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arxiv: 2503.14371 · v3 · pith:2VO4YIZBnew · submitted 2025-03-18 · 🪐 quant-ph

Superdiffusion resilience in Heisenberg Chains with 2D interactions on a quantum processor

Keerthi Kumaran , Manas Sajjan , Bibek Pokharel , Kevin Wang , Joe Gibbs , Jeffrey Cohn , Barbara Jones , Sarah Mostame
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Sabre Kais Arnab Banerjee
This is my paper

Pith reviewed 2026-05-22 23:38 UTC · model grok-4.3

classification 🪐 quant-ph
keywords superdiffusionHeisenberg chainquantum simulationspin transport2D interactionsSU(2) symmetryFloquet model
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The pith

SU(2)-preserving 2D interactions show highest resilience to superdiffusion breakdown in Heisenberg chains.

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

The paper generalizes the integrable 1D Heisenberg chain to a 2D Floquet model by adding tunable 2D interactions and simulates the resulting spin transport on quantum hardware. It finds that superdiffusive scaling breaks down at different rates depending on the form of the 2D term, with the SU(2)-symmetric interaction surviving to the largest strength. The authors attribute the ordering to differences in scattering coefficients of excitations off each 2D perturbation. The work directly addresses how real materials with integrability-breaking terms might still support superdiffusive transport.

Core claim

By increasing the strength of various 2D interactions from zero in an otherwise 1D superdiffusive Heisenberg model, the SU(2) preserving interaction maintains superdiffusive spin transport to the highest coupling value among those studied. Quantum hardware reproduces the theoretical resilience ordering with high accuracy, and scattering analysis explains why certain 2D terms disrupt transport less than others. These results indicate conditions under which superdiffusive scaling can persist in two-dimensional lattices.

What carries the argument

Scattering coefficients of excitations off the added 2D interactions within otherwise 1D chains, which set the relative strength at which each term destroys superdiffusion.

If this is right

  • The SU(2) preserving interaction allows superdiffusive spin transport to survive at finite 2D coupling strengths.
  • Quantum processors can faithfully rank the resilience of different integrability-breaking terms.
  • Superdiffusive scaling may be observable in 2D lattices when the dominant perturbation preserves SU(2) symmetry.
  • The breakdown threshold of superdiffusion can be tuned by choosing the symmetry properties of added interactions.

Where Pith is reading between the lines

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

  • Real materials whose dominant couplings are close to SU(2) symmetric could exhibit extended superdiffusive regimes before crossing over to diffusion.
  • The scattering-coefficient approach could be applied to classify resilience in other integrable spin chains or higher-dimensional generalizations.
  • Variants of materials like KCuF3 engineered with stronger SU(2) character might serve as test beds for 2D superdiffusion.

Load-bearing premise

The quantum hardware implements the generalized 2D Floquet model without decoherence, gate errors, or readout noise that would reorder the observed resilience of different interactions.

What would settle it

An exact calculation or clean experiment showing that all studied 2D interactions produce identical scattering coefficients and therefore identical breakdown thresholds.

Figures

Figures reproduced from arXiv: 2503.14371 by Arnab Banerjee, Barbara Jones, Bibek Pokharel, Jeffrey Cohn, Joe Gibbs, Keerthi Kumaran, Kevin Wang, Manas Sajjan, Sabre Kais, Sarah Mostame.

Figure 1
Figure 1. Figure 1: Summary: (a) We study the extension of the 1D Floquet Heisenberg Hamiltonian, represented by black bonds, known to exhibit superdiffusive scaling in discrete time evolution [36, 37], to a 2D Floquet model native to the heavy-hex lattice, represented by the vertical brown bonds. Discrete time evolution is performed by sequentially applying three types of bonds (colored red, green, and blue) at a kicking per… view at source ↗
Figure 2
Figure 2. Figure 2: Different types of superdiffusion breakdown Using noiseless simulations of a 28-qubit system based on the model in Fig. II, we show that superdiffusion (∝ 𝑡 −2∕3) can break down toward either the diffusive (∝ 𝑡 −1∕2) or ballistic (∝ 𝑡 −1) regimes, depending on the interaction type. The figure presents running averages of scaling exponents ⟨ 𝑑(ln(𝐶 𝑧𝑧(𝑡))) 𝑑(ln(𝑁)) ⟩ , compared against the 1D reference mode… view at source ↗
Figure 3
Figure 3. Figure 3: (a) Scattering coefficients. Computed from 45-qubit simulations of two coupled 22-qubit 1D chains joined by a 2D interaction rung. The plots show |𝑇same|, |𝑇cross|, and |𝑅| as functions of time steps 𝑁 for three interaction cases: uncoupled 1D, 𝜆⃗ = (1, 1, 0), and 𝜆⃗ = (0, 0, 1) with a fixed interaction strength ratio 𝐽⟂∕𝐽 = 4. Only 𝑇cross transmission is observed for 𝜆⃗ = (1, 1, 0), indicating reduced ref… view at source ↗
Figure 4
Figure 4. Figure 4: (b) shows the superdiffusion breakdown observed in IBM’s Heron processors (see Appendix E for calibration de￾tails) for different interaction types, along with a comparison to noiseless simulations shown in panel (a), run with the same parameter settings (𝑐, 𝜏). The running averages of the scaling exponents in the plots show remarkable agreement with the noiseless simulations at early times. At intermediat… view at source ↗
Figure 5
Figure 5. Figure 5: Trotter circuit for the time evolution of 𝐽ℎ × 𝜆⃗ = 𝐽ℎ (𝜆𝑥 , 𝜆𝑦 , 𝜆𝑧 ) for time 𝑡: The circuit is equal to 𝑒 −𝑖𝐽ℎ ( 𝜆𝑥 4 𝜎𝑥𝜎𝑥+ 𝜆𝑦 4 𝜎𝑦𝜎𝑦+ 𝜆𝑧 4 𝜎𝑧𝜎𝑧 )𝑡 up to a global phase. 2. 𝜏 dependence The model described in section II comes with an inherent parameter 𝜏. While setting a low value of 𝜏 << 1 mimics the behavior of a continuous time model, it requires a higher number of trotter steps (and hence depth) to … view at source ↗
Figure 6
Figure 6. Figure 6: 𝜏 optimisation: We study the effect of 𝜏 on the superdiffusion breakdown in our model. We do so by setting 𝐽 = 1.0 and tuning up the 𝜏. Dash-dotted lines in each plot indicate the superdiffusive decay. (a) We reduce the trotter error by setting a value of 𝜏 as low as 0.2 to effectively mimic the continuous time model. We observe the superdiffusion breakdown to diffusion and ballistic regime happening even … view at source ↗
Figure 7
Figure 7. Figure 7: Correlation values 𝐶 𝑧𝑧(𝑡) for 2D interaction strengths from 10−4 to 4.0, illustrating superdiffusion breakdown through qualitative deviations from the power law decay. Dash-dotted lines in each plot indicate the superdiffusive decay [PITH_FULL_IMAGE:figures/full_fig_p012_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Scaling exponents for 2D interaction strengths from [PITH_FULL_IMAGE:figures/full_fig_p013_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Standard error of correlation values across five runs: The figure shows the standard error in correlation values, computed as the mean over five independent runs for different parameter settings (𝑐) in the 20-qubit system described in Section II. The standard deviation is normalized by the square root of the number of runs (five). As the number of cycles increases from 5 to 9 and 20, the standard deviation… view at source ↗
read the original abstract

Observing superdiffusive scaling in the spin transport of the integrable 1D Heisenberg model is one of the key discoveries in non-equilibrium quantum many-body physics. Despite this remarkable theoretical development and the subsequent experimental observation of the phenomena in KCuF$_3$, real materials are often imperfect and contain integrability breaking interactions. Understanding the effect of such terms on the superdiffusion is crucial in identifying connections to such materials. Current quantum hardware has already ascertained its utility in studying such non-equilibrium phenomena by simulating the superdiffusion of the 1D Heisenberg model. In this work, we perform a quantum simulation of the superdiffusion breakdown by generalizing the superdiffusive Floquet-type 1D Heisenberg model to a general 2D model. We comprehensively study the effect of different 2D interactions on the superdiffusion breakdown by tuning up their strength from zero, corresponding to the 1D Heisenberg chain, to finite nonzero values. We observe that certain 2D interactions are more resilient against superdiffusion breakdown than others and that the $SU(2)$ preserving 2D interaction has the highest resilience among all the 2D interactions we study. Importantly, this observed resilience has direct implications for sustaining superdiffusive spin transport in two-dimensional lattices. We reason out the relative resilience against the superdiffusion breakdown through an analysis of the scattering coefficients off the 2D interaction in otherwise 1D chains. The relative resilience of different interaction types against superdiffusion breakdown was also captured in quantum hardware with remarkable accuracy, further establishing the current quantum hardware's applicability in simulating interesting non-equilibrium quantum many-body phenomena.

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

1 major / 2 minor

Summary. The paper generalizes the integrable 1D Heisenberg Floquet model to include tunable 2D interactions and uses quantum-processor simulations to study how these terms break superdiffusive spin transport. It reports that the SU(2)-preserving 2D interaction shows the highest resilience to superdiffusion breakdown, with a clear ordering across interaction types; this ordering is rationalized by scattering-coefficient analysis in the 1D limit and is reproduced on hardware, with implications for 2D lattices.

Significance. If the hardware ordering is robust, the work supplies a concrete link between specific integrability-breaking perturbations and the stability of superdiffusion, together with a scattering-based explanation that is independent of fitting parameters. The successful hardware reproduction also adds to the evidence that current quantum processors can address non-equilibrium many-body questions beyond simple 1D chains.

major comments (1)
  1. [Hardware validation section] Hardware validation section: the claim that the resilience ordering is reproduced 'with remarkable accuracy' on the processor does not include a quantitative assessment of how gate errors, decoherence, or readout noise—whose strength can depend on the symmetry properties of the added 2D term—shift the extracted diffusion exponents or alter the relative ranking. Because the central claim rests on the hardware data faithfully reflecting unitary dynamics, this omission is load-bearing.
minor comments (2)
  1. [Abstract] The abstract states that the SU(2)-preserving interaction 'has the highest resilience' but does not define the quantitative resilience metric (e.g., critical interaction strength at which the diffusion exponent drops below a threshold) until later in the text; an early definition would improve readability.
  2. [Theoretical analysis] Scattering-coefficient derivation: the text presents the coefficients as explaining the ordering, yet the explicit formulas and the limit in which they are computed are not cross-referenced to a numbered equation or appendix, making it hard to verify independence from fitting parameters.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for highlighting an important point regarding the hardware validation. We address the major comment below.

read point-by-point responses

  1. Referee: [Hardware validation section] Hardware validation section: the claim that the resilience ordering is reproduced 'with remarkable accuracy' on the processor does not include a quantitative assessment of how gate errors, decoherence, or readout noise—whose strength can depend on the symmetry properties of the added 2D term—shift the extracted diffusion exponents or alter the relative ranking. Because the central claim rests on the hardware data faithfully reflecting unitary dynamics, this omission is load-bearing.

    Authors: We agree that a quantitative assessment of hardware noise effects is necessary to substantiate the claim of faithful reproduction of the resilience ordering. In the revised manuscript we will add an error analysis subsection that models gate errors, decoherence, and readout noise using hardware-calibrated parameters. For each 2D interaction type we will propagate these noise channels through the circuit and recompute the extracted diffusion exponents, explicitly checking whether the relative ordering is preserved. We will also examine whether symmetry properties of the 2D terms lead to measurably different noise strengths and report the resulting uncertainty bands on the exponents. This addition will directly address the load-bearing concern that the observed ordering might be an artifact of symmetry-dependent noise. revision: yes

Circularity Check

0 steps flagged

No significant circularity in derivation chain

full rationale

The paper's claims rest on direct quantum-hardware simulation of the generalized 2D Floquet Heisenberg model (tuning 2D interaction strength from the 1D limit) together with a separate scattering-coefficient analysis performed in the ideal 1D-chain limit. Neither step is shown to reduce to a fitted parameter renamed as a prediction, a self-definitional loop, or a load-bearing self-citation whose content is itself unverified. The hardware results are presented as external reproduction rather than as the sole justification for the theoretical ordering, and no ansatz or uniqueness theorem is imported from prior author work in a manner that collapses the argument. The derivation therefore remains self-contained against the stated inputs.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Abstract-only review yields no explicit free parameters, invented entities, or ad-hoc axioms beyond standard domain knowledge of the 1D Heisenberg model; the 2D generalization itself is the primary addition.

axioms (1)
  • domain assumption The integrable 1D Heisenberg model exhibits superdiffusive spin transport
    Stated as established prior result in the abstract.

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Forward citations

Cited by 1 Pith paper

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

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    A 50-qubit quantum processor produces dynamical structure factors for KCuF3 that quantitatively match neutron-scattering measurements of its spinon spectrum.

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    Trotterization To compute the expectation of𝜎𝑖 𝑧(𝑡)in Eq A2, we evolve the initial state|Ψ𝑅,𝑖⟩as described in Eq 4. This involves the application of two-qubit gates at𝑟,𝑔, and𝑏-type bonds (Fig 1) for the two local Hamiltonian terms acting on them. If a two-local Hamiltonain,ℎ, acts on sites𝑘and𝑙with interaction given by𝐽ℎ( 𝜆𝑥 4 𝜎𝑘 𝑥𝜎𝑙 𝑥 + 𝜆𝑦 4 𝜎𝑘 𝑦 𝜎𝑙 𝑦 +...

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