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arxiv: 2604.18711 · v1 · submitted 2026-04-20 · ❄️ cond-mat.mes-hall

Large Scale Optimization of Disordered Hubbard Models through Tensor and Neural Networks

Jacob R. Taylor , Sankar Das Sarma This is my paper

Pith reviewed 2026-05-10 03:27 UTC · model grok-4.3

classification ❄️ cond-mat.mes-hall
keywords disordered Hubbard modelsquantum dot gridsneural networkstensor networkscharge stabilityspin qubitssliding window2D arrays
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The pith

Neural networks trained on 3x3 charge-stability data can tune the central dot in larger 5x5 disordered arrays.

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

The paper demonstrates that vision-based neural networks, trained on charge-stability diagrams from tensor-network simulations of small 3x3 Hubbard models, contain sufficient information to predict tuning parameters for the central quantum dot in much larger arrays. This validates a sliding-window method where local tuning is applied and then shifted across the lattice, avoiding the need to simulate full large systems whose Hilbert space grows exponentially. A reader would care because this makes calibration of practical 2D quantum-dot grids for spin qubits feasible despite disorder and computational limits. When only on-site disorder is unknown, predictions achieve R squared over 0.99 in 3x3 and about 0.98 in 5x5 after fine-tuning.

Core claim

A simulatable local 3×3 window contains sufficient information to tune the central dot within a much larger array. This validates a sliding-window approach in which one tunes a local region and then translates that window across the lattice to calibrate a larger device. For only on-site disorder unknown, the neural network predicts parameters with R² > 0.99 in 3×3 and retains R² ≈ 0.98 in 5×5 after fine tuning. Even when all parameters are unknown, on-site disorder prediction remains robust with R² > 0.9.

What carries the argument

Vision-based neural networks trained on tensor-network generated charge-stability data from local 3×3 windows to enable sliding-window tuning of larger arrays.

If this is right

  • High accuracy in predicting on-site disorder for both small and scaled-up arrays.
  • Robust inference of key disorder parameters even in fully disordered cases.
  • Scalable calibration without computing ground states of exponentially large systems.
  • Translation of local tuning across the entire lattice via repeated window application.

Where Pith is reading between the lines

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

  • The approach suggests local correlations dominate for initial parameter estimation in these models.
  • Similar local-window strategies could apply to tuning other complex quantum devices facing Hilbert space explosion.
  • Real-device tests would need to account for noise levels not present in the tensor simulations.

Load-bearing premise

The local 3x3 charge-stability data is representative enough that the neural network generalizes accurately to the central dot in larger arrays without major degradation from long-range effects or noise.

What would settle it

A significant drop in prediction accuracy below R² of 0.9 when testing the neural network on charge-stability data from actual or simulated 5x5 arrays that include long-range interactions would show the local window is insufficient.

Figures

Figures reproduced from arXiv: 2604.18711 by Jacob R. Taylor, Sankar Das Sarma.

Figure 1
Figure 1. Figure 1: FIG. 1: Sliding-window process diagram. The process [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 3
Figure 3. Figure 3: We found it necessary to include a small number of 5 × 5 samples because, without them, the network still appears to predict the relative positions of ϵi , but with a residual discrepancy that may be approximately lin￾ear. (See Fig. S6) In principle, this discrepancy could be calibrated experimentally even for very large systems. Similarly, we expect the effect of increasing system size on the charge stabi… view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: Neural network diagram. The network is [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4: Predicted vs. expected [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: Predicted vs. expected [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
read the original abstract

We theoretically demonstrate a practical method for tuning randomly disordered 2D quantum-dot grids underlying spin qubit platforms using vision-based neural networks trained on tensor-network generated charge-stability data. We show that a simulatable local $3\times 3$ window already contains sufficient information to tune the central dot within a much larger array, thereby validating a sliding-window approach in which one tunes a local region and then translates that window across the lattice to calibrate a larger device. This avoids the computationally intractable necessity for obtaining the ground states for large systems with exponentially large Hilbert space. For the experimentally relevant case where only the on-site disorder is unknown, the neural network predicts the relevant parameters with very high fidelity in the $3\times 3$ setting [$R^2 >0.99$], and after fine tuning on only a small number of larger-device samples, it retains high accuracy for the central dot of a $5\times 5$ plaquette [$R^2\approx 0.98$]. When all the dots parameters are treated as unknown, prediction of the on-site disorder remains robust [$R^2>0.9$ for both $3\times 3$ and $5\times 5$], although the remaining parameters are substantially more difficult to infer from the same charge-stability data. This shows that the most practically important disorder parameter for tuning can still be inferred reliably even in the fully disordered setting for the computationally difficult 5x5 arrays.

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

2 major / 2 minor

Summary. The paper demonstrates a neural-network approach trained on tensor-network simulations of charge-stability diagrams from 3×3 windows of the disordered Hubbard model to predict on-site disorder and other parameters for the central dot in larger arrays. It reports R² > 0.99 for 3×3 on-site disorder, R² ≈ 0.98 for 5×5 after fine-tuning on a few larger samples, and R² > 0.9 for on-site disorder even when all parameters are unknown, thereby supporting a sliding-window tuning protocol that avoids direct simulation of large systems.

Significance. If the local-window sufficiency holds beyond the tested sizes, the method would provide a computationally tractable route to calibrating large-scale disordered quantum-dot arrays for spin-qubit applications, where full Hilbert-space simulations become intractable. The high fidelity for the experimentally dominant on-site disorder parameter is a concrete practical strength, and the use of independent tensor-network data for training avoids obvious circularity.

major comments (2)
  1. [Abstract] Abstract and results on 5×5 performance: the central claim that a simulatable 3×3 window already contains sufficient information for the central dot in a 'much larger array' is supported only by data up to 5×5 plaquettes. In the disordered Hubbard model, virtual hopping and global particle-number constraints can generate size-dependent corrections to the central dot's chemical potential and charging energy; no direct test or scaling analysis is provided for arrays larger than 5×5, so the extrapolation required for the sliding-window protocol remains unverified.
  2. [Results] Section on fully disordered case: when all dot parameters are treated as unknown, on-site disorder is still recovered with R² > 0.9, but the remaining parameters are substantially harder to infer. If the paper's primary practical goal is reliable extraction of the dominant disorder term, this distinction should be quantified with an explicit error budget or ablation showing which parameters drive the tuning accuracy.
minor comments (2)
  1. The abstract states R² > 0.99 for 3×3 and R² ≈ 0.98 for 5×5; the methods section should report the precise definition of R² (e.g., over which parameter set and test-set size) and any cross-validation protocol used to obtain these numbers.
  2. Notation for the neural-network input (charge-stability diagrams) and output (predicted disorder values) should be made consistent between the abstract, methods, and figure captions to avoid ambiguity when readers attempt to reproduce the training pipeline.

Simulated Author's Rebuttal

2 responses · 1 unresolved

We thank the referee for the positive assessment of our work and the constructive major comments. We address each point below with clarifications and revisions to the manuscript where appropriate.

read point-by-point responses

  1. Referee: [Abstract] Abstract and results on 5×5 performance: the central claim that a simulatable 3×3 window already contains sufficient information for the central dot in a 'much larger array' is supported only by data up to 5×5 plaquettes. In the disordered Hubbard model, virtual hopping and global particle-number constraints can generate size-dependent corrections to the central dot's chemical potential and charging energy; no direct test or scaling analysis is provided for arrays larger than 5×5, so the extrapolation required for the sliding-window protocol remains unverified.

    Authors: We agree that our numerical validation is limited to 5×5 arrays, which represent the practical limit for tensor-network simulations with sufficient accuracy. The modest degradation from R² > 0.99 (3×3) to R² ≈ 0.98 (5×5 central dot) after minimal fine-tuning already indicates that local 3×3 data captures the dominant physics. In the revised manuscript we have updated the abstract to qualify the claim as applying to 'larger arrays (demonstrated up to 5×5)' and added a dedicated paragraph in the discussion section. There we argue, based on the short-range nature of the Hubbard interactions and electrostatic screening, that size-dependent corrections to on-site disorder and charging energy are expected to remain small beyond 5×5. A full scaling study for much larger arrays is not feasible with current methods, which is the central motivation for the sliding-window protocol. revision: partial

  2. Referee: [Results] Section on fully disordered case: when all dot parameters are treated as unknown, on-site disorder is still recovered with R² > 0.9, but the remaining parameters are substantially harder to infer. If the paper's primary practical goal is reliable extraction of the dominant disorder term, this distinction should be quantified with an explicit error budget or ablation showing which parameters drive the tuning accuracy.

    Authors: We thank the referee for highlighting this distinction. In the revised manuscript we have added an ablation study in the results section that systematically removes or fixes subsets of parameters during training and evaluates the resulting impact on on-site disorder prediction. We have also included an explicit error budget that propagates the inference uncertainties through to the effective chemical potential and charging energy of the central dot. This analysis confirms that the robust recovery of on-site disorder (R² > 0.9) dominates the tuning accuracy, while errors in the other parameters contribute only marginally to the overall calibration error for qubit operation. revision: yes

standing simulated objections not resolved
  • Direct numerical tests or scaling analysis for arrays substantially larger than 5×5 remain computationally intractable with tensor networks, preventing empirical verification of the sliding-window protocol beyond the sizes already reported.

Circularity Check

0 steps flagged

No circularity: independent tensor-network data generation and NN prediction on unseen larger systems

full rationale

The paper generates training data via tensor-network simulations of 3x3 Hubbard models, trains a vision-based neural network to map charge-stability diagrams to on-site disorder parameters, and reports R^2 scores on held-out 3x3 cases plus fine-tuned 5x5 cases. No equation or step reduces a claimed prediction to a fitted input by construction, no self-citation supplies a load-bearing uniqueness theorem, and no ansatz is smuggled in. The sliding-window claim is an empirical generalization tested within the simulated data regime rather than a definitional tautology.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The central claim rests on the standard disordered Hubbard model for quantum dots plus the paper-specific assumption that local windows suffice; no new physical entities are introduced, but the neural network introduces many fitted parameters.

free parameters (1)
  • Neural network weights and biases
    The vision-based neural network is trained on tensor-network data, so its parameters are fitted to reproduce the simulated charge-stability patterns.
axioms (2)
  • domain assumption The disordered Hubbard model accurately captures the physics of the quantum-dot grid
    All simulations and training data are generated under this model as stated in the title and abstract.
  • ad hoc to paper A local 3x3 window contains sufficient information to tune the central dot in a larger array
    This is the load-bearing hypothesis that the sliding-window method is designed to validate.

pith-pipeline@v0.9.0 · 5566 in / 1517 out tokens · 53509 ms · 2026-05-10T03:27:03.261147+00:00 · methodology

discussion (0)

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