Quantum Attention for Vision Transformers in High Energy Physics

Alessandro Tesi; Gopal Ramesh Dahale; Katia Matcheva; Konstantin T. Matchev; Kyoungchul Kong; Sergei Gleyzer; Tom Magorsch

REVIEW 4 major objections 6 minor 1 cited by

Quantum Attention for Vision Transformers in High Energy Physics

T0 review · 4 major / 6 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read A quantum-enhanced vision transformer with orthogonal attention layers matches the classical model on quark-gluon jet classification (test AUC 0.7369 vs 0.7385).

desk verdict A clean benchmark undermined by a sign inconsistency in the unary loader that likely invalidates the claimed quantum attention computation; worth a real referee only if code and error bars are supplied. read the letter →

arxiv 2411.13520 v1 pith:TVN3EN44 submitted 2024-11-20 quant-ph cs.LGhep-exhep-ph

Alessandro Tesi , Gopal Ramesh Dahale , Sergei Gleyzer , Kyoungchul Kong , Tom Magorsch , Konstantin T. Matchev , Katia Matcheva This is my paper · ORCID

classification quant-phcs.LGhep-exhep-ph PACS 03.67.-a07.05.Mh

keywords quantumvisiontransformerorthogonalneuralnetworkquark-gluonjetclassificationCMSOpenDataRBSgatehigh-energyphysicsmachinelearningattentionmechanism

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 aims to show that a vision transformer whose attention mechanism is built from quantum orthogonal neural networks (QONNs) performs as well as an ordinary classical vision transformer on a high-energy physics classification task. The test case is distinguishing quark-initiated from gluon-initiated jets using multi-detector images from CMS Open Data. On a 50,000-image subset, the quantum model reaches a validation AUC of about 0.675, effectively the same as the classical model, and a test AUC of 0.7369 versus 0.7385 for the classical transformer. The authors read this near-parity as evidence that quantum attention can be substituted for classical attention without loss of accuracy, while inheriting the stability and parameter efficiency of orthogonal transformations. If true, this opens a concrete route for quantum-enhanced machine learning at the High Luminosity LHC, where data volumes outpace classical resources.

What carries the argument

The object that carries the argument is the QONN layer: a pyramid-shaped circuit of RBS gates that implements an $n \times n$ orthogonal matrix using $n(n-1)/2$ tunable angles. A unary amplitude loader encodes each normalized input vector into a superposition with only $n-1$ RBS gates, and each attention coefficient is produced by a circuit that loads the key vector, applies the orthogonal weight matrix $W$, and overlaps the result with the query vector, with the measured first-qubit probability supplying the attention score. The orthogonality of $W$ is what the paper credits for stable gradients and efficient parameterization in high-dimensional spaces.

What would settle it

Run a statevector simulation of the trained QViT, record the attention coefficients actually produced from a batch of test jet images, and compare them with the classical formula $x_i^T W x_j$ evaluated on the same embeddings; any disagreement—expected if embeddings contain negative components—would show the quantum and classical attention mechanisms are not computing the same quantity.

Watch

Extended reading notes

Core claim

The central claim of the paper is that replacing the linear projection layers that generate queries, keys, and values in a vision transformer with quantum orthogonal layers yields a model that is as effective as the classical ViT. The QViT uses pyramidal circuits of reconfigurable beam splitter gates to implement orthogonal weight matrices, and a quantum circuit to compute each attention coefficient from loaded query and key states. On quark-gluon jet classification, the authors report test accuracy 0.6755, test AUC 0.7369, and validation AUC converging to roughly 0.675, against 0.6788, 0.7385, and roughly 0.675 for the classical model. They conclude that the quantum attention mechanism matches the classical one and that orthogonal quantum layers offer a scalable alternative for the data demands of the HL-LHC.

Load-bearing premise

The load-bearing premise is that the circuit that turns data into quantum states can exactly represent any patch embedding produced by the network; the circuit's angle formula requires every entry to be nonnegative and no intermediate factor to vanish, but the embeddings are unconstrained real numbers, so this premise is not guaranteed by the architecture.

Editorial extensions

If this is right

If quantum attention is as effective as classical attention, QONN-based vision transformers become a candidate architecture for HL-LHC-era jet classification, where the orthogonal layers' parameter efficiency could reduce training cost.
The reported numbers—test AUC 0.7369 versus 0.7385, accuracy 0.6755 versus 0.6788—provide a concrete benchmark that future quantum transformer proposals can be compared against on the same CMS Open Data task.
The architecture's linear-depth data loading and $n(n-1)/2$-parameter orthogonal layers imply that the quantum resources per image grow with the square of the number of patches (25 patches require 26×26 attention circuits), so the scalability argument is architectural rather than a demonstrated speedup on current simulators.
Replacing generic variational circuits with orthogonal quantum layers should improve gradient behaviour during training, which is the main practical motivation the authors offer for preferring QONNs over other quantum attention designs.

Reading between the lines

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

The attention circuit's output is naturally $|x_i^T W x_j|^2$, a squared, sign-free kernel, while classical softmax attention uses signed dot products; the parity result therefore shows that a network with this squared kernel can match the classical AUC, not that the two models compute the same attention function.
A clean ablation would replace the quantum orthogonal layer with a classical orthogonal layer (for example, a weight matrix constrained by QR decomposition) while keeping the same nonnegative unary-loading constraint; if that model also matches the classical ViT, the quantum hardware is not essential to the observed parity.
Repeating the 15-epoch training with several random seeds would show whether the 0.0016 test-AUC gap is within run-to-run variance; the paper reports a single run for each model.
Inspecting the distribution of learned patch embeddings would settle whether the loader's nonnegativity requirement clips or distorts the features; if it does, the reported comparison is between classical attention and a quantum circuit acting on a constrained, altered representation.

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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

You should know two things. First, the paper is a straightforward benchmark: a quantum vision transformer with QONN pyramid attention versus a classical ViT on CMS quark/gluon jet images. Test AUC is 0.7369 versus 0.7385, essentially a tie. Second, the quantum attention circuit as written does not compute the stated dot product. The RBS matrix in Sec. 2.2 puts -sin on the |10> to |01> crossing, but the recursive loader assumes a positive sine. For x = (1/sqrt2, 1/sqrt2), the circuit loads (1/sqrt2, -1/sqrt2), not x. So the attention coefficients in the central comparison are likely computed from corrupted embeddings. The stress-test note holds up. Also, the paper says the measured quantity is |x_i^T W x_j|^2, a squared coefficient, while the classical baseline uses softmax attention; that is a different model, and the text never reconciles the two.

What the paper does well: the authors run a genuine head-to-head training comparison, use public CMS Open Data, report both validation curves and test metrics, and keep the setup simple. The self-citations to earlier QViT papers are natural; this is a continuation, not a disguised repeat. The prose is readable and the computational-cost caveats are at least stated, even though the abstract's "promising scalability" is not measured anywhere.

Soft spots, in proportion: (1) no error bars or multiple seeds; a 0.0016 AUC gap is noise without a variance estimate. (2) no code and no verified data loader; the sign issue cannot be resolved from the manuscript. (3) the HL-LHC scalability claims are speculative, and the paper's own Sec. 3.2 says the simulation is computationally prohibitive. (4) the classical baseline is a weak single-block ViT with 25 patches, so "matching the classical ViT" is a low bar.

Who this is for: the QML-for-HEP subgroup, and maybe people tracking hybrid vision transformers. It is not a result that changes practice. My recommendation: conditional acceptance at best, and only if the authors release code, fix or clarify the loader convention, add error bars, and drop or substantiate the scalability claims. As it stands, I would not cite it, but it is worth a serious referee's time because the flaw is concrete and fixable.

Referee Report

4 major / 6 minor

Summary. The manuscript proposes a hybrid quantum-classical vision transformer (QViT) in which the query–key attention coefficients are computed by a quantum circuit built from reconfigurable beam-splitter (RBS) gates, forming a quantum orthogonal neural network (QONN). The model is trained and evaluated on 50,000 CMS Open Data jet images for quark–gluon classification, with the class token and two jet-level features passed to a classical multilayer perceptron head. The central empirical claim is that the QViT matches a classical ViT in performance, with test AUC 0.7369 vs 0.7385 and test accuracy 0.6755 vs 0.6788 (Table 1). The paper also claims that the quantum attention mechanism is as effective as the classical mechanism and that the approach offers promising scalability.

Significance. If the implementation is correct and reproducible, the paper would provide a useful benchmark for hybrid quantum attention in HEP jet classification, with the virtue of using a public dataset and an independently implemented classical baseline. The claimed AUC parity is a concrete, falsifiable result. The paper, however, does not ship code, does not report statistical uncertainties, and contains an internal inconsistency in the unary loader/RBS sign convention that prevents verification of the central claim. The strengths are the use of public CMS Open Data, the explicit classical baseline comparison, and the clear identification of the orthogonal-layer parameter count.

major comments (4)

[Section 2.2, RBS gate matrix and vector loading circuit] The stated RBS matrix in Section 2.2 maps the basis state |10> to cos(theta)|10> - sin(theta)|01>. Starting from the initialized state X|0...> = |10...>, the cascade of RBS gates therefore produces a negative amplitude on the second unary basis state. With the recursive angle formula alpha_0 = arccos(x_0), a valid nonnegative input such as x = (1/sqrt(2), 1/sqrt(2)) is loaded as (1/sqrt(2), -1/sqrt(2)) rather than x itself. Unless the implemented circuit uses the opposite RBS sign convention, every attention coefficient computed by the circuit in Figure 5 is a function of a sign-corrupted embedding, so the AUC comparison in Table 1 does not test the proposed quantum attention mechanism. The manuscript gives no procedure for handling negative components or for choosing an alternative RBS orientation.
[Section 2.2, 'Attention Coefficient Circuit' and Figure 5] The circuit is claimed to compute |x_i^T W x_j|^2, but no derivation links the measurement probability of the first qubit in state |1> to this quantity, nor is it explained how loading |x_j>, applying W, and loading <x_i| implements the transpose operation. Additionally, the attention mechanism in Section 2.1 uses softmax(QK^T / sqrt(d_k)), a linear inner product, whereas the quantum circuit outputs a squared absolute value. Without an explicit mapping from the circuit output to the attention weights and a specification of how the softmax and scaling are applied, the forward pass of the model is undefined, and the comparison with the classical ViT is not a like-for-like test.
[Table 1 and Section 4] The central claim that the QViT is 'as effective' as the classical ViT rests on test AUC 0.7369 vs 0.7385 and test accuracy 0.6755 vs 0.6788. No error bars, multiple seeds, or significance tests are reported, and no code is provided to reproduce the single run. Given that the differences are well within typical stochastic variation for a 15-epoch training run, the evidence as presented does not support the claim beyond an anecdotal single-run observation.
[Section 2.2, vector loading circuit applicability] The unary amplitude loader requires the input vector to be normalized and to have nonnegative components, as the recursive angles are defined through arccos of quotients of the vector entries. Patch embeddings are outputs of a learned linear projection E and are not constrained to be nonnegative or within [0,1]. The paper states that normalization does not degrade performance but does not address the sign restriction or provide a procedure for out-of-range values. Consequently, the loader as written cannot be applied to general patch embeddings, which is load-bearing because the attention coefficients in Figure 5 are computed from those embeddings.

minor comments (6)

[Section 6] The heading 'Aknowledgments' should be spelled 'Acknowledgments'.
[Author line and footnote] The author name appears inconsistently as 'Alessandro Tesi' in the author list and 'Alessandro Tessi' in the acknowledgment footnote.
[Figure 2] The figure shows a decomposition of the RBS gate using Hadamard, controlled-Z, and Ry rotations, but the text does not verify that this decomposition realizes the matrix given in Section 2.2; a short algebraic check would help.
[Section 2.1 and Section 3.2] The classical attention formula uses a scaling by sqrt(d_k), but the quantum attention coefficient circuit does not mention any such scaling; the relationship between the two should be clarified.
[Section 3.2] The statement that 'the simulation requires 26 x 26 attention circuits per self-attention block' is not explicit about whether this is per image and per epoch; please clarify the counting.
[References] Reference [1] is a webpage without a stable identifier; please provide a persistent DOI, CERN document number, or accession date and URL.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: the central claim is a benchmark result against an independent classical ViT on external CMS Open Data; self-citations are descriptive, not load-bearing.

full rationale

The paper's central claim—that QONN-based quantum attention performs comparably to classical attention for quark/gluon jet classification—is an empirical benchmark, not a derived prediction. The QViT is trained on CMS Open Data and compared in Table 1 with a classical ViT; the reported test AUC values are external measurements obtained on a held-out test set, not outputs of a fitted parameter renamed as a prediction. The RBS pyramid and unary loader implement QONN-style orthogonal transformations cited from [11,12], and the QViT line of work cites the authors' own prior papers [5,6], but those citations only situate the architecture and do not supply a uniqueness theorem or force the numerical outcome. While there is an internal consistency question about the unary loader's sign convention and the squared-modulus description of the attention circuit, that is a correctness concern, not circularity: the comparison with the classical ViT does not reduce by construction to any fitted input. The evaluation is self-contained against an independent baseline on external data, so any self-citation is minor and non-load-bearing.

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

The central claim rests on the quantum data loader and attention coefficient circuit behaving as described; the paper does not provide code or derivations for these components. No external physical constants or ad hoc free parameters are introduced beyond standard ML hyperparameters.

assumptions (4)

domain assumption The recursive arccos construction loads any normalized input vector into the unary quantum state.
Section 2.2 gives alpha_k = arccos(x_k / product sin(alpha_j)). This assumes nonnegative components and that every intermediate sine is nonzero; learned patch embeddings can be negative, and no handling is described.
domain assumption The probability of measuring |1> on the first qubit yields |x_i^T W x_j|^2 and can be used as the attention score.
Figure 5 and Section 2.2 equate the measured probability with the attention coefficient, but Section 2.1 defines A_ij = x_i^T W x_j. The sign loss and squaring are unaddressed.
domain assumption The classical ViT with identical hyperparameters is an appropriate baseline for asserting comparable performance.
Section 4 compares only to a single small classical ViT; no error bars, seeds, or comparisons to refs [5,6,7] are provided, so equivalence is not established with statistical support.
standard math RBS gates and pyramid circuits parameterize orthogonal matrices with n(n-1)/2 angles.
Used in Section 2.2, citing refs [11,12]; accepted in the QONN literature.

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Cite this review

Pith. "Pith review of Quantum Attention for Vision Transformers in High Energy Physics." pith.science (2026). https://pith.science/paper/TVN3EN44

@misc{pith2026241113520,
  author       = {Pith},
  title        = {Pith review of: Quantum Attention for Vision Transformers in High Energy Physics},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/TVN3EN44}},
  note         = {Machine review of arXiv:2411.13520}
}

read the original abstract

We present a novel hybrid quantum-classical vision transformer architecture incorporating quantum orthogonal neural networks (QONNs) to enhance performance and computational efficiency in high-energy physics applications. Building on advancements in quantum vision transformers, our approach addresses limitations of prior models by leveraging the inherent advantages of QONNs, including stability and efficient parameterization in high-dimensional spaces. We evaluate the proposed architecture using multi-detector jet images from CMS Open Data, focusing on the task of distinguishing quark-initiated from gluon-initiated jets. The results indicate that embedding quantum orthogonal transformations within the attention mechanism can provide robust performance while offering promising scalability for machine learning challenges associated with the upcoming High Luminosity Large Hadron Collider. This work highlights the potential of quantum-enhanced models to address the computational demands of next-generation particle physics experiments.

Figures

Figures reproduced from arXiv: 2411.13520 by the authors.

**Figure 2.** Decomposition of the RBS(θ) gate Vector Loading Circuits To prepare classical data for processing within quantum circuits, we implement vector loading circuits that efficiently map input vectors into quantum states. Specifically, we utilize unary amplitude encoding, where each feature of the input vector ⃗x = (x0, x1, . . . , xn−1) is assigned to a corresponding qubit, ensuring the vector is normalized (∥⃗x∥2 = 1) f… view at source ↗

**Figure 3.** 4-Qubit Vector Loading Circuit with Reconfigurable Beam Splitter (RBS) Gates. [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗

Figures from the paper (4 more)

**Figure 4.** Figure 4: Pyramid Circuit with RBS Gates The pyramid structure of the circuit ensures efficient implementation of orthogonal transformations. For an n × n orthogonal matrix, the circuit uses n(n−1) 2 RBS gates, matching the degrees of freedom of an orthogonal matrix. Each row of…

**Figure 5.** Figure 5: Quantum circuit to compute |x T i W xj | 2 , a single attention coefficient, using data loaders for xi and xj , and a quantum orthogonal layer for W. 3 Experiments In this section, we describe the dataset used, the data preprocessing steps, and the hyper-parameters cho…

**Figure 6.** Figure 6: Jet Component Visualization: Tracks, ECAL, HCAL, and Combined Data. [PITH_FULL_IMAGE:figures/full_fig_p006_6.png]

**Figure 7.** Figure 7: Validation metrics for QViT and classical ViT across 15 epochs. [PITH_FULL_IMAGE:figures/full_fig_p007_7.png]

Discussion (0). Continue with ORCID to comment.

Forward citations

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Reference graph

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Pith tools

Reviewed August 12, 2026 · model on record in the stance chip above.

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