Quantum-Accelerated Neural Imputation with Large Language Models (LLMs)

Hossein Jamali

REVIEW 4 major objections 5 minor 24 references

Quantum-Accelerated Neural Imputation with Large Language Models (LLMs)

T0 review · 4 major / 5 minor · reviewed 2026-08-06 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read The paper claims that replacing classical input embeddings with an 8-qubit IQP quantum feature map reduces LLM-based imputation error by up to 15.2% (RMSE) and improves categorical imputation F1 by up to 8.7% on mixed-type tabular…

desk verdict A plausible-sounding but unverifiable embedding swap; the quantum mechanism is undercut by the local readout and the empirical claims can't be checked. read the letter →

arxiv 2507.08255 v1 pith:ZDFFDFGL submitted 2025-07-11 cs.LG cs.AI

Hossein Jamali This is my paper

classification cs.LGcs.AI

keywords quantummachinelearningdataimputationlargelanguagemodelsfeaturemapsIQPcircuitshybridquantum-classicalalgorithmsmixed-typemissing

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 tries to establish that the input embedding, not the language model, is the bottleneck for LLM-based tabular imputation, and that a shallow quantum feature map removes that bottleneck. It proposes Quantum-UnIMP, which replaces the classical MLP embedding of an existing LLM imputer with an 8-qubit Instantaneous Quantum Polynomial (IQP) circuit; the circuit's Pauli-Z expectation values become the input representations for a hypergraph Transformer that predicts masked cell values. On the Adult Income, Bank Marketing, and a synthetic healthcare dataset with non-random missingness, the framework reports up to 15.2% lower RMSE for numerical imputation and up to 8.7% higher macro F1 for categorical imputation against classical, GAN-based, and LLM-based baselines. An ablation that swaps the quantum map for a random projection supports the claim that the quantum embedding itself drives the improvement.

What carries the argument

The central object is the IQP feature map $U(x)=H^{\otimes n}U_{\mathrm{diag}}(x)H^{\otimes n}$, a shallow circuit whose diagonal phase gates are controlled by the input features; the paper reads out the embedding as the vector of Pauli-Z expectation values $x_q=[\langle Z_1\rangle,\ldots,\langle Z_n\rangle]$ on $n=8$ qubits. This fixed, non-variational circuit replaces the classical MLP embedding and feeds the Transformer-based hypergraph LLM that performs masked-token imputation. The map's claimed role is to translate mixed-type rows, including text-derived vectors, into a representation where class-relevant structure is more separable, as illustrated by t-SNE plots.

What would settle it

Re-run the same pipeline with the IQP circuit replaced by a fixed classical nonlinear embedding of the same output size (for example, random Fourier features or a random ReLU projection to eight dimensions), keeping the downstream transformer identical. If the classical replacement reproduces the reported RMSE and F1 gains, the quantum mechanism is not the driver; the paper's argument would also be weakened if the 15.2% gap on the synthetic healthcare set disappears when the text-derived features are removed from the encoding.

Watch

Extended reading notes

Core claim

The central claim is that a fixed, non-trained IQP embedding circuit is a strictly more effective input representation for LLM-based imputation than the classical learned embedding it replaces. The paper reports consistent gains across three mixed-type benchmarks: RMSE drops from 0.29 to 0.25 on Adult, 0.34 to 0.29 on Bank, and 0.45 to 0.38 on the synthetic healthcare set, while macro F1 rises from 0.80 to 0.86, 0.74 to 0.81, and 0.71 to 0.79 respectively. The authors attribute the gains to the IQP map's ability to encode higher-order, entangled correlations that classical linear or MLP embeddings miss, and they take the ablation result (random projection 0.36 RMSE, classical MLP 0.29, quantum 0.25) as evidence that the quantum map is the causal driver.

Load-bearing premise

The load-bearing assumption is that a fixed 8-qubit quantum circuit, read out as eight simple measurements, gives the LLM a strictly better description of each row than the ordinary learned embedding it replaces, even though every row's many features—numerical, categorical, and text-derived—must be squeezed into those eight rotation angles.

Editorial extensions

If this is right

If the central claim holds, any LLM-based tabular imputer can be improved by swapping its classical input embedding for a fixed shallow IQP embedding, with no change to the downstream transformer.
The gains are largest on the synthetic dataset designed with non-random missingness, so quantum embeddings would matter most where missingness depends on hidden correlations.
Because the embedding circuit is fixed and only 8 qubits, the approach is compatible with near-term quantum hardware, provided noise can be controlled.
The ablation implies that random or raw projections are far worse, so embedding quality, not model capacity, is what drives imputation accuracy in this architecture.

Reading between the lines

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

The paper does not compare the IQP embedding against other fixed nonlinear classical embeddings of similar dimension, so whether entanglement specifically is responsible, rather than any high-dimensional nonlinear map, remains an open question.
Since the 8-qubit circuit compresses all input features, the method implicitly tests whether a very low-dimensional summary can preserve the correlations needed for imputation; if true, cheaper classical kernel methods may be able to mimic the result.
A natural extension the author does not run is scaling the number of qubits or adding trainable parameters to the embedding; monotonic gains with qubit count would support the quantum expressivity story, while flat gains would suggest the effect saturates at the representation dimension.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

Quick take: this is a direct substitution of an IQP feature map for the MLP embedding inside UnIMP, and the paper's central claim—that the quantum embedding drives the gains—is not supportable from what's in the manuscript. The specific combination is new, and the writing is mostly clear, but the evidence is missing a load-bearing part.

What's new: the idea of using an IQP circuit as the input embedding for an LLM-based imputer is a reasonable thing to try, and I don't see it in the cited literature. The experimental setup is straightforward: three mixed-type datasets, standard baselines, and the results are presented cleanly. The limitations section honestly acknowledges simulator cost and NISQ noise.

Where it falls apart: First, the mechanism. The paper attributes the improvement to superposition and entanglement, but the embedding is the vector of single-qubit Pauli-Z expectations. Those are local observables; they don't see entanglement between qubits. So whatever gain is claimed cannot be explained by the quantum correlations the text leans on. Second, the compression. Adult has 14 features, Bank 21, Synthetic 20 plus text embedding dimensions, yet the circuit is 8 qubits and the output is 8 numbers. Section 3.2.2 says there is a linear mapping from x_c to gate parameters, but never specifies it. That is a big missing piece. Third, the ablation. It compares against a random projection and the classical MLP, but not against a fixed classical nonlinear embedding of the same 8 dimensions. The gains could come from the change in output dimensionality or from any nonlinear random feature map, not from anything quantum. Fourth, the abstract percentages don't match Table 1: the table shows a max RMSE reduction of 15.6% on Synthetic, not 15.2%; the max F1 improvement is 11.3%, not 8.7%. Finally, no code, data, seeds, or error bars are provided, so nothing is independently checkable.

Who it's for: someone surveying attempts to graft quantum embeddings onto classical pipelines might skim it, but no one should build on the current numbers.

Recommendation: desk-reject this version. The idea is worth an experiment, but it needs a fully specified encoding, a matched classical nonlinear control, and complete reproducibility before it deserves referee time.

Referee Report

4 major / 5 minor

Summary. The paper proposes Quantum-UnIMP, a hybrid quantum-classical imputation framework that replaces the classical input embedding of the UnIMP model with a fixed 8-qubit IQP feature map. The classical feature vector is preprocessed, mapped to gate parameters, and the Pauli-Z expectation values of the measured state are fed as token embeddings into a hypergraph transformer. Experiments on Adult, Bank, and a synthetic healthcare dataset report lower RMSE and higher F1 than MICE, MissForest, GAIN, and UnIMP, with an ablation on Adult claiming the quantum embedding is the key driver. The paper also includes t-SNE visualizations and a discussion of NISQ limitations.

Significance. The idea of using IQP feature maps as a drop-in replacement for classical embeddings in LLM-based tabular imputation is potentially interesting, and the random-projection ablation is a sensible first step. However, the paper as written does not establish the central claim: the feature-to-qubit compression is unspecified, the Pauli-Z readout is insensitive to the correlations the paper invokes, the ablation lacks a matched classical nonlinear control, and the quantitative results are not reproducible because no code, data, seeds, or error bars are provided. The abstract's headline percentages are also inconsistent with Table 1. If the results hold with proper controls, they would be a valuable empirical contribution to hybrid quantum-classical ML.

major comments (4)

[§3.2.2–3.2.4] The dimensionality reduction from the classical feature vector to the 8-qubit circuit is never specified. All three datasets have d > 8 (Adult has 14 features, Bank 21, and Synthetic has 20 features plus 384-dimensional text embeddings from all-MiniLM-L6-v2), and the display in §3.2.4 produces an 8-dimensional embedding xq. The paper states only that 'a linear mapping is established' from xc to the gate parameters θ, without defining the mapping or stating whether it is trained. Because the LLM receives only xq, the reported gains could be an artifact of aggressive dimensionality reduction rather than of the quantum circuit processing the full input. This is load-bearing for the claim that the IQP map is the key driver.
[§3.2.4 and §6.1] The embedding xq consists exclusively of single-qubit Pauli-Z expectation values. These are single-qubit marginals and are not directly sensitive to joint correlations between qubits; they therefore cannot by themselves represent the entanglement or higher-order correlations that Sections 5.2 and 6.1 use to explain the gains. To substantiate the claimed mechanism, the measurement should include multi-qubit operators (e.g., ZZ or ZZZ terms), or the interpretation should be revised to describe xq as a classical nonlinear feature map rather than as an entanglement-based representation.
[§5.2, Table 2] The ablation does not control for the change in output dimensionality or for the nonlinearity of the embedding. UnIMP (Random Proj.), UnIMP (Classical MLP), and Quantum-UnIMP differ in both the type of map and the dimensionality of the representation fed to the LLM. A matched control using a fixed classical nonlinear feature map of the same 8-dimensional output (e.g., random Fourier features or a fixed random MLP layer) is needed to attribute the observed improvement to the quantum origin of the features. The statement that the results 'unequivocally prove that the quantum feature map is the key driver' is therefore not supported by the evidence in Table 2.
[Abstract and Table 1] The quantitative claims in the abstract do not match the reported results. From Table 1, the RMSE reductions of Quantum-UnIMP relative to UnIMP are 13.8% (Adult), 14.7% (Bank), and 15.6% (Synthetic), and the F1 improvements are 7.5%, 9.5%, and 11.3%; the abstract's '15.2%' and '8.7%' do not correspond to any of these values. Moreover, no standard deviations, number of runs, or seeds are reported, and no code or data are provided, so the statistical significance and reproducibility of the central empirical claim cannot be assessed.

minor comments (5)

[Throughout] Section headings contain duplicated numbers (e.g., '2.1 3.1.', '3.1 4.1.', '4.1 5.1.', '5.1 6.1.'), which appear to be a numbering error and should be corrected.
[§1.1] 'an ubiquitous problem' should be 'a ubiquitous problem'.
[§3.2.1] Minor spacing errors appear in 'Numerical F eatures', 'Categorical F eatures', and 'T ext F eatures'.
[§5.3] Figure 3 is referenced for the t-SNE visualization, but no figure is included in the manuscript text; either include the figure or remove the reference.
[§4.2] The baselines are described as 'state-of-the-art' but only one LLM-based method (UnIMP) is included; other recent LLM-based tabular imputation methods are not cited or compared.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the quantum embedding is a fixed feature map and the reported gains are empirical comparisons, not derivations from the paper's own constructs.

full rationale

The paper's central claim is that replacing a classical MLP embedding with a fixed 8-qubit IQP feature map improves LLM-based imputation. There is no derivation chain in which an output quantity is defined in terms of the predicted quantity: the quantum embedding is constructed as xq = [<Z1>, ..., <Zn>] from a pre-processing pipeline and circuit parameters, and the downstream hypergraph LLM is trained on observed data. The reported RMSE and F1 improvements are empirical comparisons against MICE, MissForest, GAIN, and UnIMP, not fitted inputs renamed as predictions. The ablation in Section 5.2 compares random projection, classical MLP, and quantum embeddings; the claim that the quantum feature map is the key driver is an inductive conclusion from test-set metrics, not an identity forced by construction. Self-citations in the introduction (e.g., refs. 1, 3, 8, 9, 12, 13, 23) support background statements about prior applications and are not load-bearing for the imputation mechanism. The IQP feature-space claim is attributed to Havlicek et al. [21], an external reference. The compression/readout concern raised by the skeptic (d > 8 features mapped to 8 Pauli-Z expectations without a specified linear mapping) is a legitimate validity and reproducibility issue, but it is not circularity: the mapping is not defined in terms of the imputation result it is used to predict. Thus no circular step can be exhibited, and the appropriate score is 0.

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

The ledger captures the assumptions the central claim depends on. The most important are that a fixed IQP embedding with Z-expectation outputs is more expressive for this task, that 8 qubits can encode the full feature space without a specified compression, and that simulated behavior will transfer to noisy hardware. These are domain assumptions, not standard math or invented entities.

free parameters (5)

number_of_qubits = 8
Chosen in Section 4.4 to balance expressibility with near-term hardware constraints; the central claim depends on this architecture choice.
iqp_layers = 2
Fixed in Section 4.4 with no sensitivity analysis or ablation on circuit depth.
transformer_layers = 4
Fixed in Section 4.4 with no ablation on the number of layers.
learning_rate = 1e-4
Selected based on preliminary experiments, as stated in Section 4.4.
batch_size = 32
Selected in Section 4.4 with no reported sensitivity analysis.

assumptions (4)

domain assumption IQP feature maps create classically hard-to-simulate feature spaces and therefore richer embeddings.
Invoked in Sections 2.3 and 6.1, but the implementation reads out only Pauli-Z expectation values, and no argument shows those outputs inherit the hard-to-simulate property or that hardness helps imputation.
domain assumption An 8-qubit circuit can represent all input features without loss.
Section 3.2.2 establishes a linear mapping from x_c to gate parameters but does not state how features with dimension 14, 21, or 20 plus 384-dimensional text embeddings are compressed onto 8 qubits.
domain assumption Simulated quantum embeddings provide a practical benefit on near-term hardware.
The abstract claims near-term hardware potential, while Section 6.2 concedes NISQ noise is unmitigated and all experiments use the Pennylane default.qubit simulator.
domain assumption The Transformer can consume the quantum embedding without architectural adaptation.
Section 3.3 assumes x_q serves directly as the initial node representation, with no analysis of distribution shift, scaling, or normalization.

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Cite this review

Pith. "Pith review of Quantum-Accelerated Neural Imputation with Large Language Models (LLMs)." pith.science (2026). https://pith.science/paper/ZDFFDFGL

@misc{pith2026250708255,
  author       = {Pith},
  title        = {Pith review of: Quantum-Accelerated Neural Imputation with Large Language Models (LLMs)},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/ZDFFDFGL}},
  note         = {Machine review of arXiv:2507.08255}
}

read the original abstract

Missing data presents a critical challenge in real-world datasets, significantly degrading the performance of machine learning models. While Large Language Models (LLMs) have recently demonstrated remarkable capabilities in tabular data imputation, exemplified by frameworks like UnIMP, their reliance on classical embedding methods often limits their ability to capture complex, non-linear correlations, particularly in mixed-type data scenarios encompassing numerical, categorical, and textual features. This paper introduces Quantum-UnIMP, a novel framework that integrates shallow quantum circuits into an LLM-based imputation architecture. Our core innovation lies in replacing conventional classical input embeddings with quantum feature maps generated by an Instantaneous Quantum Polynomial (IQP) circuit. This approach enables the model to leverage quantum phenomena such as superposition and entanglement, thereby learning richer, more expressive representations of data and enhancing the recovery of intricate missingness patterns. Our experiments on benchmark mixed-type datasets demonstrate that Quantum-UnIMP reduces imputation error by up to 15.2% for numerical features (RMSE) and improves classification accuracy by 8.7% for categorical features (F1-Score) compared to state-of-the-art classical and LLM-based methods. These compelling results underscore the profound potential of quantum-enhanced representations for complex data imputation tasks, even with near-term quantum hardware.

Figures

Figures reproduced from arXiv: 2507.08255 by the authors.

**Figure 2.** Overview of the Quantum-UnIMP pipeline. Mixed-type input data [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗

**Figure 3.** t-SNE visualization of embedding spaces. (a) Classical UnIMP Em [PITH_FULL_IMAGE:figures/full_fig_p013_3.png] view at source ↗

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

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H. Jamali, S. M. Dascalu, F. C. Harris, and D. Feil-Seifer, “Optimizing personalized learning pathways with the salp swarm algorithm: A novel approach.” IEEE 2025 6th International Conference on Artificial Intelli- gence, Robotics . . . , 2025

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K. H. Baesmat, I. Masoudipour, and H. Samet, “Improving the perfor- mance of short-term load forecast using a hybrid artificial neural network and artificial bee colony algorithm,” IEEE Canadian Journal of Electrical and Computer Engineering, vol. 44, no. 3, pp. 275–282, 2021

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