteresis loops seen on D-Wave quantum annealers are genuine quantum memory effects, not classical metastability or hardware noise. In one-dimensional ferromagnetic rings with periodic boundary conditions, up to 4,906 qubits, classical Ising physics forbids stable magnetization and hysteresis, yet the annealers show clear coercivity, loop area, and even transiently negative susceptibility. The proposed mechanism combines two-level Landau-Zener transitions at avoided level crossings, where the sweep excites spin flips, with semiclassical domain-wall kinetics that relaxes the system back toward alignment. This hybrid model reproduces the measured kink densities, loop shapes, non-monotonic reversals, and longitudinal sweep-rate scaling across three different annealers. If correct, it makes programmable annealers a testbed for memory and irreversibility in driven quantum many-body systems.

What carries the argument

The load-bearing object is the interleaved evolution operator $T = \hat T^{t_\infty,t_n}_{\mathrm{sc}} U(t_n,t_{n-1}) \cdots \hat T^{t_2,t_1}_{\mathrm{sc}} U(t_0,t_1) \hat T^{t_1,t_{-\infty}}_{\mathrm{sc}}$, where $U$ is a first-order piecewise-constant propagator built by freezing the Hamiltonian on slices $\Delta t \ll \tau_{LZ} = \Delta E_{\min}/\dot h$, and $\hat T_{\mathrm{sc}}$ projects the wavefunction onto amplitudes whose domain-wall densities match a semiclassical kinetic equation. The independent level crossing approximation lets each avoided crossing behave as a separate two-level Landau-Zener scatterer with diabatic probability $p = e^{-\pi\Gamma^2/(2\hbar\dot h)}$; between crossings, domain walls drift at a velocity bounded by $v(t) \le v_0 h(t)$ and annihilate at rate $\Omega$. An iterative proportional fitting update minimizes the Kullback-Leibler divergence between quantum and semiclassical kink densities, coupling the two dynamics into one evolution.

What would settle it

A discriminating test is to fit the measured kink-density scaling and loop shapes with a purely classical thermal model at the device temperature (about 15 mK); if that model reproduces the non-monotonic dips and the $\ln(1-n_d) \propto 1/\dot h$ scaling without any Landau-Zener ingredient, the claim that the memory is quantum is falsified. Conversely, if the linear scaling breaks down in the regime where avoided crossings overlap ($\Gamma \sim J$), the independent level crossing approximation is falsified.

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Extended reading notes

Core claim

The central discovery is that magnetization reversal in the driven transverse-field Ising model is governed by the competition between diabatic and adiabatic evolution at avoided crossings, with memory supplied by transient occupation of excited states that decay through domain-wall motion. In one-dimensional rings, reversal consistently begins near $|h| = 2J$ regardless of system size, and the kink density follows a Landau-Zener scaling $\ln(1-n_d) \propto (\Gamma')^2/(\dot h)$, which the experiments confirm for intermediate transverse-field strengths. The model's interleaved evolution, a first-order piecewise-constant propagator $\exp[-iH(t_n)\Delta t/\hbar]$ combined with kinetic equations that move and annihilate domain walls, reproduces the measured loop shapes, including the non-monotonic dips and negative susceptibilities that pure unitary or mean-field treatments miss. The paper concludes that the observed coercivity is a quantum memory effect arising from local entanglement at crossings, with relaxation supplied by domain-wall kinetics rather than sustained global coherence.

Load-bearing premise

The load-bearing assumption is the independent level crossing approximation: avoided crossings in the $N$-qubit ring are well separated in time and energy so each spin flip can be treated as an isolated two-level Landau-Zener transition, and the paper itself states that the transverse-field Ising model typically violates the required conditions except in restricted subspaces, with the approximation breaking down at weak transverse field.

Editorial extensions

If this is right

  • In one-dimensional rings, magnetization reversal begins near $|h| = 2J$ independent of system size, supporting a local domain-nucleation picture for the reversal.
  • Stronger transverse fields and longer anneal times shrink the hysteresis loop and move reversal to smaller $|h|$, consistent with quantum fluctuations and dwell time near crossings easing spin flips.
  • The kink density obeys the Landau-Zener scaling $\ln(1-n_d) = [A(s)\Gamma']^2 T_{\mathrm{sweep}}/(\hbar B(s)^4 |h'_{\max}|)$ in the intermediate coupling range, giving a quantitative prediction for future sweep-rate experiments.
  • Non-monotonic magnetization reversals and transiently negative susceptibility are signatures of short-lived occupation of excited states, a feature suppressed in two-dimensional systems where domain growth is more costly.
  • Mean-field dynamics captures the loop-area scaling $A \sim \Gamma^2$ but deviates at large $\Gamma$, so a complete account requires the discrete transitions and domain relaxation that the hybrid model includes.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Editorial inference: the same interleaving construction should transfer to oscillatory or Floquet longitudinal drives, where successive crossings repeat each period and could produce frequency-dependent loop areas that the current single-cycle experiments do not report.
  • Editorial inference: the semiclassical update acts like a phenomenological dissipation channel; replacing it with an explicit Lindblad master equation and comparing the fitted $\alpha_0$ and $\kappa$ to measured relaxation times would test whether domain-wall kinetics is really the decoherence mechanism.
  • Editorial inference: the model's stated failure at weak transverse field ($s_{\mathrm{pause}}>0.5$), where simulations no longer match experiment, hints that thermal-assisted tunneling takes over; a temperature-variation experiment on the same devices would separate that from pure Landau-Zener dynamics.
  • Editorial inference: because the reversal field pins near $|h|=2J$ and the dip shape depends on $J/\Gamma$, the annealers could be used as metrology for spurious couplings by fitting the non-monotonic feature position, not just the loop area.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

5 major / 6 minor

Summary. The manuscript reports magnetic hysteresis experiments on D-Wave quantum annealers for transverse-field Ising models in one-dimensional rings (up to 4,906 qubits) and two-dimensional grids, with a time-dependent longitudinal field. It proposes a hybrid theoretical framework that interleaves a first-order piecewise-constant unitary propagator with semiclassical domain-wall kinetics and an iterative-proportional-fitting-like amplitude update, Eqs. (5)-(10). The authors claim that this framework reproduces measured kink densities, hysteresis loop shapes, non-monotonic magnetization reversals, transient negative susceptibilities, and longitudinal sweep-rate scaling, and they interpret these as genuine quantum memory effects. The paper includes comparisons with mean-field theory, DMRG, an interaction-picture model, and pure unitary evolution, and reports the scaling laws in Eqs. (11) and (14).

Significance. The experimental dataset is substantial: hysteresis loops on three different devices, multiple system sizes up to 4,906 qubits, parallel-annealing tiling, ferromagnetic and antiferromagnetic gauge checks, and several annealing times. If the central claim is established, the paper would demonstrate a programmable quantum annealer as a testbed for non-equilibrium quantum hysteresis and provide a useful phenomenological modeling framework. The authors are honest about several limitations. However, the model contains free parameters, the central 'genuine quantum memory' claim lacks a classical stochastic baseline, and the quantitative agreement is partial and selective. As it stands, the paper is a promising but incomplete case for the quantum-memory interpretation.

major comments (5)
  1. [Section III.A, IV, VI] The central claim that the observed 1D hysteresis, non-monotonicities, and negative susceptibilities are 'genuine quantum memory effects' is not tested against a classical stochastic spin-dynamics baseline. Section III.A concedes that a finite-size 1D classical Ising chain can exhibit dynamical hysteresis at zero temperature (ref. [47]), and finite-temperature kinetic Ising models generically produce hysteresis under finite-rate sweeps. The paper compares experiments with DMRG, mean-field theory, and an interaction-picture model, but never with Glauber or kinetic Monte Carlo dynamics under the same protocol. Since the hybrid model's semiclassical kinetic equations (Eq. 7) and IPF amplitude filter (Eq. 8) contain free parameters, a classical baseline is needed to determine whether the observed loop shapes and transient negative susceptibilities require quantum transitions. Without this control, the 'genuine quantum memory' conclusion is underdetermined.
  2. [Section III.B, Appendix B] The model's quantitative core rests on the independent level crossing approximation, which the authors themselves state is violated by the one-dimensional TFIM: Appendix B says the TFIM 'typically violates these, except in restricted subspaces (e.g., single-spin flip states). Hence, the LZ model does not apply exactly to one-dimensional systems under a hysteresis protocol.' This is load-bearing because Eq. (3)/(B2) and the scaling law Eq. (11) use the single-level-crossing LZ transition probability. The paper needs a quantitative test of the approximation over the parameter range used, for example by comparing exact-diagonalization transition probabilities with the LZ prediction for N=3,4,6 at the spause values of Fig. 3. Without such a test, the regime of validity of the LZ-based scaling predictions is unclear, especially since SI S1 shows qualitative failure at weak transverse field and Fig. 1 shows incomplete reversal at intermediate J/Γ=7.87.
  3. [Section III.E, Eq. (8)] The IPF update in Eq. (8) is introduced with a 'heuristic weighting factor' α=α0+κ/(2N)Σ|n_t−n_ψ|, and α0 and κ are free parameters 'tuned for agreement with experiments.' The paper does not report the values used, whether the same values were applied across all spause values, system sizes, and devices, or any sensitivity analysis. Without this information, the fits in Figs. 1 and 6 cannot be evaluated for overfitting, and the predictive content of the model is unclear. The authors should report the fitted parameters, their stability, and a cross-validation or leave-one-out analysis.
  4. [Fig. 1, Section IV, SI S1-S2] The evidence supporting the claim that the framework 'reproduces the measured kink densities, hysteresis loop shapes, and longitudinal sweep-rate scaling trends' is partial and selective. The numerical simulations in Fig. 3 are limited to N=3,4,6, while the headline experiments reach N=4,906. The caption of Fig. 1 reports that at J/Γ=7.87 the simulation does not undergo complete reversal but re-magnetizes and reverses only at larger fields. SI S1 reports that for spause∈{0.6,0.7} the simulated loops do not qualitatively match experiments. Moreover, spause=0.3 data are excluded for two devices at 11.2 μs (Section IV and SI S2). The R² values in SI S2 are not consistently high, and the paper gives no global quantitative error metric for loop shapes. The reproduction claim should be restricted to the validated parameter regimes, and all data, including outliers, should be shown.
  5. [Section V, Eq. (11)] The scaling law Eq. (11) is presented as following from the LZ model, but the derivation from Eq. (B2) is not shown. Eq. (B2) for a single two-level system gives ln p = −πΓ²/(2ℏ hdot), whereas Eq. (11) contains additional factors A(s)²/B(s)⁴ and a prefactor 5Tsweep/|h'_max|. The mapping between these expressions, including how the hardware schedule functions enter the effective ramp rate and what the 2/5 Tsweep factor represents, is not given. Because Eq. (11) underlies the quantitative comparison in Fig. 6, this derivation must be supplied before the scaling claim can be evaluated.
minor comments (6)
  1. [Section III.D, Eq. (7)] Eq. (7) as printed has dn+/dt on both sides; the intended advection term is presumably a spatial derivative, ∂n+/∂x. Please correct the equation and the analogous expression for n−.
  2. [Fig. 2 caption] The caption for panels (c.i)-(c.iii) calls the displayed curves 'simulations,' but the text and context indicate these are experimental D-Wave data. This is confusing and should be corrected.
  3. [Section V, Eq. (12)] The text says 'α the dampening parameter' but the LLG equation is written with λ; the notation should be made consistent.
  4. [SI S5] The DMRG comparison uses a truncated variational DMRG search with one sweep per field step, which is not a real-time non-equilibrium evolution. The statement that DMRG 'fails to reproduce experimental results' should be qualified accordingly, since the method is not designed to capture diabatic dynamics.
  5. [Section IV and SI S10] The exclusion of spause=0.3 for the two Pegasus devices at 11.2 μs is an important caveat; it should be stated in the main text with the same emphasis as in the supplementary material.
  6. [Throughout] There are several typographical errors, including 'heurstic' (Section III.E), 'valued' for 'valid' (Section III.B), and 'the the independent crossing approximation' (Appendix B). A careful proofread is needed.

Circularity Check

0 steps flagged · score 2.0 of 10

No significant circularity: the core LZ scaling comparison is an independent experimental test, while the model's tuned parameters and self-citations to prior hardware methods are limitations rather than circular reductions.

full rationale

The paper's central derivation chain is not circular in the forbidden sense. The scaling law of Eq. (11) is obtained analytically from the Landau-Zener transition probability, and it is then compared against experimentally fitted slopes in Fig. 6(a), which are not set by the theory. The corresponding simulated slopes in Fig. 6(b) come from a model that already contains the LZ exponent by construction, so the simulation agreement is expected, but the experimental agreement provides independent support. The IPF update of Eq. (8) contains free parameters α0 and κ that are explicitly 'tuned for agreement with experiments' (Section III E); this makes the claimed reproduction of loop shapes and kink densities a calibration exercise rather than a prediction, and it is a genuine limitation. However, it is not a circular reduction because the model equations are not defined in terms of the measured observables, and the fitted parameters do not force the scaling trend that is tested against experiment. The paper cites its own Ref. [11] for the experimental protocol and earlier hysteresis observations, but that self-citation is methodological and not load-bearing for the theoretical argument. The acknowledged breakdown of the independent-level-crossing approximation in one-dimensional systems (Appendix B) is an accuracy/assumption concern, not circularity. The absence of a classical Glauber or kinetic Monte Carlo baseline under the same protocol weakens the 'genuine quantum memory' interpretation, but that is a missing control and a correctness risk, not a self-referential derivation. Overall, the derivation chain is self-contained enough that no specific equation or fitted parameter is renamed as an independent prediction, so the circularity score is low.

Assumptions & free parameters 4 free parameters · 5 assumptions · 0 invented entities

The model introduces no new physical entities; it uses existing concepts (Landau-Zener, domain walls, piecewise-constant propagator). The main sources of slack are the free parameters α0, κ, Ω, and the fitting constants a, c. The independence of the level crossing approximation is a domain assumption that is explicitly acknowledged as not exactly valid, and the linear velocity law is an assumption grounded in Lieb-Robinson but not derived.

free parameters (4)
  • α0 = not disclosed
    Heuristic weighting factor in the IPF update, 'tuned for agreement with experiments' (Section III E).
  • κ = not disclosed
    Controls the strength of the semiclassical update, also tuned for agreement (Section III E).
  • Ω = not disclosed
    Annihilation probability of domain walls in Eq. (7); no value or derivation given in main text.
  • a, c = not disclosed
    Constants in the loop area scaling A = aΓα + c, 'determined for each simulation parameters' (Fig. 6 caption).
assumptions (5)
  • domain assumption Independent level crossing approximation holds for the 1D TFIM under the hysteresis protocol.
    Central to the model; the authors state in Appendix B that the TFIM typically violates the integrability conditions required for exact LZ, but they assume it holds in restricted subspaces. This is the weakest load-bearing assumption.
  • domain assumption Domain-wall velocity is linear in the longitudinal field, v± = ±v0 h(t), bounded by Lieb-Robinson.
    Section III D: used to write the semiclassical kinetic equations. The Lieb-Robinson bound gives a speed limit but not the exact velocity law.
  • domain assumption Semiclassical approximation: between avoided crossings the system can be described by classical domain-wall particles with negligible quantum dispersion.
    Justified by (i) rapid phase averaging, (ii) heavy effective mass (Γ ≪ J), (iii) well-separated level crossings. This is plausible but not rigorously proven for all parameters.
  • domain assumption The first-order piecewise-constant propagator with Δt/τ_LZ < 10⁻² gives negligible error.
    Section III C and Appendix B: local O(Δt²) error is argued to be small, but the cumulative error over long sweeps is not analyzed.
  • standard math The heat bath is Markovian and weakly coupled, leading to a Lindblad-type/markovian master equation for the mean-field model.
    Appendix D: assumes the bath correlation function yields a constant relaxation rate λ, and the first moment of the coupling vanishes. Standard Born-Markov approximation.

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Cite this review

Pith. "Pith review of Magnetic Memory and Hysteresis from Quantum Transitions: Theory and Experiments on Quantum Annealers." pith.science (2026). https://pith.science/paper/7FWFWYA4

@misc{pith2026250718079,
  author       = {Pith},
  title        = {Pith review of: Magnetic Memory and Hysteresis from Quantum Transitions: Theory and Experiments on Quantum Annealers},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/7FWFWYA4}},
  note         = {Machine review of arXiv:2507.18079}
}
read the original abstract

Quantum annealing leverages quantum tunneling for non-local searches, thereby minimizing memory effects that typically arise from metastabilities. Nonetheless, recent work has demonstrated robust hysteresis in large-scale transverse-field Ising systems implemented on D-Wave's analog quantum hardware. The quantum nature of these intriguing results remains to be understood at a deeper level. Here, we present a conceptual framework that explains the observed behavior by combining two-level Landau-Zener transitions via a first-order piecewise-constant propagator with semiclassical domain-wall kinetics. We test this approach experimentally on a quantum annealer, where we observe clear coercivity even in one-dimensional rings with periodic boundary conditions comprising up to 4,906 qubits-regimes where classical hysteresis is forbidden, but quantum hysteresis is not. Our framework reproduces the measured kink densities, hysteresis loop shapes, and longitudinal sweep-rate scaling trends observed in data from three different D-Wave quantum annealers. In particular, it captures striking non-monotonic features and transiently negative susceptibilities, identifying them as genuine quantum memory effects. These results establish programmable quantum annealers as powerful testbeds for exploring memory-endowed non-equilibrium dynamics in quantum many-body systems.

Figures

Figures reproduced from arXiv: 2507.18079 by the authors.

Figure 1
Figure 1. FIG. 1: (Left) Schematics of a ring or plaquette of four spins in the transverse field Ising model. Individual spins are [PITH_FULL_IMAGE:figures/full_fig_p007_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2: Hysteresis protocols and magnetic hysteresis loops with standard deviation for one dimensional and two [PITH_FULL_IMAGE:figures/full_fig_p009_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3: (a) Simulated hysteresis with a combined first-order piecewise-constant propagator and semiclassical domain [PITH_FULL_IMAGE:figures/full_fig_p010_3.png] view at source ↗
Figures from the paper (4 more)
Figure 4
Figure 4. Figure 4: FIG. 4: Eigenstate evolution as a function of time during the simulated hysteresis protocol. (a) For a [PITH_FULL_IMAGE:figures/full_fig_p011_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5: Representative single spin configurations from various points along the one-dimensional and [PITH_FULL_IMAGE:figures/full_fig_p012_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6: (a) Linear fit of defects density ln(1 [PITH_FULL_IMAGE:figures/full_fig_p013_6.png]
Figure 7
Figure 7. Figure 7: FIG. 7: Three components of magnetization determined by the mean field approximation, eq. (13), are plotted [PITH_FULL_IMAGE:figures/full_fig_p023_7.png]

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Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Geometry-Induced Domain-Wall Pinning and $\mathbb{Z}_2$ Asymmetry in Nominally One-Dimensional Rydberg Arrays

    quant-ph 2026-07 conditional novelty 4.0 of 10

    Corner geometry and atom vacancies in planar folded 1D Rydberg arrays pin domain walls and break Z2 symmetry between Rydberg and ground states.

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    Nonzero longitudinal field Returning to eq. (S12), we can incorporate a longitudinal field H(t) = −J L−1X i=1 (c† i − ci)(c† i+1 + ci+1) − Γ(t) LX i=1 (1 − 2c† i ci) + h(t)Πj<i(−1)c† j cj (ci + c† i ). (S20) Immediately we can see the longitudinal field introduces a nonlocal t...

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Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.