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arxiv: 2605.13807 · v1 · submitted 2026-05-13 · ❄️ cond-mat.str-el · cond-mat.dis-nn· cs.LG· physics.comp-ph· quant-ph

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Parallel Scan Recurrent Neural Quantum States for Scalable Variational Monte Carlo

Ejaaz Merali , Mohamed Hibat-Allah , Mohammad Kohandel , Richard T. Scalettar , Ehsan Khatami
Authors on Pith no claims yet

Pith reviewed 2026-05-14 17:36 UTC · model grok-4.3

classification ❄️ cond-mat.str-el cond-mat.dis-nncs.LGphysics.comp-phquant-ph
keywords neural quantum statesrecurrent neural networksvariational Monte Carloparallel scanspin latticesautoregressive modelsquantum many-body
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The pith

Recurrent neural networks become parallelizable and reach accurate simulations of 52 by 52 spin lattices in variational Monte Carlo.

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

Neural-network quantum states are a variational method for approximating ground states of quantum many-body systems. Recurrent architectures have been viewed as limited because their sequential processing scales poorly with system size. This work shows that combining autoregressive recurrent wave functions with parallel-scan recurrence removes the sequential bottleneck while preserving the ability to compute probabilities and samples efficiently. The resulting models are trained within variational Monte Carlo and achieve energies that match available quantum Monte Carlo benchmarks on two-dimensional lattices up to 52 by 52 sites when iterative retraining is used. The approach therefore demonstrates that recurrent networks can serve as a computationally modest route to scalable neural quantum state calculations in one and two dimensions.

Core claim

Parallel scan recurrent neural quantum states (PSR-NQS) are constructed from autoregressive recurrent wave functions whose recurrence is made parallelizable via the parallel scan algorithm. These ansatze are trained by variational Monte Carlo and, with iterative retraining, produce energies on two-dimensional spin lattices as large as 52 by 52 that remain in agreement with independent quantum Monte Carlo data.

What carries the argument

The parallel-scan recurrence applied to autoregressive recurrent networks, which parallelizes the hidden-state computation while keeping the conditional probability factorization intact for efficient sampling and local energy evaluation.

Load-bearing premise

The autoregressive structure combined with parallel scan recurrence yields a variational ansatz whose energy minimum stays sufficiently close to the true ground state without systematic biases that grow with lattice size.

What would settle it

For a 52 by 52 lattice, a calculation in which the PSR-NQS variational energy lies more than a few percent above the best available quantum Monte Carlo energy while the same model remains accurate on smaller lattices would falsify the claim of size-independent accuracy.

Figures

Figures reproduced from arXiv: 2605.13807 by Ehsan Khatami, Ejaaz Merali, Mohamed Hibat-Allah, Mohammad Kohandel, Richard T. Scalettar.

Figure 1
Figure 1. Figure 1: FIG. 1. Runtime per training step comparison between the [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Finite-size scaling of the ground-state energy per [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗
read the original abstract

Neural-network quantum states have emerged as a powerful variational framework for quantum many-body systems, with recent progress often driven by massively parallel architectures such as transformers. Recurrent neural network quantum states, however, are frequently regarded as intrinsically sequential and therefore less scalable. Here we revisit this view by showing that modern recurrent architectures can support fast, accurate, and computationally accessible neural quantum state simulations. Using autoregressive recurrent wave functions together with recent advances in parallelizable recurrence, we develop variational ans\"atze, called parallel scan recurrent neural quantum states (PSR-NQS), which can be trained efficiently within variational Monte Carlo in one and two spatial dimensions. We demonstrate accurate benchmark results and show that, with iterative retraining, our approach reaches two-dimensional spin lattices as large as $52\times52$ while remaining in agreement with available quantum Monte Carlo data. Our results establish recurrent architectures as a practical and promising route toward scalable neural quantum state simulations with modest computational resources.

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 introduces parallel scan recurrent neural quantum states (PSR-NQS) by combining autoregressive recurrent neural network wave functions with parallelizable recurrence techniques. This enables efficient variational Monte Carlo training for quantum many-body systems in one and two dimensions. The central claim is that, with iterative retraining, the method scales to two-dimensional spin lattices as large as 52×52 while producing results in agreement with available quantum Monte Carlo benchmarks, establishing recurrent architectures as a practical route for scalable neural quantum state simulations with modest resources.

Significance. If the results hold with quantitative validation, the work is significant for demonstrating that recurrent architectures can overcome their perceived sequential limitations and compete with transformer-based approaches for large-scale variational Monte Carlo. It provides a concrete engineering path to access system sizes (e.g., 52×52) that are computationally challenging for many existing NQS methods, using only modest resources and without requiring massive parallelism beyond the parallel-scan construction.

major comments (2)
  1. [Abstract] Abstract and results: the claim of agreement with QMC data on 52×52 lattices is presented without quantitative error bars, energy differences, or benchmark tables. This is load-bearing for the scalability assertion, as the reader's assessment notes the absence of convergence criteria and data-exclusion details leaves the central claim only moderately supported.
  2. [Results] The weakest assumption—that the autoregressive parallel-scan construction yields an expressive ansatz whose energy minimum stays close to the true ground state without size-dependent bias—is not directly tested or bounded in the provided text. A concrete check (e.g., comparison of variational energies versus exact or high-precision QMC across multiple system sizes with reported variances) is needed to substantiate the claim.
minor comments (2)
  1. [Methods] Clarify the precise complexity scaling of the parallel-scan recurrence versus standard sequential RNN evaluation, including any constants or memory overheads, to make the efficiency advantage explicit.
  2. [Introduction] Add references to the original parallel-scan algorithm literature and specify which network hyperparameters (e.g., hidden dimension, number of layers) are held fixed versus tuned during iterative retraining.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the detailed and constructive report. The comments highlight the need for stronger quantitative validation of the scalability claims, which we address by expanding the benchmarks in the revised manuscript. We provide point-by-point responses below.

read point-by-point responses

  1. Referee: [Abstract] Abstract and results: the claim of agreement with QMC data on 52×52 lattices is presented without quantitative error bars, energy differences, or benchmark tables. This is load-bearing for the scalability assertion, as the reader's assessment notes the absence of convergence criteria and data-exclusion details leaves the central claim only moderately supported.

    Authors: We agree that quantitative support is essential for the central scalability claim. In the revised manuscript we have added Table II, which reports variational energies per site for the 52×52 lattice together with the corresponding QMC reference values, including statistical uncertainties from our VMC sampling (typically 10^7 samples) and the published QMC error bars. Relative energy differences are now stated explicitly (e.g., ΔE/E_QMC < 0.1 %). We have also inserted a short paragraph in Sec. IV B describing the iterative retraining schedule, the convergence threshold on the energy variance, and the data-exclusion protocol used to avoid overfitting to early samples. These additions make the agreement quantitative and reproducible. revision: yes

  2. Referee: [Results] The weakest assumption—that the autoregressive parallel-scan construction yields an expressive ansatz whose energy minimum stays close to the true ground state without size-dependent bias—is not directly tested or bounded in the provided text. A concrete check (e.g., comparison of variational energies versus exact or high-precision QMC across multiple system sizes with reported variances) is needed to substantiate the claim.

    Authors: We concur that a systematic size-dependent check is required. The revised Results section now contains a new subsection (IV C) and Figure 3 that plot the energy per site versus linear system size L for both 1D chains (L up to 128) and 2D lattices (L up to 52). For small systems we compare directly with exact diagonalization; for larger systems we overlay high-precision QMC data with error bars. The PSR-NQS energies track the reference values within statistical uncertainty across the entire range, with no detectable systematic drift. We also report the variance of the local energy estimator as a function of L, confirming that the ansatz remains sufficiently expressive. A brief discussion of possible bias sources and why the parallel-scan construction plus iterative retraining suppresses them has been added. revision: yes

Circularity Check

0 steps flagged

No significant circularity identified

full rationale

The paper constructs PSR-NQS by combining the established autoregressive RNN wave-function ansatz with an external parallel-scan recurrence algorithm from the machine-learning literature. This is a direct architectural implementation whose training proceeds via standard variational Monte Carlo; the reported energies on 52×52 lattices are validated against independent quantum Monte Carlo benchmarks rather than being recovered from any internal fit or self-referential definition. No equation reduces a claimed prediction to a fitted parameter by construction, no uniqueness theorem is imported from the authors’ prior work, and no ansatz is smuggled through self-citation. The derivation chain therefore remains self-contained and externally falsifiable.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 1 invented entities

The central claim rests on the variational principle for energy minimization, the sufficiency of the autoregressive factorization for the wave function, and the correctness of the parallel scan implementation for the chosen RNN cell. No new physical entities are postulated.

free parameters (1)
  • network architecture hyperparameters
    Hidden dimension, number of layers, and learning-rate schedules are chosen and optimized during training to achieve the reported energies.
axioms (2)
  • standard math Variational theorem: the expectation value of the Hamiltonian is an upper bound to the true ground-state energy
    Invoked implicitly when the network parameters are optimized to minimize the variational energy.
  • domain assumption The parallel scan recurrence exactly reproduces the sequential RNN computation
    Required for the claimed computational speedup to preserve the original autoregressive wave-function form.
invented entities (1)
  • PSR-NQS ansatz no independent evidence
    purpose: Scalable recurrent representation of quantum wave functions
    New named architecture introduced by combining parallel scan with autoregressive RNN-NQS; no independent experimental signature is provided.

pith-pipeline@v0.9.0 · 5493 in / 1454 out tokens · 59297 ms · 2026-05-14T17:36:39.452350+00:00 · methodology

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