Quantum Rationale-Aware Graph Contrastive Learning for Jet Discrimination
Authors: Md Abrar Jahin
Md Akmol Masud
Dr. M. F. Mridha
Nilanjan Dey
Zeyar Aung
Venue: Accepted by TMLR ()

Abstract: In high-energy physics, particle jet tagging plays a pivotal role in distinguishing quark from gluon jets using data from collider experiments. While graph-based deep learning methods have advanced this task beyond traditional feature-engineered approaches, the complex data structure and limited labeled samples present ongoing challenges. More broadly, our primary focus is the development of a rationale-aware graph contrastive learning framework designed to operate under strict resource constraints; we use quark-gluon jet discrimination as a representative and practically relevant use case. However, existing contrastive learning (CL) frameworks struggle to leverage rationale-aware augmentations effectively, often lacking supervision signals to guide salient feature extraction and facing computational efficiency issues, such as high parameter counts. In this study, we demonstrate that integrating a quantum rationale generator (QRG) within our proposed Quantum Rationale-aware Graph Contrastive Learning (QRGCL) framework enables competitive jet discrimination performance, particularly in parameter-constrained settings, reducing reliance on labeled data, and capturing rationale-aware features. Evaluated on the quark-gluon jet dataset, QRGCL achieves an AUC score of 77.5% while maintaining a compact architecture of only 45 QRG parameters, achieving competitive performance compared to classical, quantum, and hybrid benchmarks. These results highlight QRGCL’s potential to advance jet tagging and other complex classification tasks in high-energy physics, where computational efficiency and limitations in feature extraction persist. The source code for QRGCL is available at https://github.com/Abrar2652/QRGCL.

Published in Transactions on Machine Learning Research (01/2026)
Quantum Rationale-Aware Graph Contrastive Learning for Jet Discrimination
Md Abrar Jahin" University of Southern Colifornia
jahinSusc.edvy edu, jahin edu
Md. Akmol Masud Juhangirnagar University
masud.stu:211888hmmii edu
M. F. Mridha
frroz.mrihaahakuu edu
Americon International University- Bangladesh
Nilanjan Dey
nilonjan, dew@tint.@@ddeeee edwnntt.ed..cc in
Techno International New Town
Zeyar Aung
zeyor.aung@kuu.cc.o
Khalifa University
Reviewed on OpenReview: https: openreviee.. net/ forum? id= HrAb1jCC22
Abstract
In high-cnergy physics, particle jet tagging plays a pivotal role in distinguishing quark from gluon jets using data from collider experiments. While graph-based deep learning methods have advanced this task beyond traditional fenture-engineered approaches, the complex data structure and limited labeled samples present ongoing challenges. More broadly, our pri- mary focus is the development of a rationale-aware graph contrastive lcarning framework designed to operate under strict. resource constraints; we use quark-gluon jet discrimination as a representative and practically relevant use case. However, existing contrastive learning (CL) frameworks struggle to leverage rationalo-aware augmentations effectively, often lacking supervision signals to guide salient feature extraction and facing computational efficiency issues, such as high parameter counts. Tn this study, we demonstrate that integrating a quantum rationale generator (QRG) within our proposed Quantum Rationale-aware Graph Coutrastive Learning (QRGCL) framework enables competitive jet discrimination performance, partic- ularly in parameter-constrainee settings, reducing reliance on labeled data, and capturing rationalo-aware features. Evaluated on the quark-gluon jet dataset, QRGCL achieves an AUC score 77.5% while maintaining a compact architecture only QRG parameters, achieving competitive performance compared classical, quantum, and hybrid benchmarks. These re- sults highlight QRGCL's potential to advance jet tagging and other complex classification tasks in high-energy physics, where computational efficiency and limitations in feature extraction persist. The source code for QRGCL is available at https: //g/ thub. com/ Abrar2652/QRea QRRCL.
1 Introduction
Particle jet tagging, fundamental task in high-energy physics, aims identify the originating parton-level particles by analyzing collision byproducts at the Large Hadron Collider (LHC). While traditional approaches have relied on manually engineered features, modern deep learning methods offer promising alternatives for processing vast amounts of collision data (Kogler et al., 2019). The representation of jets as collections of constituent particles has emerged as more natural and flexible approach compared to image-based mothods,
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allowing for the incorporation of arbitrary particle features (Qu & Gouskos, 2020; Forestano et al., 2024). However, the challenge of limited labeled data in particle physics necessitates innovative solutions beyond purely supervised learning approaches. Self-supervised pretraining followed by supervised fine-tuning has shown particular promise in this domain. Self-supervised contrastive learning (CL) (Wang et al., 2025b;a; Xuan et al., 2024; Li et al., 2022) has gained significant allention in the field of graph neural networks (GNNs) (Veličković, 2023; Wu et al., 2021), leading to the development of graph CL (GCL). This approach involves pre-training a GNN on large datasets without manually curated annotations, facilitating effective fine-tuning for subsequent tasks (You et al., 2020).
A review of existing GCL approaches reveals a common framework that combines two primary modules: (1) graph augmentation, which generates diverse views of anchor graphs through techniques, specifically random node dropping (ratio 0.1), edge perturbation, and feature masking, to generate invariant views, and (2) CL, which maximizes agreement between augmented views of the same anchor while minimizing agreement between different anchors. However, these methods face inherent challenges due to the complexity of graph structures, where random augmentations may obscure critical features, potentially misguiding the CL process. In response to these challenges, recent studies have shifted focus towards understanding the invariance properties (Misra & van der Maaten, 2020; Dangovski et al., 2022) of GCL. The necossity for augmentations was emphasized to maintain semantic integrity, arguing that high-performing GCL frameworks should improve instance discrimination without compromising the intrinsic semantics of the anchor graphs. Building on this foundation, invariant rationale discovery (IRD) techniques (Li et al., 2022; Wu et al., 2022; Chang et al., 2020) were proposed, aligning closely with the objectives of GCL. These techniques highlight the importance of identifying critical features that inform predictions effectively.
Despite these advancements, gaps remain in effectively leveraging rationales for augmentation. Existing frameworks often lack the necessary supervision signals to effectively reveal and utilize the most salient features, and many approaches are difficult to deploy in sesource-construii costs, or limited supervision restrict model scale. In this work, our primary goal is methodological: we develop a rationale-aware graph contrastive learning framework that remains effective under strict resource constraints, and we study quark gluon jet discrimination as a representative high-energy physics use case that is both practically relevant and structurally challenging.
regimes where parameter budgets, simulation
These limitations are particularly visible in jet lagging, where current stale-of- approaches at LHC experiments (ATLAS and CMS) increasingly rely on sophisticated deep learning architectures, such as ParticleNet (Qu & Gouskos, 2020) and DeepJet (Bols et al., 2020). While these models siguificantly outperform traditional BDT-based approaches, they are inherently data-intensive and often operate as
'black boxes'. This motivates approaches that can prioritize task-relevant substructures and improve data and parameter efficiency. To address both the feature-extraction and computationallcompleett hybrid muantum-classical design choices (Havlícek et al., 2019; Jahin et al., 2023). Recognizing the pivotal role of the rationale generator in the GCL framework, we propose enhancing this component with quantum-basee based subroutine. Our proposed Quantum Rationale-aware Graph Contrastive Learning (QRGCI. integrates a quantum rationale generator (QRG) that identifies salient substructures within graphs, guiding rationale- aware augmentations without substantially increasing parameter count. We implement QRGCL with the ParticleNet (Qu & Gouskos, 2020) encoder, a projection head, and a lightweight classifier. Experiments on the quark-gluon jet tagging dataset show that QRGCL achieves competitive performance in low-data, parameter-consttrainee settings compared to classical, quantum, and hybrid baselines.
challenges, we also consider
Our main contributions are: (i) We propose a novel hybrid quantum-casssiaa framework, Quantum Rationale- aware Graph Contrastive Learning (QRGCL), that integrates quantum rationalc generator to identify salient substructures in graph-structured particle physics data for improved CL; (ii) We design a parameter-efficient QRG based on a 7-qubit variational quantum circuit, enabling salient feature extraction with only 45 trainable parameters; (iii) We introduce a new quantum-enbanced contrastive loss that incorporates rationale-aware, contrastive pairs, and alignment losses, with quantum fidelity as a distance metric; (iv) We conduct targeted experiments on the simulated quark-gluon jet tagging dataset as representative use case, showing that QRGCL achieves competitive performance against classical, quantum, and hybrid benchmarks in terms of Area Under the Receiver Operating Characteristic Curve (AUC), while maintaining a compact and computationally efficient architecture.
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2 Background
2.1 Contrastive Representation Learning
Contrastive representation learning (Peng et al., 2025; Mo et al., 2024; Kottahachchi Kankanamge Don ct al., 2024; Don & Khalil, 2024; Padha & Sahoo, 2024) is an effective framework for extracting meaningful representations from high-dimensional data by mapping it into a lower-dimensional space. CL uses a self- supervised approach to differentiate between positive pairs (similar data) and negative pairs (dissimilar data), particularly when labeled data is scarce. The framework consists of three components:
Data A Augmentation Module: This module generates multiple invariant views of given sample using invariance- preeeervigg transformations. The goal is create variations of the same input that retain negative pairs.
essential characteristics, forming positive pairs, while views from different samples For instance, augmenting a quark jet should retain its distinguishing features even when transformations like noise addition or spatial shifts are applied. This ensures that the learned representations remain general and robust to different data variations.
2. Encoder Network: The augmented views are processed through encoder, which maps each view into lower-dimensional embedding space. Each view in a pair is passed independently through the encoder, generating embeddings that capture the intrinsic features of the input data while abstracting away specific details.
3. Projection Network: While optional, the projection network is often used to adjust the dimensionality of the embeddings, enabling finc-tuning of the representation space. Typically, this is implemented as a single linear layer that transforms the encoded embeddings into a space suitable for CL objectives.
The goal is to train the encoder to minimize the distance between positive pair embeddings and maximize the distance between negative pair embeddings, enhancing representation quality for downstream tasks like classification.
2.2 Quantum Contrastive Learning (QCL)
Recent studies have begun to explore how quant computing can advance traditional CL frameworks (Jia et al., 2025). Quantum systems can potentially offer superior computational capabilities, allowing for more complex feature extraction and representation learning. One study (Jaderberg et al., 2022) proposed a hybrid quantun-classical model for self-supervised learning, showing that small-scale QNNs could effectively improve visual representation learning. By training quantum and classical networks together to align augmented image views, they achieved higher test accuracy in image classification than classical model alone, even with limited quantum sampling. Another approach (Kottahachchi Kankanamge Don et al., 2024) integrates Supervised CL (SCT. with Variational Quantum Circuits (VQC) and incorporates Principal Component A Analysis (PCA) for effective dimensionality reduction. This method addresses the limitations posed by scarce training data and showcases potential in medical image analysis. Experimental results reveal that this model achieves impressive accuracy across various medical imaging datasets, particularly with a minimal mumber of qubits (2 qubits), underscoring the benefits of quantum computing. A different research effort presents Q-SupCon (Don & Khalil, 2024), a fully quantum-enhanced Supervised CL (SCL) model tailored to tackle issues related to data scarcity. Experiments demonstrate that this model yields significant accuracy in image classification tasks, even with very limited labeled datasets. Its robust performance actual quantum devices illustrates its adaptability in sccnarios with constrained data availability. Furthermore, quantum-cnhanced self-supervised CL framcwork has been proposed for effective mental health monitoring (Padha & Sahoo, 2024). This framework leverages a quantum-enlan -ehannee Long Short- Term Memory (LSTM) encoder to improve representation learning for time series data through CL. The results indicate that this model significantly outperforms traditional sclf-superviood learning approaches, achieving high F1 scores across multiple datasets. To take advantage of QCL, as evident in these studies, we attempted to replace the classical rationale generator with VQC in our proposed framework.
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2.3 Rationale-Aware Graph Contrastive Learning (RGCL) Concept
RGCL (Li et al., 2022) represents a self-supervised CL approach that overcomes several limitations common to traditional graph CL (GCL) frameworks. Standard GCL methods often suffer from challenges such as augmentation strategies that can inadvertently alter or remove critical graph structure and semantics, and attempts to preserve graph-specific domain knowledge sometimes result in overfitting, limiting the model's adaptability to diverse, unseen data (Ji et al., 2024). RGCL addresses these issues by focusing on the concept of rationale learning, where the essential, discriminative information for graph classification is typically concentrated within a subset of nodes or edges in the graph. In RGCL, this discriminative subset, or rationale, is identified and emphasized during training, allowing the model to prioritize meaningful patterns while minimizing reliance on irrelevant features. In RGCL, specialized neural networks, known as the rationale generalor (RG), are used to assign importance scores to each node. This generator evaluates each node's 's contribution to the graph's 's overall representation. The higher-score nodes form the rationalc subset, while the remaining nodes comprise the complement subset. The rationale subset undergoes targeted augmentations during training, capturing the core discriminative features essential for downstream tasks. In contrast, the complement subset is augmented to encourage the exploration of less critical correlations, thus avoiding overfitting and improving generalization. RGCL pipeline leverages these dual views, rationale and complement, to guide the encoder network in learning a balanced ura space. By focusing on rationale views, the model learns robust, task-relevant features, while the complement views prevent it from becoming overly sensitive to spurious relationships, fostering a more gencralized understanding.
3 Methodology
3.1 Dataset and Preprocessing
3.1.1
High-Energe Physics Dataset
This study uses the Pythiu8 Quark and Gluon Jels for Energy Flow (Komiske et al., 2019) dataset, a well- established dataset in high-energy physics. The dataset contains two million simulated particle jets, equally split between one million quark-initiated jets and one million gluon-initiated jets. All events are generated at the Monte Carlo generator level using Pythia, with no detector simulation applied. The quark category includes only light. flavors (u,d,s), while heavy-flavor jets (c,b) are intentionally excluded to isolate the intrinsic topological differences between light-quark and gluon showers. These jets are generated through collision events at the LHC with a center-of mass energy vs 14 TcV. Jets were selected based on their transverse momentum range PT between 500 and 550 GeV and their pseudorapidity |yk<t| < 1.7. Each jet a is labeled as a quark jet (ya 1) or a gluon jet (ya, = =),, providing a binary classification target for model training. The fundamental differences between quark and gluon jet populations, specifically in particle multiplicity and kinematic distributions, are visualized in Figure 1. These distributions highlight distinct physical signatures, such the higher multiplicity and broader radiation patterns in gluon jets, arising from QCD color factors and serving as the primary discriminants for our model. Additional details about Figure 1 and aggregate kinematic distributions for the complete dataset are provided in Appendix 1.1.1. Each particle i within jet is characterized by several key attributes: transverse momentum pT,,- rapidity y/ azimuthal angle (i) and its Particle Data Group (PDG) identifier r!! Comprchensive details regarding the comparative analysis of quark and gluon jets, including their statistical significance, are discussed in Appendices A.1.1 and A.1.2.
3.1.2 Graph Representation of Jets
A graph Gs defined as set of nodes V and edges F,, represented as (V,F.. Fach node ( E VVin connected to its neighboring nodes o(5) through edges e(i)) E E. In the context of this study, each jet is modeled as a graph Ja, where the nodes vn represent the particles in the jet, and the edges ex represent the interactions between these particles. Each node (i) is associated with a set of features n(0 which describe its propertics, while the edges have attributes da that characterize the relationship between connected nodes.
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(a) Jet Multiplicity
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Figure 1: Key distinguishing features between quark and gluon jets. (a) Particle multiplicity shows gluons have significantly more particles (u=53.2) compared to quarks 33.4), reflecting the larger color charge of gluons. (b) Jet width demonstrates that gluons produce broader jets (μ= 0.089) than quarks (μ= (==0.06) 0.061) due to increased soft radiation. (c) Leading particle pr fraction reveals quarks exhibit harder fragmentation (==00 0.284) compared to gluons (μ= = 0.174), with energy more concentrated in the leading particle. (d) Jet mass shows gluons have systematically larger invariant mass (μ= 52.8 GeV) than quarks (μ=37.6 GeV). All distributions are normalized to unit area for direct comparison, with highly significant statistical differences (KS test <<I 10-100 for all features).
The number of nodes in each graph can vary significantly, reflecting the varying number of particles within each jet. This variability is particularly pronounced in particle physics, where jets can differ greatly in their particle multiplicity. Consequently, each jet graph Ja is composed of m, particles, each with I distinct features that capture various physical properties. This graph representation provides a natural way to encode the complex interactions within jets, enabling models to leverage the relational structure among particles. An illustration of this sraph-based data representation is shown in Figure where the graph indices (Graph 1, Graph 2) denote the underlying souroed jet prior to augmentation. A 'Positive Pair' consists of two independent rationalc-aware views derived from a single sourced jet, while a 'Negative Pair' represents the contrast between views originating from two distinct sourced jets.
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Positive Pair Graph (Label: 1)
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Plot of sample of graph views used in our CL-based approach. Each graph represents a jet as collection of nodes (particles) with associated physics-based features. The indices (Graph 1, Graph 2) correspond to distinct physical jets before the augmentation pipeline generates their respective positive and negative views for CL. The graphs are constructed as undirected, reflecting the geometric proximity in fcature space utilized by the ParticleNet architecture, rather than the causal temporal evolution of the parlon shower.
Figure 2:
3.1.3 Feature Engineering
(6) Additional kinematic variables are derived from the original features (Pr. Ma ; using the 'Particle' package to improve the model's ability to learn from the data. These engineered features include transverse mass, energy, and Cartesian momentum components, providing more complete description of each particle's dynamics. More details about these engineered features are shown in Appendix A.3.
3.1.4 Edge Construction and Attributes
These features are then normalized by their maximum values across all jets to ensure consistent input scales, enhancing the stability of the training process. Edges between particles in a jet are defined based on the spatial proximity of particles in the (d.y) plane, calculated utilizing relative coordinates (AΦ,Ay) (Fuclidean distance) ensure translational invariance:
A (()) = = (11) = (0a (1)
0a (()))²
+ +(112)
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ya
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This metric measures the angular separation between two particles, capturing their spatial relationships within the jet. The resulting matrix A R is provided as an edge feature (rather than a fixed adjacency weight) to the graph network. This allows the model to learn the optimal spatial dependencies, determining whether close or Published in Transactions on Machine Learning Research (01/2026)
distant particles carry more significance for the classification task.
3.1.5 Graph-Based Augmentation and Contrastive Learning
We applied graph-based CL techniques to improve the discriminative capability of our models by generating augmented graph views. The augmentation strategies included node dropping, edge perturbation, feature masking, and jet-specific transformations. The augmentation ratio (Taug) defines the probability with which a specific transformation (e.g., node dropping) is applied to the nodes or edges of the identified rationale subgraph. Details of the augmentation pipcline, view pairing, and the construction of positive and negative pairs are provided in Appendix A.4.
3.1.6 Enforcing Infrared and Collinear Safety
To ensure compliance with infrared and collinear (TRC) safety, we adopt perturbation and regularization techniques inspired by the principles of QCD, as outlined by Dillon et al. (Dillon et al., 2022). Further theoretical and implementation details are provided in Appendix A.4.1.
3.1.7
Data Splitting
To ensure manageable computational complexity and adapt the model for quantum processing, we focused on jets containing at least ten particles, resulting in a dataset of N=1,999,4455 jets, of which 997,803 were classified quark jets. Unlike classical GNNs, which offer flexibility in adjusting the number of hidden features, quantum networks constrained by the scaling of quantum states and Hamiltonians. Specifically, the computational cost of simulating the quantum state vector on classical hardware scales as 2", where represents the number of qubits, corresponding to the number of nodes (na) in the graph. Each node represents a particle in the jet, making jets with many particles challenging to handle due to the exponential growth in quantum computational requirements.
To address the challenge of varying particle numbers in jets, we simplified the problem by limiting the number of active nodes (particles) per jet to n, 77 This truncation to n. = is constraint imposed by the exponential cost of classically simulating quantum state vectors (2N). While this selection acts as groomer that may remove soft radiation characteristic of gluon jets, selecting the highest transverse momentum (pr) constituents ensures adherence to IRC safety by retaining the dominant kinematic energy flow. This was done by selecting the 7 particles with the highest pr from each jet. Consequently, each jet graph is represented by a fcature set h, = (h&)) _naa ,...,h?'), (7)), ) where each ha E ETR corresponds to the enriched feature vector of particle. The complete representation of each jet is thus given by ha E 7xx8, capturing key physical attributes of the selected particles. A subset N = 12,500 jets was randomly selected for model training, with 10,000 jets used for training, 1, 1,250 for validation, and 1,250 for testing. These subsets maintained the original class distributtinn, resulting in 4,982 quark jets the training sct, 658 in the validation, and 583 in the testing set.
3.2 Proposed QRGCL
Quantum rationalo-aware GCL (QRGCL) consists of 4 major components, as illustrated by Figure 3: rationale generator (RG), encoder network, projection head, and loss function.
3.2.1 Quantum Rationale Generator (QRG)
The QRGCL model substitutes its classical RG (CRG) (Li et al., 2022) with a quantum RG (QRG). This component crucial in generating augmented graph representations by assigning significance scores each node. The QRG is built using 7-qubit parameterized quantum circuit (PQC), where each qubit represents a node in the graph.
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Figure 3: Overview of the proposed QRGCL framework. Given an input jet represented as graph (anchor graph), QRG assigns importance scores to nodes (particles) using a parameterized quantum circuit. Based on these scores, a rationale subgraph and a corresponding complement subgraph are sampled to construct multiple rationale-are aware augmented views. These views are processed by a shared ParticleNet GNN encoder, producing graph-level embeddings via global average pooling. The embeddings are passed through a projection head obtain representations used for CL. The framework jointly optimizes the QRG, encoder, and projection head by minimizing combined objective that includes rationale-aware, alignment, uniformity, contrastive and InfoNCE) losses. During fine-tuning, the learned representations are fed into lightweight classifier head for supervised discrimination of quark-gluon jets.
Permutation symmetry. Our QRG processes the n. =7 selected constituents in fixed order (sorted by Pr), hence the rationale-scoring subroutine is not permmutation-eqquivariint However, the downstream ParticleNet with symmetric neighborhood aggregation (EdgeConv) and
encoder operates on unordered particle pooling, preserving permutation invariance of the learned graph-level representation.
The quantum circuit for the QRG consists 3 main components, as shown in Figure data encoding, parometerized unilaries, and entanglement. The encoding process starts by initializing each qubit, typically using a Hadamard (H) gate create a uniform superposition state:
1 (10)+11) -2
(2)
Next, the classical node feature vectors are embedded into the quantum state using parameterized rotation gates (c.g., Rx, or Hadamard-bascc encodings, mapping classical data to the Hilbert space of the quantum circuit. The specific choice of encoding can be customized, with RX encoding being implemented for proposed angle-based representations. Node feature vectors x; encoded rotation angles using RX, RY,
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Figure 4: QRG circuit of the proposed QRGCL. The circuit operates on seven qubits, with each qubit corresponding to node in the graph. Symbols denote: H (Hadamard gate) for superposition; R Rz (Rotation gates) for feature encoding; CRZ (Controlled-Rotatia 2) for entangling edge topology; and the meter symbols for measurement in the computational basis. The top portion shows the data encoding stage, where each qubit is initialized using an H gate followed by R.X-based angle encoding node features. CRZ gates encode edge relationships between qubits. The bottom portion includes parameterized rotations (RX, RY, RZZ for adaptable representations and entanglement layers using SWAR AP gales. Measurement results are obtained computational basis, with classical registers collecting the output.
RZ gates. For example, the RX gate is defined
cos(0/2) -isin(0/2)
RX = (0/n( (0s())2
(3)
where 0 determined by the value of x,. To map the high-dimensional node features (1 E R to the single dogree of froedom available the rotation gates, we first employ classical trainable lincar projection layer P: 8 1 This layer reduces the feature vector of each node to a scalar value 0,, which is then normalized via arctangent function to the range 2, Following this projection, the encoding process initializes each qubit into superposition state using the H gate, followed by the feature encoding via an Rx rotation:/p/ 8 "_ Rx (O). This hybrid classical-quanturr encoding strategy allows the model to learn the optimal linear combination of particle features (e-g-, Pr, Φ) that drives the quantum interference pattern.
Edge relationships are encoded using controlled-phase (CRZ) gates between pairs of qubits. The matrix representation defined in the standard computational basis [[00).[01), [10), [11)], where the first qubit corresponds to the control state and the second to the target. This is diagonal, asymmetrie gate that applies

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phase to the target qubit depending on the control qubit's state.
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U3(a,B,7)= cos(a/2)
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which allows the QRG to learn adaptable representations through trainable parameters a, 3, and y. These parameterized gates form the trainable part of the circuit, allowing the QRG to adaptively learn the significance scores based on the input data during training. The parameters of these gates are optimized through the Adam optimizer.
The entanglement layers utilize fixed circular topology, where the i-th qubit acts as the control for the (-++)-th target qubit (with the last qubit controlling the first), ensuring complete pairwise correlation across the circuit layers. Entanglement is introducod using fixed topology of two-qubit gates (specifically SW AP gates in circular tern) lo capture correlations between the sequence of input particles. These entanglement patterns are designed based on the graph's is structure, ensuring that important correlations between nodes are captured. For example, SW AP gates can exchange quantum states between qubits, preserving relationships between specific nodes:
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The output of the QRG is obtained by measuring the qubits on a computational basis. The squared amplitudes (00000100.) provide node significance scores normalized
of states with a Hamming weight of (e.g., into a discrete probability distribution. To ensure the framework remains end-to-end differentiable, we utilize the Gumbel-Softtax reparameterization trick (Jang et al., 2017). This allows gradients to flow from the contrastive loss function back through the discrete sampling of rationale subgraphs, updating the parameters of the QRG and the projection layer. With the QRG generating significance scores, augmented views are created for the downstream CL process. For optimistic view, nodes with the highest significance scores are relained, preserving the most relevant information for classification. Negative views, on the other hand, are constructed by using less significant nodes or by introducing random variations, helping the model learn to distinguish between genuinely informative structures and noise.
Integration into the encoder. In practice, the QRG's measured probabilities are used select the top-k most salient nodes (and their incident edges) to form rationale subgraph. This subgraph then fed to the classical ParticleNet encoder, which applies EdgeConv on the selected nodes to produce embeddings for CL and, later, classification. This makes explicit the data flow: full jet - QRG importance scores - selected subgraph
+ ParticleNet + cenjectioonclassiiiee
3.2.2 Encoder Network
We used the ParticleNet (Qu & Gouskos, 2020) model our encoder to convert the augmented views of input particle fcatures into low-dimensional embeddings. ParticleNet is graph-based neural network optimized for jet lagging, leveraging dynamic graph convolutional neural networks (DGCNN) to process unordered sets of particles, treating jets as particle clouds. The encoder is initialized with random weights and fully trainable during the contrastive pre-training phase, allowing it learn optimal representations alongside the rationale generator. It only during the downstream supervised fine-tuning that the encoder weights are frozen. More details about ParticleNet are shown in Appendix B.1.
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3.2.3 Projection Head
Our architecture includes a projection head that maps the 128-dimenia encoder output 128-dimensional latent space optimized for the contrastive loss function. Following the design principles of SimCLR (Chen et al., 2020), we preserve the encoder output dimensionality (128) rather than compressing it directly, non-linear projection head has been shown to mitigate information loss prior to applying the contrastive objective. The projection head consists of two-layer MLP with an intermediate ReLU activation, which transforms the encoder reprosentations while maintaining the same latent dimensionality. CL is performod on these projected embeddings by maximizing the InfoNCE objective, which implicitly enforces mul information between anchor and rationale representations. This separation enables the encoder learn features transferable downstream tasks, while the projection head specializes in aligning represcntations for effective contrastive optimization.
3.2.4
Contrastive Loss
QRGCL model uses carefully designed loss function that integrates multiple elements: InfoNCE, alignment, uniformity, rationale-aware loss (RA loss), and contrastive pair loss (CP loss), to optimize the learning of quantum-enhanced embeddings. More details about these losses are shown in Appendix B.2.
3.2.5 Classifier Head
The classifier head, employed during the supervised fine-tuning phase, consists of a 128-neuron single linear layer (Amode! 1) followed by a sigmoid activation. This simple architecture is designed to map the frozen representations to a probability score for binary jet discrimination, ensuring that performance gains are attributable to the quality of the learned embeddings rather than the complexity of the readout layer.
3.3 Benchmark Models
To validate the effectiveness of QRGCL, benchmark against diverse set of architoctures categorized into Classical, Quantum, and Hybrid models (see Table 1 and Appendix C for detailed specifications):
Classical Baselines. We employ standard GNN (EdgeConv-based) and an Equivariant GNN (EGNN) to evaluate the impact of geomet ric symmetry preservation in the classical domain. We also compare against. CRGCL (Table 2), the classical counterpart our proposed method, to isolate the quantum advantage.
Quantum Baselines. We utilize QGNN and EQGNN, which map graph structures directly to variational quantum circuits. These baselines test the expressivity of pure quantum approaches without classical pre- processing.
Hybrid Baselines. We include QCL and CQCL, which combine classical convolutional encoders with quantum projection heads or classifiers, representing the current state-of-tho-art in hybrid quantum machine learning.
While Transformer-based architectures like Particle Transformer (ParT) (Qu et al., 2022) and ParticleNet (Qu & Gouskos, 2020) achieve state-of-the-art performance (approx. 84% accuracy) quark-gluon discrimination, they are eesource-intensivee utilizing full particle inputs (30-50 constituents) and large parameter spaces (e.g., ParticleNet: =366k, ParT: x2. 14M). In contrast, this study evaluates QRGCL under strict NISQ-compatible regime: restricted to 7 input particles and highly compact total parameter count of RJ x126k (with only 45 learnable quantum parameters the rationale generator). Consequently, a direct numerical comparison with full-scale Transformers not appropriate. We selected GNN basclines as they provide a comparable topological framework isolate the specific impact of the quantum rationale mechanism within these specific computational constraints.
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Table Performance benchmarking and ablation test of the proposed QRGCL. Bolded values indicate the best
performance. Results represent the mcan and standard deviation calculated over 3 random sceds using the
optimal hyperparameter configurations identified in Table 2.
Model
Test Acc. (1)
AUC (1)
P1 Score (1)
W Params (1) R6. (4)
Wlayer (4)
Hatch sise
Epoch
Encoder
QGNN
72.2% 2..6
70.4%
72.1% 22.1%==2.49 4%%
5156
6
MLP
73.9%
63.4%%10.99%
73.9%
EGNN
78.9%=00.9%
67. 07.0%
7..6%
5252
3
4
64
19
MLP
EQGAN
71.4%* 2%6
74.4%++1.8%
71.2% 55%
5140
3
6
19
MLP
QCL
30.4%
53.3%:10.5%%
51.8%
3
256
1000
Amplitude
CQCL
80.0%=0.8%%
49.8%=+1.6%%
48.3%+1.33
1000
Amplituuk
QOGCL
57.4%f=:1.5%
62.4%%22..6%
66.7%=116%
7448
6
128
Mi
Augle (RY + RX)
QOGCL
65.49%11.00%
71.1%:10.5%
60.8% 1.0%
7418
6
125
50
Angle (RY)
QOCCL
65.8%
20.8%:m0.88%
64.3%
Amplitude Angle
CRGCL
70.49.10..5%
78.3%%10..22 2%
08.2%
127025
7
2000
GAT
QRGCL wariant
70.99:1:1 (05
77 77.35;:1
10.4%
126015
3
2000
50
RX + II + RX
Proposed QRGCT
71.88:20.88
77.5%+0..9%
70.4%:00.8%
125015
Parameter breakdown: The reported QRCCL parameter count (126,015) includes the ParticleNet et encoder (125,961 params) and
the QRG (54 params: 45 quantum + 9 classical), used during pre-training and frozen for fine-tuning. The downstream classifier is separate linear head (129 params) trained on frozen embeddings.
Table 2: Comparison between classical and quantum RG of RGCL. Reported values represent the mean validation accuracy across stratified 10-fold cross-validation (with shuffling enabled) on the training set. Standard deviations indicate the variability across folds. Bolded values indicate the best performance.
Classical RG
Quantum RG
Parameter type
Parameter
Accuracy (1)
AUC (?)
FT
(1)
Accuracy
ADC
70.4% 1 1.2%
76.3% 1 1.1%
69.1% 1.2%
70.8% 1: 0.9%
75.9% 1 1..8%
69.9%
0.9%
68.2% 1.3%
74.1% 11.2%
67.9% 1.33%
70.8% 0.9%
75.6%
70.5% 0.9%
Nodes graph
68.4% 1.4%
73. 11.4%.1..99
67 2% 1.4%
67 6% + 1.1%
71.5%+1.00%
67.5% 1.11%
67.0% 1.5%
73.4%
1.5%
70.7% 0.99%
7..7%
70.3%
0.9%
68.8% 1. 1.3%
74.5% 1:66:1111 1.2%
68.8% 1.111..1 1.3%
66.8% 1: 1.0%
71.4% 1.0%
66.5% 1.0%
Number of layers
66.7% + 1.5
73. 6% 1.44%
66.7%
1.5%
68.6% 0.9%
74.7% 0.8%
68.5% 0.9%
71.2% + 1.1
76 8% + 0%
71.1% = 1.111.11 1%
66.4% 9% 1.2%
72.3% 1.1%
66. 4% = 1.2%
63.0% + .%%
67. 177.5%
1.7%
63.0% 1.9%
67.4% 4: 1.3%
1.2% 71.2%
67 67.3% 1.3%
0.0
65.2% # 6%
71.5% 10%%%1.0 3%
65. 15.1% 1.7%
69 8% = 1.0%
73.2% 11.0%.1.000 1.0%
69.5% ..0%
Augmentation ratio
0.1
67.8%
.4%
74.1%
.3%%
67.8% 1.4%
72.1%
78.8%
7%
72.1
0.8%
0.2
84.6% 1: 1.7%
69.8% 1 1.6%
64.5% 1.7%
65.6% d: 1.4%
71.1%
1.3%
65.6% à 1.4%
699.6% 1
63.7%
1.8%
71.3%
77.0%
71.3% 0.9%
Table 3: Scalability comparison of classical, quantum, and hybrid models as the number of active nodes per graph (na) increases beyond 3. Entries marked "_' indicate training failures due to out-of-memory (OOM) errors resulting from exponential circuit width growth at n. 7. Bolded values indicate the best performance.
Model
Test Acc.
AUC
Fl-score
Ra
# Params
Blayer
Batch size
Epoch
Encoder
EGNN 54.2%
64.4%
68.5%
64
MIP MLP + H
EQGNN
47.8%
55.1%
30.9%
990100
1
19
QGNN
54.6%
13.9%
51.6% 6%
7
1021076
1
19
MLP +
GNN
52.2%
57.8%
35.8%
5252
64
19
MLP
QCL
44.8%
48.3%
61.9%
384 5
256
1000
Amplitude
QCL
256
1000
Amplitude Angle (RY+RXX
CQCL
45.2%
48.4%
60.7% 5
354
128
50
CQCT
128
50
Angle (RY)
Clarification: Models marked "CL" " used CL but did not rationale generator. All other modcls (EGNN, EQGNN, GNN,
QGNN) full subgraphs of size nar without rationale selection or angmentation.
4 Experimental Setup
4.1 Simulation Tools and Environment
We implemented all the models using the PyTorch 2.2.0 (Paszke et al., 2019) framework for classical computations and Pennylane 0.38.0 (Bergholm et al., 2018) and Torch Quantum 0.1.8 (Wang et al., 2022) for quantuu circuit simulation. We used the Deep Graph Library (DGL) 2.1.0+cu121 (Zheng et al., 2020) to handle graph operations and the Qiskit 0.46.0 (Javadi-Abhari et al., 2024) framework to simulate quantum circuits. The computing infrastructure consisted of Intel(R) Xeon(R) CPUs (x86) with a clock frequency of 2 GHz, equipped with 4 vCPU cores and 30 GB of DDR4 RAM. For GPU acceleration, we utilized two NVIDIA T4 GPUs,
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each with 2560 CUDA cores and 16 GB of VRAM, significantly boosting the performance of deep learning tasks. For reproducibility, we set random seeds to 42, 123, and 456 for the 3-seed averaging reported in Table 1. Common training utilities included: (i) learning rate warm-up with linear increase from 1 x 10 to base LR over specified epochs and (ii) gradient clipping. Quantum circuit differentiation exclusively utilized the parameter-shift rule lo ensure hardware compatibility, with statevector simulation employed for models requiring exact gradients and shot-basod simulation (with 1024 shots) specífied. The source code for QRGCL, including the quantun rationale generator implementation and benchmarking suites, is publicly available at. https://gite
4.2 Hyperparameters and Configurations
We varied hyperparameterss for CRG, QRG, data augmentation, and training in the proposed QRGCL model, and reported test accuracy, AUC, and F1 scores across various encoder types, learning rates (LR), and entanglement strategies. We used Adam optimizer with a 1 x 10-3 learning rate (31 = 0.9, 32 = 0.999, and e= 10- across all the models and Binary Cross-Fntropy (BCE) loss function. 10-fold cross- pross-validation was performed for each model, and the mean and standard deviation were calculated for each metric. The hidden feature size for classical GNN and EGNN was 10 to maintain a comparable parameter count to the quantum counterparts, while for the QGNN and EQGNN, it was 2 In the case of QCT. and CQCL, Blayer stands for the depth of the quantum circuit, and in other models, it refers to the number of GNN layers. The term Mayer in QRG refers to the number of repetitions of the variational block, which consists of the parameterized rotation gates (U3) and the entanglement layers. A deeper circuit (Nioger >> 1) increases the expressivity of the quantum ansatz. In Table 2, each row varies a single hyperparameter while keeping all others fixed to a shared default configuration (n. 7 7 nodes, two GNN layers, 10% dropout, GAT encoder, embedding dimension 128, hidden size 256, output dimension 128, no weight decay, augmentation ratio 0.1, temperature 0.1, batch size 2000, and for QRGCI, only: quantum layers). Specifically, the third row sets the number of GNN layers to 4 for CRGCL, while all other parameters remain at their default values. No joint (pairwise) hyperparameter optimization was performed due to computational constraints; thus, comparisons reflect controlled oue-factor-al--a-iin sweeps under consistent. training settings.
The choice of epochs and batch sizes varies based on the computational requirements of classical and quantum models. Classical models like GNN and EGNN use larger batch sizes (64) and fewer epochs (19) to achieve more efficient gradient updates, enabling faster convergence. In contrast, quantum models such as QGNN and EQGNN use much smaller batch sizes (1) due to quantum hardware limitations, yet still require 19 epochs to achieve adequate learning despite fewer updates per step. For fully quantum and hybrid models like QRGCL and QCGCL, larger batch sizes (2000) and more epochs (50) are used due to the longer backpropagation caused by the complex custom loss function, with multiple loss components ensuring that the model has sufficient time to learn robust quantun-based representations, as the slower convergence can hinder effective learning.
Training Protocol. For fair comparison, classical GNN, EGNN, and EQGNN baselines were trained using fully supervised learning, whereas QCL, CQCL, and QCGCL adopted contrastive objectives. Only QRGCI. and its classical counterpart CRGCL employed rationale-aware contrastive pretraining followed by fine-tuning, isolating the contribution of the QRG. All supervised benchmarks were trained using BCE loss with the Adam optimizer (Ir = 10-3, 3 = 0.9, B2- = 0.999, and e = 10-5). Contrastive benchmarks (QCL, CQCL) utilized InfoNCE loss (T = 0.1) during pre-training treiitiiinn...... We adopt a two-stage procedure for QRGCL: (i) self-supervised pretraining for 50 epochs using a rationalc-aware contrastive objective defined as LQRCEL. = (CRA + +XCCP + +.8 + H LInONCEE) and (ii) supervised fine-tuning with a linear classifier for 1000 epochs on the learned graph-level embeddings (during fine-tuning, the encoder parameters are kept fixed). Convergence of the contrastive loss was monitored using a validation set during the 50-epoch pretraining phase to ensure sufficient feature alignment before the extensive 1000-epoch fine-tuning stage. This step evaluates the quality of learned representations in a supervised downstream setting. Figure 5 illustrates the learning dynamics over 1000 epochs. While the accuracy begins to stabilize around 500-800 800 epochs, we extended training to 1000 epochs to ensure complete convergence of the projection head. Crucially, no degradation in validation performance was observed in the later epochs, indicating that the model is robust against overfitting even with prolonged training.
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Table 4: Hyperparameter optimization results of the proposed QRGCL. Reported values represent the mean validation accuracy across stratified 10-fold cross- cross-validation (with shuffling enabled) on the training set. Standard deviations indicate the variability across folds. Bolded values indicate the best performance. Unless otherwise varied in a specific row, the default configuration uses na = nodes, 3 quantum layers, a learning rate of x 10-3; SW AP entanglement, and RX encoding.
Parameter type
Parameter
Accuracy (1)
AUC (t)
F1 Score (t)
Amplitude
69.3% 1..1%% 1.1%
74.7%
10.3%%11.11.
IQP
68.9% 2%
76. 76.1%
68.5% 1.2%
Displacement-ampline
66.2% +1.5%
72.1%+1..4%
66.0%+166%
Displacement-ppae
70.2% 1.00%
76.2% 0.99%
69.1%..:11
Encader type
RY
67.0%
73.9% 1.1%
67.0%
RX
70.8%++0.99
76.3%+0..8
69.6%=0.88
RZ
62.9% +.%.1%..1%
67. 0..9%
62 8%%%%0%
H
70.8%
76.7%%10.77
69. 70.7%
Phose
68. + 1.2%
74.2% 1.1%%
68 68.3%+111 1.2%
68.6% 1.1%
74.4%
68.4%%1 1.1%
1E-03
70.3%+0..88 8%
76 2% 8%
70.3% = 8%
Learning rate
3E-03
63.9% + 6%
68 68.8%
63 63.7%+11777
5E-03
66.0% 1.4.%
70.9% 1.33%
66 66.0%:11.49
1E-02
69.5%
75.8%++0.9%
69 10.5%+1.00 1.0%
CNOT
69.8%
70.6%
60.8% 1.0%
CZ
11.%%
73.3%+1.19%
68. 18.1%+1.225
Entanglement type
SWAP
0..9%
76.2%%+0.8%
70. 0..9%
CNOT Butterfly
68.0% 1.3%
74.6% 1.2%
68.0% 1.3%
C7 Butterfly
67.7% +: 1.4%
73.2% 2 1.3%
67.7% 1.4%
SWAP Butterfly
68.0%
73.2%
67.8%1 1.3%
Scalability. Models ending with "CL" Table 3 used CL but lacked rationale generation. For other models, increasing na corresponds to including more raw particle features in the encoder without explicitly learning which ones are most informative. As na increases, both quantum and hybrid models experience exponential scaling in circuit width and memory usage, making larger graphs harder to simulate reliably and resulting in failed runs for QCL and CQCL at n,, 7. It is important to note that this exponential bottleneck applies to the classical simulation of the quantum state. On actual quantum hardware, the resource scaling would be linear with respect to the number of nodes (qubits), limited primarily by gate fidelity and coherence times rather than memory. In contrast, classical graph- based models such as GNN and EGNN maintain stable accuracy and F1 Fl-cccess, reflecting linear computational scaling. QGNN and EQGNN remain trainable but incur a steep parameter cost (< 108) without proportional performance gains, The absence of consistent improvement, and occasional degradation, with larger na supports central finding: simply enlarging the particle subgraph does not improve jet discrimination unless the most salient constituents are identified, as done by QRGCL. The observation that performance does not improve and often worsens with higher supports our main claim: larger input subgraphs do not necessarily improve discrimination in jet data unless the substructure is meaningfully selected, as in QRGCL.
5 Results and Discussion
We evaluate the performance of QRGCT, against the baseline architectures defined in Section 3.3 (see also Appendix B.3 and C for detailed specifications). AUC was selected as the benchmark metric due to its effectivencss in assessing binary classification performance across all thresholds. While specific working points (e.g., background rejection at fixed efficiency) are often used in HEP, AUG provides a holistic measure of the discriminator's scparation power independent of specific operating conditions, facilitating architectural comparison. The number of trainable parameters of CRG was 1,073, compared 45 for QRG.
The hyperparameters specific to QRGCL include encoder type, learning rate, and entanglement type, detailed in Table 4. See Appendix B.3 for detailed definitions of the specific quantum encoders tested, including Amplitude, IQP, and Angle-based variants. Among the encoders, RX and H achieved the highest AUC values at 76.3% and 76,7% respectively, while displacement- -amptttdd and RZ encodings performed poorly, with AUCs of 72.1% and 67.3%. The optimal learning rate of x 10-3 produced the highest AUC of 76.2%, with higher rates resulting in decreased performance. The SW AP entanglement type yielded the best overall results, achieving an AUC of 76.2%. CNOT and CZ entanglements performed strongly, while other configurations
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Training and Testing Loss
Training and Testi Accurecy
0.70
Test Loss
70
65
0.84
40
0.62
0.50
0.38
Thain Ac Acsunicy
Test
200
450
600
800
1000
300
400
600
200
3000
Figure 5: Training and testing dynamics of QRGCL over 1000 epochs. The lest graph illustrates loss curves, while the right graph presents accuracy curves.
1.0
0.8
Positive Rate (TPR)
0.6
ORGCL (H (AUC 77.53%)
OCGCL (Amplitude Embedding) (AUC 70.83%
OCGCL (Angle Embedding) (AUC 62.26%)
QCGCL (RY) (AUC 71.07%)
Hybrid Classical CL (AUC 49.79%)
Fully Quantum
53.26%)
EQGNN
EGNN (AUC 67.88%)
OGNN (AUC 70.37%)
GNN (AUC 63.36%)
Random Guess (50%)
0.8
False Positive Rate (FPR)
Figure 6: ROC curves comparing the proposed QRGCL with classical, quantum, and hybrid bascline models the quark gluon jel discrimination task. QRGCL achieves competitive AUC performance across wide range of operating points. In particular, QRGCL maintains higher TPR at low FPRs, highlighting its effectiveness in regimes relevant for high-purity jet tagging. These results confirm that incorporating -entuum-enhaneed rationale selection can improve discriminative performance while remaining parameter-effict -ffficceet.....
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underperformed. For the proposed QGRCL, two possible combinations of RX and H encoders, the learning rate of x 10-3 and SWA AP entangler were tried.
For both the classical RGCL and QRGCL models, tunable parameters included the number of nodes per head (na) ranging from 7 to 10, the number of classical or quantum layers (Niayer) ranging from 2 to 5, and the augmentatiin ratio ranging from 0.1 to 0.3. As shown in Table 2, QRGCL achieves comparable AUC values to the classical RGCL across different node counts (8 and 10 nodes). At layers, QRGCL achieves performance comparable to the classical model (74.7% 73.6%, within statistical uncertainty). However, it underperformed at 2 and 4 layers. With 0.1 augmentation ratio, QRGCL achieved its strongest performance of 78.8%, compared to the classical approach's s 74.1%. The optimal paramcters for QRGCL were found to be Ro -7, 7, Maaye = 3, and an augmentation ratio of 10%.
Based on Table 1 and Figure 6, it is evident that our proposed QRGCL model achieves a robust mean AUC score of 77.5% (averaged over 3 scods), with peak performance reaching 78.8% in optimal configuration runs (Table 2). While QRGCL achieves the highest mean AUC, the error margins indicate competilive performance with state-of-the-ee thetooof-----ttttoee classical models, suggesting that the quantum advantage lies primarily in parameter efficiency and rationale interpretability rather than raw accuracy alone. We selected the two best-performing encoders from Table 4 and developed two variants by hybridizing them. Further experimentation revealed that H initialization followed by Rx encoding demonstrated greater stability, achieving the highest mean AUC and lowest standard deviation across validation folds. Additionally, the relatively large number of parameters in the QRGCL is due to the utilization of the ParticleNet GNN encoder, which contains 125k parameters, while the QRG circuit only has 45 parameters. Tables 1,2, and complement the ablation studies for QRGCL by presenting results for configurations without rationalc-awareness (QGNN, GNN, EGNN, EQGNN), analyzing VQC components (such as encoding variants, entanglement structures, and variations in qubits and layers), exploring different classical-quantee a classical-only baseline), and examining the effects of rationale-guide data augmentation. Figure 5 shows stcadily decrcasing training and testing losses in QRGCL, indicating effective lcarning. While the training and lesting curves stabilize around 800 epochs, we observe a persistent gap (~ 2%) and a slight decline in test accuracy in later epochs, indicating mild overfitting typical of deep learning models trained on restricted datascts (10k samples). Additionally, we observe that classical GNNs perform slightly better in the high-purity regime (tight cuts, Figure 6 bottom-left), likely because they utilize the full feature set without the information bottleneck imposed by the quantum rationale generator. Training and testing accuracies increase rapidly within the first 200 epochs and plateau near 800 epochs. Test accuracy stabilizes slightly above 70%, with training accuracy close behind, indicating stable performance and limited gains from further training. Figure 6 presents the ROC curves for the top-performing models, highlighting that QRGCL (blue curve) maintains a competitive true positive rate across most false positive thresholds compared to the classical GNN and hybrid basclines.
interfaces (including quantum-only and hybrid architectures, as well as
6 Broader Impacts
QRGCL enables efficient, low-supervision feature extraction that can accelerate particle physics discoveries, inspire coantum--ugmeenerr ML methods, raise ethical and interpretability considerations, and generalize to broader graph-structured problems across science and industry.
7 Conclusion
This paper introduced QRGCL, a resource-constrainedd rationale-aware graph contrastive learning framework that integrates quantum rationale generator into a hybrid quantum -lassical pipeline. We evaluate this methodology on quark -luon jet discrimination as representative use case, demonstrating that rationale- aware contrastive pretraining with a compact QRG can yield competitive downstream performance. Our results show that QRGCL achieves a robust mean AUC of 77.5%, with peak performance reaching 78.8% in optimal configuration runs, while keeping the quantum rationale module extremely lightweight (45 parameters). Hyperparameter analysis further indicates that the H RX encoder and the SW AP entanglement gate improve stability and performance, emphasizing the importance of circuit design choices in this regime. These findings support QRGCL as a general approach for learning representations from graph-structured data when resources
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(parameters, simulation cost, supervision) are limited, with jet tagging serving concrete and challenging testbed.
8 Limitations
A primary limitation of this study is the of generator-level data and aggressive jet grooming (n, 7) necessitated by current quantum simulation constraints. While real LHC analyses involve full detector reconstruction and ((50) particles, this work serves a proof-of-coneept for the parameter efficiency of Quantum Rationales. Our experiments are limited to a narrow pr range (500-550 GeV) and exclude detector effocts/pilcup, which limits conclusions regarding real-world LHC performance. The use of only 10k training samples, necessitated by quantum um simulation costs, may disadvantar the larger classical benchmark models. Additionally, our current QRG architecture utilizes classical linear layer to project the 8-dimensional particle feature vectors onto single scalar for angle encoding. While this ensures parameter efficiency, it acts as an information bottleneck that may limit the quantum circuit's ability to leverage complex nonlinear correlations between the original raw features compared to full-width classical encoder. Future work could focus on reducing paramcter complexity to streamline model efficiency, exploring other satt-oo--theart encoder networks, such as LorentzNet (Gong et al., 2022) and Lorentz- EQNNNN (Jahin et al., 2025), and also hybridizing RG. We also plan to extend the model to other high-energy physics tasks, such as anomaly detection in particle collisions and event reconstruction. We look forward improving the explainability of GCL and exploring how retrospective and rospectiee learning in rationale discovery can guide discrimination tasks and improve the generalization of backbone models.
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A Details of Dataset and Preprocessing
A.1 Details of High-Energ. Physics Dataset
This study uses the Pythia8 Quark and Gluon Jets for Energy Flow (Komiske et al., 2019) dataset, a well- est established benchmark in high-energy physics for jet classification. The dataset comprises million simulated particle jets, evenly divided into 1 million quark-originated jets and 1 million gluon-originated jets. The dataset was gencrated using Pythia 8.220 with the default Monash 2013 tune. The hard-scatter processes simulated were ((=v²)) (u,d,s) for quark jets and Z(- vD)+ + for gluon jets, computed at leading order (LO). Hadronization was performed using the Lund string model. The quark jets consist exclusively of light quarks (u,d,s) and do not include heavy flavor (c.b) jets. No detector simulation or pileup interactions were included. These jets are generated through collision events simulating the Large Hadron Collider (LHC) conditions with a center-of-mant oa-sass energy V== 14 TeV. Jets were selected based on their transverse momentum range jet between 500 and 550 GeV and their pseudorapidity | 1.7. Each jet a is labeled as a quark jet (ya 1) or a gluon jet -0)= providing a binary classification target for model training.
Each particle i within a jet is characterized by several key attributes: transverse momentum pl.a: rapidity (4) , azimuthal angle da and its Particle Data Group (PDG) identifier (()) The particle mass ma is derived directly from the PDG identifier, allowing for the complete reconstruction of the 4-momentum vector used in subsequent feature engineering (Fq. 7). From these basic features, we derive additional physically motivated
quantities including particle masses (from PDG identifiers), transverse masses MT ma +PT energies
(1)2 (8)2
(t) E = coshya" and momentum components.
340
182
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123
Court
300
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30
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Kumeer Pettolonaat
300
509
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503
543
Pc (Gev)
1230
300c
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1343
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(b)
(c)
(d)
Figure 7: Aggregate kinematic distributions of the Pythia-generate dataset: (a) Particle multiplicity across all jets; (b) Transverse momentum (Pr.a): (c) Total momenta (p.);; and (d) Energy (E,). These distributions represent the combined quark and gluon populations before grooming and class-specific analysis.
A.1.1 Comparative Analysis of Quark and Gluon Jets
General kinematic distributions for the entire simulated dataset, including particle counts and energy ranges before class separation, visualized in Figure 7. To provide comprehensive understanding of the underlying class structure and the distinguishing features bet ween quark and gluon jets, we present detailed comparative analyses in Figures 1, 8, and 9.
Figure presents the four most discriminating features that clearly distinguish quark and gluon jets:
Particle Multiplicity (Fig. 1a): Gluon jets contain approximately 59% more particles on average than quark jets (Agluon = 53.2 vs. Mquark= = 33.4). This fundamental difference arises from the QCD color factors: gluons carry color charge of 8 (adjoint representation with CA=3) compared to quarks' charge 3 (fundamental representation with OF = 4/3). While the color factor ratio CA/Cr = 9/4 ~ 2.25 predicts that gluons radiate approximately 2.25 times more strongly than quarks, the observed 59% difference in this study is attributed to hadronization effects and the n,, = truncation (grooming) required for quantum simulation. This truncation specifically suppresses the soft radiation contributions that typically drive higher multiplicity in gluon jets.
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Jet Width (Fig. 1b): Gluon jets exhibit 46% larger spatial extent in the n-6 plane compared to quark jets (Mgluon 0.088 vs. Mquar= 00061). This increased width reflects the stronger coupling of gluons to the color field and their enhanced emission of soft, wide-angle radiation. The jet width is computed as w w= / momentum.
where the angular distances are weighted by particle transverse
Quark jets demonstrate significantly harder fragmentation, with the leading particle carrying 63% more of the lotal jet momentum on average than in gluon jets (Hquark -.2884 vs. Pyluon 0.1744. This reflects the fact that quarks tend to fragment into a dominant. hadron that preserves much of the original quark's momentum, while gluons distribute their energy more democratically among multiple softer particles through cascading radiation.
Leading Particle pr Fraction (Fig. 1c):
Jet Mass (Fig. 1d): Gluon jets have 40% larger invariant mass compared to quark jets (Fgluonn = 52.8 GeV vs. Mquark=31 377.6 GeV). This increased mass is consistent with their higher multiplicity and softer partiele spectra, as more particles with broader angular distribution contribute to larger invariant mass through m²= ======2 =2
Figure 8 provides a systematic overview of all twelve engincered features across both jet classes. Only the final 8 particle-level features are used as model inputs; the remaining variables are shown for completeness and comparison. Beyond the four key features discussed above, several additional discriminating characteristics are evident:
Particle pr Statistics: and softer spoctrum), while the standard deviation higher (indicating greater variation in particle energies). The leading particle pr shows clear separation, with quark jets having significantly higher values.
The mean particle pr is lower in gluon jets (reflecting their higher multiplicity
Fragmentation Patterns: The top-3 partiele pr fraction demonstrates that not only the leading particle, but the entire high-pr component is more prominent in quark This indicates fundamentally different fragmentation dynamics between the two parton types.
Energy Distributions: Mean particle energies show similar patterns pr distributions, with gluons having lower mean values but higher standard deviations. Total jet energy, constrained by the selection criteria jet E [500,550] GeV), shows relatively similar distributions but with gluons extending to slightly higher values due to their larger mass contributions.
All features demonstrate highly significant statistical differences between classes (Kolmogorov-Smirnoo test p< 10 10-11), confirming that the dataset contains rich discriminative structure across multiple complementary observables.
Figure 9 explores the multivariate structure of the feature space through two-dimensional projections. These visualizations reveal several important patterns:
1. Correlated Discrimination: Multiple feature pairs show clear class separation, indicating that the discriminative information is distributed across many complementary dimensions. For example, the multiplicity-width planc (Fig. 9a) shows that gluons consistently occupy the high-multiplicity, large-width quadrant, while quarks cluster in the low-multiplicity, narrow-jet region.
2. Physical Corrclations:
The strong correlation between jet width and mass (Fig. 9d) reflects the physical connection between spatial exlent and invariant mass, broader jets naturally have larger masses due to the geometric contribution to m². Similarly, multiplicity and mass are correlated (Fig. 9b) as more particles generally contribute to larger total mass.
3. Anti-correlatioss: The negative correlation between fragmentation hardness and jet width (Fig, 9c) demonstrates that jets with more concentrated energy (high leading Pr fraction) tend to be more collimated (narrow), consistent with the physical picture of hard fragmentation producing tightly- clustered particle showers.
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Multiplicity
jet Distribution
by Distribution
jet
0.00
p- C.
Olces
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Jet Multiplicity
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Standard Deviation
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Loading Particle Fraction
5.5
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Clora
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Energy Standard Deviation
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Clya
6.25
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Density
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0.000
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Figure 8: Comprehensive comparison of twelve features characterizing quark and gluon jets. Each panel shows normalized distributions (probability density) for both classos, with statistical significance indicated by Kolmogorox-Smirnov test p-values. Top row: fundamental jet properties including multiplicity, mass, transverse momentum, and spatial width. Middle row: particle-level pr characteristics showing mean, standard deviation, lcading particle value, and leading particle fraction. Bottom row: fragmentation and energy properties including top-3 particle fraction and energy distributions. All features show highly significant differences between classes 10-11), demonstrating the rich discrininative structure in the dataset. Quark jets (red) consistently show harder, more collimated fragmentation patterns, while gluon jets (teal) exhibit softer, more diffuse radiation.
4. Class Overlap:
While clear separation exists in feature space, there is non-trivial overlap between the classes, particularly in the intermediate regions of the parameter space. This overlap presents a genuine classification challenge and explains why sophisticated machine learning approaches are necessary to achieve optimal discrimination.
A.1.2 Statistical Significance and Effect Sizes
To quantify the discriminative power of each feature, we computed Cohen's d effect sizes and performed two-sample Kolmogorov-Smirno (KS) tests. Table 5 summarizes these statistics for all features. The results show that:
All features exhibit highly significant differences (KS test p < 10-100), far exceeding conventional significance thresholds.
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(a) Multpliccty Width
(b) plicity Mass
(c) Fragmennation Width
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Uuars Chaots
LuarS Claste
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Hewn Pacteee Ererryy (CWM))
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Noan Porticlo [GeV]
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Figure 9: Two-dimensional feature space projections revcaling class scparation patterns. Each panel shows scateer plots of 5,000 randomly sampled jets from each class. (a) Multiplicity vs. width shows clear separation with gluons occupying the nigh-multiplicty, warge-width region. (b) Multiplicity
mass demonstrates correlated increases in both quantities for gluons. (c) Fragmentation (leading pr fraction) vs. width shows anti-correlated behavior, with harder fragmentation (higher fraction) corresponding to narrower jets. (d) Width vs. mass shows strong positive correlation, particularly for gluons. (e) Mean pr vs. energy reveals the kinematic relationships between transverse and total energy. (f) Multiplicity vs. fragmentation shows clear class separation, with quarks clustering at high fragmentation fractions and low multiplicitics. The scatter patterns demonstrate that multivariate combinations of features provide improved discriminative power compared single features alone.
Particle multiplicity shows the largest effect size (d=1.89), indicating that this single feature provides strong discriminative power.
Multiple features demonstrate large effect sizes (ld) > 0.8), suggesting that optimal classifier should leverage the information from multiple complementary obscrvables.
The relative differences between classes range from 20% to 63%, with the most dramatic differences appearing in multiplicity (+59.4%) and lcading pr fraction (+63.2%).
A.2 Details of Graph Representation of Jets
A graph G is defined as set of nodes V and edges F,, represented as (V,F..). Fach node ( E VV connected to its neighboring nodes o(5) through edges eli)) E E. In the context of this study, each jet is modeled as a graph Ja, where the nodes vn represent the particles in the jet, and the edges ex represent the interactions between these particles. Each node
(t) is associated with a set of features 1(0) which describe its propertics, while the edges have attributes da that characterize the relationship between connected nodes.
(ij)
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Table Statistical comparison of quark and gluon jet features. Cohen's d measures effect size (standardized difference between mcans), with |d] > 0.8 indicating large effects. All features show highly significant differences
(0<10-110 Relative differences are computed as (HAgtoo (qunnk)
Mquark
Feature
Quarks (mean + std) Gluons (mean + std)
Relative Diff (%)
Cohen's
Multiplicity
10.4
53.2+12.8
+59.4
1.89
Jet pr [GeV]
14,
14.5
40.1
0.05
Jet Mass [GeV]
37.6
52.8+18.3
+40.4
0.98
Jet Width
0.001
0.089
+45.9
1.01
Mean Particle pr [Gev]
15.8+7.4
10.1
-36.1
-1.12
Leading Pr [GeV]
172.3189.4
92.4+41.8
-6.44
-1.28
Leading PT Fraction
0.284+0.134
0.174+0.074
-38.7
-1.11
Top-3 Pr Fraction
0.523=00168
0.365
30.2
-1.21
Total Jet Energy [GeV]
7
821.41171.3
182
0.40
The number of nodes each graph can vary significantly, reflecting the varying number of particles within each jet. This variability particularly pronounced in particle physics, where jets can differ greatly in their particle multiplicity. Consequently, each jet graph Ja is composed of ma particles, each with / distinct features that capture various physical properties. This graph representation provides a natural way to encode the complex interactions within jets, enabling models to leverage the relational structure among particles. An illustration of this graph-based data representation, along with an example jet depicted in the (d:y) plane, is shown in Figure 10. Here, particles are visualized as nodes and their interactions as edges, offering a clear view of the underlying structure and relationships within the jet.
Jet
4.4
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Transverse Momentum PT
4.3
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-1.3
-1.2
-1.1
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y
(6) Figure 10: Plot of sample jet shown in (6.)) plane with each particle color-coded by its Pr.a"
A.3 Details of Feature Engineering
Additional kinematic variables are derived from the original features (p)) Mo (606') using the 'Particle' package to improve the model's ability to learn from the data. These engineered features include transverse mass, energy, and Cartesian momentum components, providing a more complete description of each particle's dynamics. Specifically, the transverse mass per multiplicity (m of particle in jet a is calculated as:
(6)
(8)
(8)² (1)
m a.
ma +Par
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( where m is the rest mass of the particle and pr is its transverse momentum. Energy per multiplicity (Ea²) of particle i is computed using:
E =m m a
(0)
(8)
Kinematic momenta components per multiplicity (pa) (pr (8)
(p are derived from:
Pz.a = PT. coso (1)
p PT sino! (3) P/.0 - m T, sinhy,
(9)
These components decompose the momentum of cach particle into Cartesian coordinates, providing additional leatures for analysis.
The original and derived features are combined into an enriched feature for each particle, defined as:
1 = { .T D6 (1) Ta P (1)
E. 2.
(10)
where (0) represents the feature vector for particle i in jet a. We further calculate aggregate kinematic properties for each jet using the individual particle features. The total momentum vector of jet (Ha) is obtained by summing the momentum components of its constituent particles:
Po
(11)
with the Lransverse momentum um of the jet (pT,a) calculated as:
PFa
Eplo
Σ
10) Paia
+
Dplla
1c) Pijaa
(12)
which measures the momentum of the jet perpendicular to the beam axis. The jet mass (ma) and rapidity (ya) are defined as:
ma (E= 1 E. PPsa
(13)
E. -Pz.a
where E,, is the sum of the energies of the jet's constituent particles and Pz,a is the component of the jet's momentum along the beam axis.
A.4 Details of Graph-Based Based Augmentation and Contrastive Learning
Next, the preprocessed graph data creates pairs or 'views' as input for our CL framework. In CL, pairs of similar and dissimilar views are generated to help the model learn discriminative representations. Positive views are created by laking a graph and generating an augmented version of it, such as applying transformations like node dropping, edge perturbation, or feature masking. For instance, an augmented view of quark jet remains labeled as similar (1), while a dissimilar pair may consist of quark jet and gluon jet, labeled as 0. The differentiation between positive and negative pairs is established solely through the loss function, with the model lacking an inherent understanding of the concept of 'view.. The loss function guides the model toward clustering similar samples in proximity. Figure ?? shows positive and negative pairs created for our CL process. The distorting jets mothod was applied to shift the positions of the jet constituents independently, with shifts drawn from a normal distribution. The shift applied to each constituent's 's and Φ values, scaled by their pr, ensuring that lower pr particles experience more significant shifts. The collinear fill technique added collinear splittings to the jets, filling zero-pate paro-padded entries by splitting existing particles. A random proportion is applied for each selected particle to create two new particles that share the original momentum and position information.
A.4.1 Enforcing Infrared and Collinear Safety
To ensure that our methodology adheres to the principles of infrared and collinear (IRC) safety, we follow the guidelines established by Dillon et al. (Dillon et al., 2022) avoid sensitivities soft and collinear emissions, which are irrelevant to the physical properties of jets. Infrared safety is maintained by applying small
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perturbations to the n/ and o' of soft particles. These perturbations follow normal distributions, r// ~N( Awols pr and o' No Aoc)), where Asoft = 100 McV and pr is the transverse momentum of the jet. Collinear safety is ensured by requiring that the sum of the transverse momenta of two collinear particles equals the total transverse momentum of the jet: PT,a Pr,3 = Pr Additionally, the n and Φ of the two particles are kept identical, Le., 1/ - ?h = and Φo - Φb = Φ, preserving the collinear structure of the jet during training and testing. Techniques like node dropping and edge perturbation alter the graph's structure by randomly removing changing connections between nodes. This helps to train the model with varying graph structures, ensuring it can adapt to different particle distributions and topologies.
B Details of Proposed QRGCL
B.1 Details of Encoder Network
We used the ParticleNet (Qu & Gouskos, 2020) model our encoder to convert the augmented views of input particle features into low-dimensional embeddings. ParticleNet is graph-based neural network optimized for jet tagging, leveraging dynamic graph convolutional neural networks (DGCNN) to process unordered sets of particles, treating jets as particle clouds.
The input to the encoder is matrix X RRxd, where n represents the number of particles and d the feature dimension (e.g., momentum, energy). ParticleNet constructs k-nearest neighbor (k-NN) graph, connecting each particle to its & closest neighbors in feature space. The EdgeConv block begins by computing the l nearest. neighbors using the particles' spatial coordinates. Edge features are constructed based the feature vectors of these neighbors. The core operation of EdgeConv is 3-layer multi-layer perceptron (MLP), where each layer consists of a linear transformation, batch normalization, and a ReLU activation. To improve information flow and avoid vanishing gradients, a shortcut connection inspired by the general ResNet architecture runs parallel to the EdgeConv operation, allowing input features to bypass the convolution layers. The two main hyperparameters of each EdgeConv block are k the number of nearest neighbors, and C = (C), the number of units in each MLP layer.
ParticleNet's s architecture consists of three EdgeConv blocks. In the first block, distances between particles are computed in the pseudorapidity-azzine azimuth (n.0) plane. In the following blocks, learned feature vectors from the previons layers serve as the coordinates. The number of nearest neighbors & is 16 across all blocks. The channel configurations C are (64, 64, 64), (128, 128, 128), and (256, 256, 256), respectively, indicating the units per MLP layer. After the Edgeeonn blocks, global average pooling aggregates the learned features from all particles into a single vector. This vector is passed through a fully connected layer with 256 units and a ReLU activation. A dropout layer with a 0.1 probability is applied to prevent overfitting before the final fully connected layer. The output layer, with two units and softmax function, produces the jet-level embeddings. These embeddings are then weighted according to node importance scores, emphasizing the most relevant particles. A global mean pooling operation is used further to aggregate the weighted features into fixed-size jet representation.
B.2 Details of Quantum- Enhancced Contrastive Loss
QRGCL model uses a carefully designed loss function that integrates multiple clements: InfoNCE (van den Oord et al., 2018), aligument, uniformity, rationale-aware loss (RA loss), and contrastive pair loss (CP loss), to optimize the learning of quantum-ene enhanced embeddings. In this section, provide detailed derivations and theoretical interpretations for these components. The overall objective is designed to learn discrininative graph embeddings by contrasting different views derived from graph rationales and their complements, while ensuring desirable geometrii properties in the embedding space.
quantum-enhanced
B.2.1 Core Contrastive Losses: InfoNCE, RA, and CP
These losses form the foundation of the CL process QRGCI, aiming to distinguish between positive pairs (derived from similar rationales or views) and negative pairs (dissimilar rationales, complements, or other instances).
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InfoNCE Loss The InfoNCE loss (van den Oord al., 2018) serves general contrastive objective. In our context, it can be applied to augmented views of the entire graph or specific components. Tt maximizes a lower bound on the mutual information between two views, represented by their embeddings z and z'. For a batch of pairs, it is defined as:
exp(sim (z,z()/T)
LINIONCE E log
(14)
exp(sim(z,.z))
where (2,,2/) is positive pair of embeeddings (e.g., from two augmentations of the same graph), z are embeddings from other instances (negatives) in the batch, 7> 0 the temperature hyperparameter, and sim(::) denotes
the cosine similarity function sim(u.v) " T Minimizing LIaNNNEE encourages the embeddings of positive pairs to be more similar than the embeddings of negative pairs.
Derivation of InfoNCE Loss Let 3= be batch of N positive contrastive pairs. Assume that the joint distribution p(z,z') is known, and our goal is to maximize the mutual information Z(z,z'. Using the representation of KL divergence:
log f(z,2'
I(z,z) 2 Expza)))
(15)
E Ep (f
Choose f(z,z') =xpp(sm((,2)))) Replacing the denominator with negatives in the batch (empirical estimate), get the InfoNCE bound:
N
LInINNC = N
log
(16)
2,)(
This lower bounds the mutual information I(z,z') making it suitable for contrastive representation learning.
RA Loss The RA loss specifically focuses on contrasting positive pairs derived from the graph's 'rationale' (critical subgraph identified for classification) against other rationalo-derived pairs within the batch. Let z and zi be embeddings corresponding to two different views or augmentations of the rationale of the i-th graph in batch of size N. The RA loss aims to make zî similar to z while distinguishing it from z for j The loss is calculated as:
1
N log
(sim((((=))//T
CRA = N
(17)
(sim 2//7T) (=) 25//T))
1=1
Here, the denominator sums the similarity scores between the anchor rationale embedding z and all rationale embeddings zi from the second view the batch, excluding the positive pair similarity itself. This forces the model learn representations that are highly specific the corresponding rationale pairs.
Derivation of RA Loss We reinterpret the R.A loss as a softmax- based ranking loss. Let P(il)) denote the probability of matching rationale pair (i.j):
(sim(z) 2b)/T) P(())= =
(18)
e (
To ensure the model doesn't trivially match a pair to itself, we subtract the matching term from the denominator:
(slm(())
CRA = -log-Poo((11)) -log
(19)
Σ ビj=1 (sim x ( (sitm(z
This form can be derived from maximizing modified log likelihood over rationale-based matching while excluding the anchor-positive redundancy from the normalization.
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CP Loss The CP loss introduces the concept of "complement' view (pairs involving nodes not deemed crucial for the classification task), derived from the non-rationale parts of the graph. It encourages the rationale embedding z to be similar to its corresponding rationale pair z)2 while simultaneously being dissimilar to embeddings derived from the complement regions, denoted by z.z. This helps the model distinguish between critical (ralionale) and non-critical (complement) information:
1 N
NV log
(0)m(()))))/1 و== ( 25)/T) ( 25/TT)
Cer
(20)
N
where the denominator includes the sum of similarities between the anchor rationale z and all complement embeddings z from the third view, plus the positive pair similarity. This loss helps the model differentiate genuine relationships between similar samples from spurious correlations by learning from pairs with varying significance.
Theorem 1 (Interpretation of RA and CP Losses). Minimizing the combined loss CRA + ACPP encourages the model to learn representations z such that:
Embeddings zi and 2 derived from the same rationale are pulled closer together in the embedding space.
2. Embeddings 2 derived from one ralionale are pushed uport from embeddings zi (for jti) derived from other rationales.
3. Embeddings z derived from rationale are pushed apart from embeddings ziz derived from complement regions.
This promotes learning of features that are both specific to the rationale's identity and distinct from non-critical graph components.
Proof Sketch. The structure of CRA equation 17 and LCP equation 20 follows the standard contrastive loss positive
form -log( positive-> negatives ). Minimizing this loss is equivalent to maximizing the log- probability of correctly
identifying the positive pair among set of negatives. For CRA, the 'negatives' are other rationale pairs within the batch (z)-}+i) i). Minimization increases sim(zi zz) ..25) relative to sim (enzz),ez) (z)), thus pulling positive rationale pairs together and pushing them apart from other rationale pairs. For C the 'negatives' are the complement embeddings (zz). Minimization increases sim (z}{z}) relative to sim (2),2))) thus pushing rationale embeddings away from complement embeddings. Combining these objectives achieves the stated properties.
B.2.2 Geometric Regularization Losses: Alignment and Uniformity
These losses, inspired by (Wang & Isola, 2020), aim to improve the quality of the embedding space by enforcing desirable geometric properties, preventing representation ional collapse, and improving feature diversity.
Alignment Loss The alignment loss measures the expected distance between normalized embeddings of positive pairs (Ppos), encouraging them to map to nearby points in the embedding space. Assuming the input embeddings 2 and 22 are Lg-oormalized (denoted 21 .22), the alignment loss is defined as the expected squared Euclidean distance 2L?)::
Lalign EE (2) [||2] 2
(21)
where Ppos is the distribution of positive pairs and normalization ensures embeddings lie on the unit hypersphere. Minimizing this loss forces the representations of augmented views of the same input to be identical, promoting invariance.
Quantum Fidelity Alignment (Theoretical) As thcoretical alternative motivated by quantum informa- tion, we used quantum state fidelity distance metric, replacing the traditional I,2 distance typically used
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in classical CL. Quantum fidelity measures the closeness between two quantum states. If embeddings 21. represent quantum states via density matrices 01,/2, the fidelity-based alignment loss is:
Lalign (pp [1- F F(PL)P2)) -2)0 B ~ 1- (T (VVVIioVVVV))
(22)
where P2) is the fidelity between states pi and P2- Lower values of 1 1-F indicate higher similarity between quantum states. If 1p: (o:l are pure states derived from normalized vectors Zi, then F(P1,P2) = = (0)) Therefore, alignment loss bocomes:
Lalign B (e [1 ( [
(23)
This aligns the quantum embeddings up global phase, a desirable property in quantum feature spaces.
Uniformity Loss The uniformity loss encourages the embeddings to be uniformly distributed on the unit hypersphere. This prevents the model from collapsing all embeddings to single point or small region, thereby preserving the discriminative information contained in the representations. It is defined as the expected log pairwise potential over all distinct data points:
Lumiform logB (2)aatt e l2.
(24)
where Pdata is the distribution of data samples, and t> 0 is hyperparameter (typically 2= Minimizing this loss encourages larger distances between embeddings of different samples, promoting uniformity.
Theorem 2 (Rolc of Aligument and Uniformity). Minimizing the combined loss aL + Bnuiforr regularizes the embedding space by:
Enforcing invorionce to data augmentations or view generation (Aligroment.
Mazimizing the entropy of the embbedding distribution on the wnit. lyperssphere, preserving feature diversity (Uniformity).
These properties contribute to learning higher quality, more discriminative representations.
Proof Skelch. Minimizing Lalign equation 21 directly minimizes the distance between positive pains, achieving local invariance. Minimizing Luniform equation 24 minimizes the potential energy of a system where points repel each other via a Gaussian kernel e -dd leading to a uniform distribution on the embedding manifold (unit hypersphere if normalized) (Wang & Isola, 2020). Uniformity related to maximizing the entropy the representations, thus preserving information from the input data.
B.2.3 Overall QRGCL Objective
The overall loss for the QRGCL model is weighted combination of the InfoNCE, R.A, and CP loss, with optional contributions from the alignment and uniformity terms, allowing for flexible control over the learning process:
LQRACT= = CRa + XLCP CaLlig + +3 Luniform +6LNGN
(25)
where A,,,3,8000 are hyperparameters balancing the contribution of each loss component. During experimenta- tion, the uniformity term (3Lmiffor)) might be omitted (3= if it hinders performance empirically.
Remark 1. Each component has a bounded gradient and differentiable form, ensuring compatibility with stochastic gradient descent. Further, RA and CP are mutually reinforcing, and the inchusion of alignment and uniformily ensures geomelric and muantum-consislers embeddings.
B.3 Details of Quantum Feature Encoders
To evaluate the impact of different quantum feature maps on the performance of the QRG, we benchmarked several encoding strategies.
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B.3.1 Angle Encoding (RX, RY, RZ, H)
Augle encoding embeds N classical features (...,, into the rotation angles of N qubits, maintaining a parameter-efficiett 1:1 correspondence between features and qubits. In the standard Rotation Encoding variants (RX, RY, RZ), the feature x; serves the rotation parameter for Pauli rotation gate acting on the i-th qubit. For instance, the Rx encoding prepares the state ( = X 1 Rx (zx))0) = e
exp - 20) (2) To increase the expressivity of this feature map, the H + Angle variant first places the qubits in a uniform superposition using Hadamard (If) gates before applying the rotations, resulting in the state (e) - Rx (xx)
B.3.2 IQP Encoding
The Instantaneous Quantum Polynomial (IQP) encoding embeds features into a quantum state conjectured to be hard to simulate classically. This strategy diagonalizes the encoding in the Z-basis using Hadamard gates and specific interactions. The circuit structure consists of an initial layer of Hadamard gates, followed by a layer of diagonal phase gates that encode the features, and final entangling layer. Mathematically, for feature vector the encoding unitary is defined as UTQp(z) (Ilene o (8 ( 1 H, where S' represents the set of entangled qubit pairs. In our experiments, we utilized a standard repetition pattern (Bropeats 1) to embed the correlations between features.
B.3.3 Amplitude Encoding
Amplitude encoding is a space-efficient strategy that embeds a normalized classical vector x of dimension 2 into the probability amplitudes of an N-qubit entangled state. Given a normalized input vector such that 1|, the state is prepared as | method theoretically allows for the encoding of exponentially many features into 7 qubits (up to 128 features), it generally requires state preparation circuits that can scale exponentially in depth without specific optimization. We restricted the input to the graph node features for this study.
2 - zzli),, where li) are the computational basis states. While this
B.3.4 Displacement Encoding
Originally derived from Continuous Variable (CV) quantum computing, Displacement encoding maps classical features to the phase space displacement of a quantum mode via the operator D(a)= -a* In the context of our variational circuit, we implemented two variants this embedding: Displacement-Amplite where the feature z; is mapped to the magnitude of the displacement (a=x;,, and Displacement-Plase where the feature determines the phase (.)) This encoding provides distinct non-linear feature map compared to standard qubit rotations, allowing us to test the model's sensitivity to phase-space geometric embeddings.
C Details of Benchmark Models
We developed two classical models (GNN and EGNN), three quantum models (QGNN, EQGNN, and QCL), five hybrid classical-quantum models (CQCL, QCGCL variants, and QRGCL with RX encoding) (see Table 1), and the classical counterpart of QRGCL, i.c., CRGCL (see Table 2). This section provides comprehensive architectural specifications and training configurations for each benchmark, ensuring reproducibility.
C.1
Classical RGCL (CRGCL)
C.1.1
Architecture
The classical RG (CRG) of RGCL is a GNN estimator designed to generate node reprosentations from graph- structured data, which acts as the counterpart of QRGCL. It consists of three graph attention network (GAT) layers with the following configuration: Layer 1 (input + 32 features, 4 attention heads), Layer (32 - features, 2 heads), and Layer (16 + features, head). Each layer is followed by batch normalization (momentum 0.1) to stabilize training and reduce internal covariate shifts. ReLU activation applied after the first two layers, while dropout (p 0.1) is used to mitigate overfitting. The final output passes through
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linear layer to yield single value per node, followed by softmax for probabilistic node importance scoring. For fair comparison between the CRG and QRG, we use the well-established ParticleNet as the encoder network, followed by the same projection head used in QRGCL.
C.1.2 Training Configuration
CRGCL employs a combined loss function: LERGCI. = LRA + XCCP + a + -.. + &LINNNNC with hyperparameters x= 1.0, 0.5., 0=0. (uniformity term disabled), 0.5,5, and temperature 0.1 for all contrastive components. We use the Adam optimizer with lcarning rate 1 x 10-3, 31 = 0.9, 82 = 0.999, and c=10 with no weight decay. Training follows a two-stage procedure: (i) self-supervised pre-training for 50 epochs with batch size 2000 and gradient clipping (max norm 1.0), and (ii) supervised fine-tuning for 1000 epochs with frozen encoder parameters using BCE loss. Data augmentation includes node dropping (0.1), edge perturbation (0.05), and feature masking (0.1) with augmentation ratio of 0.1.
C.2
GNN
C.2.1 Architecture
The bascline GNN architecture consists of 5 EdgeConv blocks with k=16 nearest neighbors per block. The architecture processes input features through: EdgeConv Block 1 (channels= (22,,, EdgeConv Block ([64,64,64)); EdgeConv Block 3 (664,64,64)), EdgeConv Block ([64,644664)), and EdgeConv Block (110,10100), Each block contains 3-layer MLP with Narch and ReLU activation, followed by max pooling opera vionation over neighboring elements. The message- message-passing mechanism updates node features based neighboring nodes using edge features constructed as Afú f -- - fi. Residual connections are applied around each block. After all EdgeConv layers, global mean pooling aggregates node features into a graph-level representation, which is passed through a linear layer (110 + 2)) with softmax for classification. GNNs can inherently handle node permutations due to their graph- graph-based based nature.
C.2.2 Training Configuration
where a is the sigmoid function. We employ Adam optimizer with learning rate x 10 and ReduceL scheduler (factor=0.5, patience=5, min 1r=1 x 10-9). Training runs for epochs with a batch size of 64, using gradient clipping and early stopping (paticnce of epochs on the validation loss). The dropout rate is 0.1 after each EdgeConv block. No data augmentation is applied (supervised baseline).
GNN is trained using BCE loss: -p-
C.3 Equivariant GNN (EGNN)
C.3.1 Architecture
EGNNs extend GNNs by incorporating SE(3) equivariance, ensuring predictions remain invariant to rotations
and translations. The architecture consists of 4 EGNN layers with hidden dimensions [32, 64, 64, 10] and edge dimensions fixed at 32. Each layer updates both node features h; and coordinates 2; E R through: (i) edge features m (h(, -11 (ag)), (ii) coordinate updates x; [+1 - (2: (z--2;) (mij), and (iii)
node fcature updates 1 &r (K!,m.) where m; m, mij- Each & is 2-layer MLP with SILU activation and layer normalization. Initial coordinates are derived from kinematic features: r= cosy (Ø), y (Ø),
z prsinh(n)) After all layers, global mean pooling over node features produces the graph representation, which is processed through an MLP readout ([10 + 32 + 2]).
C.3.2 Training Configuration
EGNN uses BCE loss with Adam optimizer (learning rale x 10-33 weight decay 1 10-9). The learning rate follows CosineAnnealingLR schedule (19 7min =1 x 10 10-6) 6) with 3-epoch linear warm-up from 1 10-5 to x 10-3 Training runs for 19 epochs with batch size of and gradient clipping (max norm: 1.0). Layer normalization applied instead of batch normalization to preserve equivariance properties. Coordinate clipping at + 10.0 prevents explosion. No dropout is used to maintain equivariance.
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C.4 Quantum GNN (QGNN)
C.4.1 Architecture
In QGNN, the graph's 's node features are first processed through a classical MLP encoder ((8 + 16 + 8) with ReLU and BatchNorm, followed by a linear projection ([8 + na]) to map features to qubit count. These features are embedded into quantum states using a parameterized quantum circuit with no 3 qubits and variational layers. The quantum circuit structure per layer consists of: (i) Hadamard gates H (ii) RY rotation encoding with 0, = =a)tan(a)), (iii) parameterized U3 gales on each qubit with 3 parameters (a,33,7), and (iv) CNOT ladder entanglement with wrap-around connection. These quantum states evolve under the parameterized Hamiltonian, which encodes node interactions based on the graph's 'ss adjacency matrix. The QGNN model utilizes unitary transformations to evolve the quantum state across multiple layers. After the final layer, quantum measurements are performed in the Z-basis, producing a 2 = 8 dimensional classical vector. The results are passed through an MLP classifier ([8 - 16 + 2]) with ReLU and Dropout (0.1) to make predictions. Total parameters: 5,156 (54 quantum + 5,102 classical).
C.4.2 Training Configuration
QGNN is trained using BCE loss with Adam optimizer (learning rate x 10 no weight decay). Quantum circuit simulation uses PennyLane's 's default qubit device with statevector simulation (no shots) and parameter-sil rule for differentiation. Due to quantum circuit overhead, the batch size is with gradient accumulation over steps (effective batch size 64). Training runs for 19 epochs with gradient clipping (max norm 0.5) prevent. barren plateaus. Quantum parameters Xavier initialization. Layer-wise learning rates are applicd: first 2 quantum layers at 5 10-A, last 4 at 1 x 10-3 classical layers at xx 10-3, Gaussian parameter noise (a (001)) is added during training for robustness.
initialized uniformly in [-T/4,m /4], while classical parameters use
C.5
Equivariant Quantum GNN (EQGNN)
C.5.1 Architecture
EQGNNs (Jahin et al., 2025; Forestano et al., 2024; 2023a;b;e) are quantum analogs of EGNNs, incorporating equivariance into the quantum architecture. The model begins with an equivariant classical encoder: Equivariant MLP Layer 1 (8++3 > 16)) and Layer 2 ([16 16)), both with Layer Norm and SiLU act Node features h R and coordinates 2; TR3 are jointly processed. Permutation-invarinnt pooling (DeepSets style) produces fixed-size feature vector projected to na values. Like QGNNs, EQGNNs operate on quantum states (3 qubits, layers, same circuit structure as QGNN) but ensure that the learned representations are equivariant under symmetries, such permutations rotations. The final quantum states are aggregated through pooling, ensuring the network remains permutation-eqquivaiiatt This aggregation is followed by classical post-processing to yield the model's predictions. The model ensures: (i) permutation equivariance in classical encoding, (ii) graph isomorphism invariance in quantum embedding, and (iii) permutation invariance in final pooling. Total parameters: 5,140 (54 quantum + 5,086 classical).
C.5.2 Training Configuration
EQGNN uses BCE loss with Adam optimizer (learning rate 1 x 10-3, weight decay 1 x 10-5). The learning rate follows the StepLR schedule (step size=5, gamma-0.5). Training runs for 19 epochs with batch size and gradient accumulation over 64 steps. Gradient clipping is set to max norm 0.5. During training, periodic oquivariance checks ensure PP for permutation P. Layer normalization is used instead of batch normalization to preserve equivariance, and no dropout applied in equivariant layers. Coordinate noise augmentation with a = 0.01 is applied.
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C.6
QCL
C.6.1 Architecture
QCL employs& a quantum convolutional neural network (QCNN) with imput size 18 x 18 (zero-padded from variable jet size) as the encoder, where lata-rouplogding circuits (DRCs) replace classical convolutional kernels. The QCNN consists of 2 quantum convolutional layers: Layer with (3x3) kernel and stride using 3-qubit DRC as filter, producing an 8x8x4 feature map; Layer 2 with the same configuration, producing a x x 4 feature map. Each DRC filter contains 3 qubits with 3 layers, where each layer includes: (i) feature encoding via (Y(aa)))); (ii) trainable rotation (f (parmm), and (iii) CNOT chain entanglement. Each filter has 18 parameters (3 qubits x 3 layers x 2 rolations). The final encoding size after flattening is 36 features, which are linearly projected to 16 dimensions. The projection network uses a 2-node linear layer ([16 + 2)). Total parameters: 280 (36 quantum + 244 classical).
C.6.2 Training Configuration
exp(sim((,=+4/r)) where sim(.,) is cosine similarity and 0.1 (temperature). Positive pairs are the same jet with different augmentations, while negative pairs are different jets. Adam optimizer with learning rate 1 100 (no scheduler, weight decay) is used. Training follows two-stage procedure: pre-training for 1,000 epochs and fine-tuning for 500 epochs, with batch size of 256 and augmented views per sample. Data augmentation includes random crop (16 16 from 18x x 18), random rotation (=15)), Gaussian noise (a= 0.05), and intensity scaling (#10% Gradient clipping is set to a maximum norm of 1.0. Quantum circuits employ shot-based simulation (with 1024 shots) and parameter-shif differentiation. Quantum parameters are initialized uniformly in [-T,a], with parameter sharing across filters for efficiency.
QCL uses InfoNCE contrastive loss: LoCL= = -log(exp(sim((222))))
C.7 Classical- Quantum CL (CQCL)
C.7.1 Architecture
Hybrid CQCL uses a fully classical CNN encoder with a quantum projection head. The classical encoder consists of: Conv2D Layer 1 (1 - 16 channels, 3x3 kernel, stride 2) with BatchNorm and ReLU, followed by Conv2D Layer 2 (16 + 32 channels, same configuration). After flattening x32x4x4=35 412 features), a linear layer projects to 256 dimensions with RcLU and Dropout (0.1). The quantum projection head utilizes amplitude encoding to embed the normalized 756-dimensional vector into qubits (logg(256) = 8). The variational circuit consists of three layers, each with RY and RZ rotations applied to all qubits, followed by linear CNOT entanglement (16 parameters per layer, totaling 48 parameters). Measurements are performed in the Z-basis on all qubits, producing an 8-dimensional output, which is finally projected to 2 dimensions. To evaluate the ability of QCL and CQCL to generate generalized representations, we make predictions using a simple ML. with an input layer of size 256 and a hidden layer of size 32, both with Batch Normalization and Icaky ReLU. Total parameters: 250 (48 quantun + 202 classical).
C.7.2 Training Configuration
CQCL employs Supervised InfoNCE loss: Looor= - -o,o.,=-\llol exxp (r/ssti(/saa////Eeeexeiiii
where P(i) includes all samples with the same label as i. Adam optimizer separate learning rates: 1x 10-3 for classical layers and 5 x 10-4 for quantum layers, with weight decay 1 x 10-4, Training consists of 1000 pre-training epochs (batch size 256) and 500 fine-tuning epochs (batch size 128). Data augmentation includes all QCL augmentations plus Mixup (a = 0.2, classical features only) and CutOut (4 x 4 patches). Mixed- precision training is used: FP16 for classical, and FP32 for quantum. The quantum-clasee claassscaa interface requires normalization Znorm 2/|||=|| for amplitude encoding, with hybrid optimization using alternating updates (5 classical steps: 1 quantum step).
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C.8
Quantum-Classical GCL (QCGCL)
C.8.1 Architecture
QCGCL architecture initially uses 6 GAT convolutional layers to capture graph features with the following configuration: GAT Layer 1 ((8 - 32), 4 heads, concat), Layer 2 ([128 + 64], 4 heads, concat), Layer ([256 64), heads, concat), Layer (128 32), 2 heads, concat), Layer (664 - 32]. head), and Layer 6 ([32 - 16], head). Each GAT layer is followed by batch normalization ReLU activation, and dropout (0.1). Residual connections are applied around each layer for improved training. The graph-level embeddiig is achieved through concatenated mean and max pooling, producing a 32-dimensional representation. A quantum circuit then processes this pooled GNN output. We benchmarked QCGCL using 3 different quantum encodors, as depicted in Table I: (i) Variant. 1 (RY+RX): qubits with encoding (0) - - RY (7:))) (xxx), 6 variat layers with (a) + (3) and circular CNOT entanglement (84 parameters); (ii) Variant 2 (RY): same structure but only RY rotations (42 parameters); (iii) Variant 3 RAmplitude++RRY: amplitude encoding followed by RY-based variational circuit (42 parameters). The classical embedding (32-d) and quantum embedding (7-d) are concatenated to form 39-dimensional fused representation, which is processed through an MT.P ((39 - 64 + 32 + 2]) with ReLU and Dropout (0.1), followed by softmax for final prediction. Total parameters: 7,448 (varies by quantum encoding).
C.8.2 Training Configuration
QCGCL uses combined loss function: LQCGCl AACiCE with Å 0.5 (contrastive weight) and 0.5 (classification weight), where InfoNCE uses temperature 0.1.1. AdamW optimizer is employed with learning rate x 10-3, weight decay 1 10-1, and Cosine Annaaing Restarts scheduler (7-110 epochs, 2, Mmii = 1 x 11100-9 10-6). 6). Training runs for 50 epochs with batch size 128, a 5-epoch warm-up, and gradient clipping (max norm: 1.0). Data augmentation includes node dropping (0.1), edge perturbation (0.05), feature masking (0.1), and graph mixup (a = 0.2). multi-view contrastive strategy uses views (two classical augmented one quantum-enhanced), with hard negative mining enabled (top 20% hardest. negatives). Regularization includes dropout (0.1) in all layers, batch normalization after each GAT layer, attention dropout (0.1), and quantum parameter noise (a 0.01). Quantum circuits utilize statevector simulation with parameter-sii differentiation and gate count optimization prior to execution.
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Reviews:
[{"review_id": "c1ZyH39hxN", "reviewer": "Reviewer_u2gV", "summary": "", "questions": "", "limitations": "", "rating": null, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "No", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "paper_topic_and_main_contributions": "", "excitement": null, "reproducibility": null, "ethical_concerns": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "summary_of_contributions": "The paper introduces Quantum Rationale-Aware Graph Contrastive Learning (QRGCL), a hybrid quantum–classical method for quark–gluon jet discrimination. It embeds a parameterised quantum circuit as a rationale generator into a graph contrastive learning pipeline, identifying salient jet constituents and guiding augmentations. Experiments on simulated jets show AUC improvements (~77.5%) over classical and hybrid baselines, using just 45 quantum parameters.\n\nStrengths:\n- Innovative integration of quantum rationale selection with contrastive learning.\n- Methodological focus on parameter efficiency and hybrid quantum–classical frameworks.\n\nWeaknesses:\n- Simplified dataset (7 jets’ constituents) limits generality.\n- Comparison versus classical rationale generator exists (Table 2) but requires clearer explanation and justification.\n- Presentation of figures, tables, and experimental setup lacks clarity.\n- The paper doesn’t clearly position itself relative to strong classical architectures. \n\nPerformance Context: \\\nQRGCL achieves ~77.5% AUC with 45 parameters, but advanced classical taggers like ParticleNet or transformer-based models like ParT  [JHEP 07 (2022) 030] can exceed 90% AUC. The paper’s contribution is rather methodological - focused on parameter-efficient hybrid learning - and should explicitly highlight this, rather than implying competitive jet-tagging performance. Or at least the authors should emphasise that, within certain constraints that should be clarified, this network developed in this work outperforms others.", "claims_and_evidence_yn": "No", "claims_explanation": "While consistent, the evidence should be strengthened implementing the following comments:\n- The choice of alternative algorithms should be better motivated and it is not clear if they hyperparameters settings used for those is optimal providing a fair comparison \n- The modelling of QRGCL’s performance should be framed as evidence of parameter efficiency and modular design, not as a direct comparison to top taggers.\n- The simplified 7-particle graph with a N = 12,500 jets dataset is understandable given resource constraints, but this limitation must be acknowledged, and ideally supplemented with additional samples or runs to provide uncertainty estimates.", "audience_yn": "Yes", "audience_explanation": "The methodology based on a hybrid quantum-classical contrastive learning with rationale guidance is compelling to researchers in graph-based semi-supervised learning and quantum machine learning. However, stronger experimental clarity and proper framing are essential.", "requested_changes": "The following changes would greatly improve the clarity and impact of the work:\n-  Clearly state that QRGCL is a methodological proof-of-concept aimed at parameter-efficient hybrid architectures—not a new state-of-the-art tagger. \n- Motivate the choice of the other networks used in the performance comparison. \n- Reference top jet tagger networks like ParT to contextualise performance. \n- Discuss dataset limitations and consider adding runs or samples for uncertainty estimation.  \n - Provide training and inference time metrics and compare them with classical alternatives to highlight the practical advantage of the quantum component.\n- Descrive, or show if possible, the correlation between rationales selected by the QRG and physical variables to verify whether the model captures meaningful jet substructures\n- All figures and tables should be referenced in the text and the captions should be more descriptive\n\nMore punctual comments can be found below:\nSection 2: \n- Define AUC here not later in section 5; \n- Figure 1 should be moved later as it is just introduced In page 6 and should be better described\n\nSection 3:\n- “Each particle “i” within a jet…” is the mass provided as an additional input? Otherwise one cannot obtain the full 4-momentum (m is needed also in Eq7)\n- Figure 2 is not highlighing the difference between quark and gluon jets as stated in the text in p4. I suggest to plot a comparison of n particles (describing which particles are considered, e.g. if also neutrinos), pT, eta, phi of the quark- vs gluon-initiated jets.\n- In the text you should refer to Figure 3 (not 3a)\n- Figure 3b is cut on the left and should be better described in the caption explaining what the 4 graphs represent.\n- Specify that the O(2^n) complexity refers to classical simulation.\n- I find the sentence “Next, node feature vectors are encoded using…using RX, RY, or RZ gates.” unclear and I suggest a rephrasing.\n- Figure 4 please improve the caption describing the several symbols in the figure\n- Eq 5: The notation for gate parameters could be improved to avoid ambiguity. Currently, the same symbol (θ) is used for both U3 parameters and for rotation angles in RX, RY, and RZ gates, which may confuse readers. We recommend using distinct symbols for U3 (e.g., U3(α, β, γ)) and reserving θ for single-axis rotations. This would make the decomposition steps and parameter mapping more transparent and easier to follow.\n- Projection Head: It would be helpful to elaborate on how mutual information is enforced between the anchor and rationale representations. This could be achieved through a specific loss function or an implicit architectural design. Alternatively, why not reduce the dimension instead of keeping the latent space dimensionality equal to the encoder output?\n- Benchmark 3.3 A brief description of the models would be helpful, especially in the main body of the document. This would make the reading easier and provide a reference for each architecture. A more detailed description could be included in the appendix.\n- Additionally, it would be beneficial to explain why these specific baseline architectures were chosen. For instance, why not include a transformer or other recent models? A brief justification would help readers understand the scope and fairness of the comparison.\n\nSection 4\n- Table 1-4 please round the % at most at the first digit to make them more readable. With same font size of the rest of the text (you could consider to  rotate them by 90deg)\n- Table 2-3 look slightly flattened\n- \"Bold indicates\" -> bolded values indicate\n- the reference to Table 1 is missing \n- Table 1: The several “Encoder types” shown in Table 1 are not described in the main text. Adding a brief description of each encoder and the corresponding tests performed to obtain the reported results would significantly improve clarity. This could be done either in the main body or by adding explicit references to the appendix where detailed explanations are provided.\n- Table 1: add the default parameters in the caption\n- Table 2: The observed performance drop when increasing the number of nodes might be due to the limited size of the statistical sample rather than an inherent limitation of the method. It would be helpful to clarify whether experiments with larger datasets were attempted or planned, as this could confirm if the trend persists under higher statistics.\n- Table 2: If I interpret it correctly, the table reports the augmentation ratio, which refers to augmentation strength (i.e., the fraction of nodes/edges perturbed), not a factor by which the dataset size increases. Please include a test with an almost-zero augmentation ratio to show that performance drops when augmentation is too weak. Otherwise, the results may imply that less augmentation is always better, rather than that there is an optimal range.\n- Table 2: Sort the learning rate in increasing order\n- Table 3: While table 2 isolates the impact of the rationale generator (classical vs quantum), here other benchmarks combine multiple factors such as encoder architecture, augmentation strategy, and loss design. An explicit statement in the main text clarifying this distinction would improve interpretability and the classical vs quantum tests should be highlighted (separated with a line) from the other cases where the architecture is varied.\n- Table 3:  seems to use different configurations (encoder, loss, augmentation) than Table 2, since I cannot find the same performance values. Is there a reason for that? I suggest to use a coherent setup.\n- Table 3: Please also add the CRGCL performance for completeness\n- Table 4: I don’t understand/appreciate what Table 4 provides compared to Table 3. It seems to me that it only reports alternative architectures with different hyperparameters and generally worse performance. Please clarify its purpose in the main text (e.g., is it meant to show robustness or limitations?). Otherwise, the distinction between Tables 3 and 4 is confusing\n- The hidden feature size for the GNN is set to 10. Please clarify why this specific value was chosen and whether sensitivity to this hyperparameter was tested.\n- \"(i) self-supervised…, contrastive, defined as L = …\"\n- \"(Encoder is frozen)\" -> is jargon. Maybe “During fine-tuning, the encoder parameters are kept fixed” \n\nSection 5\n- The beginning of Section 5 looks redundant with Section 3.3. Rephrase referring to that section for further details (that I suggested to add in a previous comment).\n- Why haven’t you stopped the training at 500 epochs to avoid overtraining?\n- “it is evident that our proposed QRGCL model achieves the highest AUC score (77.53%)” -> in the previous sentence you mentioned 78.78% with the best setup. Why not using this setup as a benchmark? \n- \"possesses\" -> contains\n- \"Figure 5a shows that … Around 800 epochs, both accuracies stabilize.\" -> you mention twice the overtraining beyond 800 epochs. The second part of this extracted text is redundant\n- Figure 5b is not referenced in the text and would benefit the QRGCL to be highlighted", "broader_impact_concerns": "No ethical or societal issues; the work is domain-specific and methodological.", "additional_comments": "", "extra_scores": {}, "extra_text": {}}, {"review_id": "lkN7zhvVuH", "reviewer": "Reviewer_TXCv", "summary": "", "questions": "", "limitations": "", "rating": null, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "No", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "paper_topic_and_main_contributions": "", "excitement": null, "reproducibility": null, "ethical_concerns": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "summary_of_contributions": "The paper implements a parameterised quantum circuit as the rationale-generator (QRG) within an existing rationale-aware self-supervised graph contrastive learning (RGCL) framework. The goal of RGCL is to learn semantically meaningful representations that can be utilised in downstream tasks. The primary motivations for the quantum circuit are (relatedly) the expressivity of the qubit representation and associated circuit, computational efficiency when run on a quantum computer, and small number of learnable parameters that in-principle promote data efficiency. They apply QRGCL to an existing dataset of simulated quark and gluon initiated jets in LHC-like experiments, using the existing ParticleNet model as the encoder, and test the learned representations in the downstream task of classifying jets as quark or gluon type. They compare performance against various classical/quantum benchmark models, focussing on AUROC but also quoting the marginal accuracy and F1 scores.", "claims_and_evidence_yn": "No", "claims_explanation": "I have three concerns. The first is the clarity of the claims. The second is the degree to which the claims of significantly improved performance are justified by (i) the extent of the experiments, and (ii) how we interpret the results of those experiments. The third is the completeness and clarity of information provided, necessary for the reader to fully understand and reproduce the work.\n\nRegarding claim justifications:\n\n- Abstract: “QRGCL significantly enhances jet discrimination performance… achieving an AUC score of 77.53%, outperforming… benchmarks.” Introduction: “Experimental results on the quark-gluon jet tagging dataset showcase the superiority of our approach… significantly outperforming current state-of-the-art GCL and GNN methods”\n  - Supporting evidence: AUROC in Table 3 and Fig 5(b) is 77.53 +- 0.88% for best QRGCL method. The best non-QRGCL method is 74.36 +- 1.78% (EQGNN). Assuming Gaussian, this is a delta of 3.17 points relative to an uncertainty of between 0.9(corr) and 2.0(uncorr) and 2.7(anticorr), depending on the degree of correlation. \n  - Concern: I don’t think this can be interpreted as significant outperformance. Firstly, the uncorrelated case is only about 1.6sigma significance. Furthermore, AUROC is only one metric, and Table 3 shows several benchmark models outperform QRGCL in marginal accuracy and F1 score. This is consistent with Fig 5(b), which shows them outperforming QRGCL for tight thresholds (bottom left), whereas QRGCL tends to dominate at weaker thresholds (upper right). The classical RG method seems to perform quite comparably in Table 2 (best AUC only 2.5% different). Finally, insufficient details are provided for the benchmarks to understand whether they are well trained.\n  - Concern: the experiments are performed in a limited setting. They consider a narrow pT band of 500-550GeV, without experimental effects, pileup, or systematic uncertainties. There is no analysis of how performance depends on jet kinematics, which are related to the simulated hard scatter process(es), which is not described (from the reference I see that they are Z(->vv)+q/g). Improved performance in realistic or diverse scenarios is therefore not proven.\n  - Concern: it appears that QRGCL has more hyper parameter tuning than the benchmarks. Furthermore, S3.1.7 states that only 10k jets are used for training, which seems small. Are the benchmark models also trained on such a small number? If so, I worry that they are not set up for success.\n  - Conclusion: I would be content with a conclusion of “competitive performance”, more recognition of the experimental limitations, and more information about the benchmarks.\n\n- Introduction: “Experimental results on the quark-gluon jet tagging dataset showcase the superiority of our approach, proving its capacity to capture distinguishing semantic nodes”; and other mentions of \"salient feature extraction\".\n  - Concern: do positive metrics on the downstream task prove that the rationale generator has captured distinguishing semantic nodes? I assume this means identifying subgraphs that drive classification accuracy. I think some analysis of the generated rationales is needed to make such a statement, given the comparable performance to QCGCL which uses regular CL augmentations and no rationales, and EQGNN which is regular deep SL.\n\n- Introduction: “We conduct extensive experiments…”\n  - Concern: See above for limitations of experiments.\n\nRegarding clarity of claims:\n\n- Verbal claims in the abstract and introduction mention many ideas: (i) improved performance, (ii) parameter efficiency, (iii) labelled-data efficiency, (iv) computational efficiency, (v) extracting semantically meaningful discriminative features. It is not clear when these claims refer to SSL vs SL, or quantum RG vs classical RG, or this jet tagging model vs other models. I see some evidence for i and ii, and accept iii if comparing SSL with SL. I don’t see that iv and v are demonstrated.\n- There are also claims made about the challenge of limited labelled data in jet tagging and HEP generally. I don't understand this, because we would typically have either zero ground truth labels (real data) or quite large labelled datasets (synthetic Monte Carlo simulations).\n\nRegarding completeness and clarity:\n\n- Insufficient details provided on the QRG training routine. For both our model and the benchmarks, insufficient details are provided on the architectures and training protocols. How are gradients passed through the augmentation sampling? Are we using the reparameterisation trick, and using what reparameterisation if so? Is the rationale learning aware of what augmentations will be applied? Is the result of the QRG output optimised by taking samples, or can we back propagate through the densities? Is the ParticleNet encoder trained jointly with the QRG, or frozen to some pre-loaded weights? \n- Insufficient details on the benchmark models or how they were trained. Presumably the regular CL methods also use a pre-training step - what losses and data are used? What losses are training protocols are used for the quantum models? What are the hyper parameters in all loss functions? How did you avoid overtraining? The small paragraph at the bottom of page 10 is insufficient.\n- Many other instances where key details are not described precisely. Instead the words “like” and “include” are used. Non-exhaustive examples:\n  - Significantly, it is not explained how we map from the jet graph to the quantum circuit - or exactly how the circuit is stacked into multiple layers (as referenced when you later vary n_layer). Fig4 does not answer these. My understanding is that the circuit should change with both the adjacency matrix and n_layer.\n  - “applying transformations like node dropping, edge perturbation, or feature masking” in A2 and s3.1.5.\n  - “these entanglement patterns are designed based on graph’s structure” in s3.2.1\n  - “optimised through gradient-based approaches” in s3.2.1\n  - “these entanglement patterns are designed based on…: in s3.2.1\n  - “further experiments revealed that H followed by RX is more robust” in S5 - what further experiments? Robust in what way?", "audience_yn": "Yes", "audience_explanation": "Empirically comparing quantum rationale generator to classical methods in terms of performance and/or data efficiency and/or computational cost would be of interest to readers in the RGCL community and HEP-ML jet tagging community.", "requested_changes": "Essential:\n- Address clarity and strength of claims as detailed in previous section.\n- Statements of performance (AUC, accuracy, F1) should have uncertainties where possible. For example, any metric on the test set can have uncertainties estimated by bootstrapping, and you have already used k-fold to calculate std devs.\n- My understanding is that all hyper parameters are selected using k-fold cross-validation on the training set, and the test set is never used until all hyper parameters have been selected for all models. This means that what we call “Test accuracy” in Tables 1 and 2 is not actually measured on the test set - it is the k-fold accuracy on the train set. Is this correct? I would be concerned if hyper parameter optimisation had been performed on the test set, so I just want to verify this has not happened. \n  - S4 says that std devs are calculated using k-fold, but no std devs are provided for Table 1,2,4. The only std devs are in Table 3, which I expect to be calculated from the test set, e.g. by bootstrapping. Please clarify this.\n  - Please make it clear which tables show metrics from k-fold on the train set vs measured on the independent test set.\n- In the first three paragraphs of S5, there are many statements about models or hyper parameters being better than others. These are questionable when we see from Table 3 that there are %-level uncertainties on all of these numbers. It seems possible that many of these comparisons are fluctuations. I would like error bars to be added and the discussion to address this if so. Also, why are the uncertainties so different? It surprises me that you would get a range of 0.5-2.1% for different models on the same dataset. Is it possible these are an artefact of k-fold?\n- The classical analogue of your method, CRGCL, is described in the text and Table 2, but not included in the final results (Table 3 and Fig5). Why is this? This appears to be one of the most essential comparisons and should be included.\n- Many figures contain errors that require fixing:\n  - They are unreadable unless zoomed in on a very large screen, due to the very small text and details\n  - The text promises that Fig2 separates quarks and gluons, which it does not\n  - Eta is used to mean both rapidity and pseudo rapidity in different places, then Fig3 uses “y” which presumably means rapidity, even though y itself was defined as the jet label in s3.1.1.\n  - Fig3b has labels cut off in many places, colours are not defined, and it is unreadable\n  - Fig4 symbols are not defined and contrast is poor\n- s3.2.1: You have an 8-dimensional feature space per particle and encode each with 1 qubit using RX, which only provides 1 degree of freedom out of the required 8. How is this possible? Please specify how we map from classical features to qubit angle. If there is a big 8—>1 dimensionality reduction I would like this be stated clearly.\n- Please clarify what n_layer means for QRG as the “depth”. Which parts of the circuit are being repeated? Is it the U3 and entanglement gates?\n- I am worried about overfitting, especially for benchmark models, given the small 10k training dataset, use of multiple epochs, and the test accuracy appears to be declining a bit in the right of Fig5a for your model. You describe variations in epochs and batch sizes among models. Is each one separately optimised, or at least verified, to ensure there is no evidence of overfitting or underfitting? I would like the appendix to state the details of all benchmark models and how they were trained, and how under/overfitting was avoided, ideally with evidence e.g. training curves.\n- Do all models use only 10k training jets? If yes, justify this. If no, please clarify. Some of the parameter counts are very high for such a small number of data.\n- Limitations section should describe the limitations of the current work, not just suggest extensions. In particular I would like it to reflect the limited scope of the experiments (in terms of realism, diversity of scenarios, number of datapoints, and depth of analysis into where/why performance is better/worse) that limit how much can be concluded about real-world performance. Another one is the tractability of simulating larger quantum circuits on classical hardware. \n- Table 3: distinguish parameter counts in the RG, encoder, and classifier, indicating if they are frozen. For QRGCL you quote many params but this is misleading as most are ParticleNet.\n- s3.1.1: I would like more information about how these events were simulated, including: what were the hard-scatter processes? At what order were they computed? Was pythia used to generate the hard scatter? What settings were used for the parton shower and hadronisation? Are all of the quark jets from q={u,d} at parton-level, or do you include flavours? What is the composition of quarks?\n\nInessential:\n- Briefly state the state-of-the-art methods for tagging quark and gluon jets currently used by ATLAS and CMS, and particularly where ML methods are used.", "broader_impact_concerns": "I don’t have concerns about broader impact that require inclusion, but this section needs to be improved. It is quite cursory, e.g. uses the generic phrase “raise ethical and interpretability considerations” without saying what these considerations might be.", "additional_comments": "Questions and comments:\n- Does ParticleNet start at a random initial state, or from a pre-trained model? Is it frozen during contrastive pretraining? If not, how can you train this model using only 10k jets?\n- s3.1.4 and Eq1: Does using dR as edge weights mean that particles that are far apart have a large adjacency weight whereas those that are close have a small weight? What is the logic in this? Or are edge weights the inverse of this?\n- s3.1.5: Are these augmentations applied to the rationale subset identified by the RG? This should be made clearer.\n- s3.1.7: Why do we limit ourselves to such a small training set of 10k jets? One of the key motivations in the abstract/intro was to handle small amounts of labelled data - but here that limitation seems to be artificially imposed, with most of the dataset thrown away. In reality I would expect us to simulate datasets with millions of jets. I worry this will degrade the performance of classical baselines (which either need to be small, heavily regularised, or barely trained.\n- s3.2.1: To encode edge relationships using CRZ, how do you decide which is the target qubit and which is the condition? Or does it not matter?\n- s3.2.1: To be followed by non-quantum experts, we need to know the basis for these matrices. Is it {|00>, |01>, |10>, |11>}? I find it hard to interpret the CRZ gate in particular without this.\n- s3.2.1: I think your Hamming codes should have a length of 7, not 5?\n- s3.2.3: The phrase “linear layer to reduce the dimensionality… to a latent space of the same dimensionality” doesn’t make sense. Same dimensionality as what? What are the output dimensions precisely?\n- Why not use the unused data to improve the statistical precision of your test set? Or to perform the hyper parameter optimisation without needing k-fold cross validation? \n- s4: I don’t see “augmentation ratio” defined anywhere.\n- Table 3: You only highlight the optimal model by AUC, which looks misleading since other models outperform your method on accuracy and F1. It would be better to highlight these as well.\n- Is it understood why the GNN methods would perform better for tight cuts (bottom left of Fig5b)?\n- S5: “the small gap between the two loss curves suggests minimal overfitting.” I'm not sure I agree. The test accuracy appears to be systematically declining, and the difference between train and test looks ~2%, comparable to the difference between models.", "extra_scores": {}, "extra_text": {}}, {"review_id": "TMrQix5FkJ", "reviewer": "Reviewer_wDig", "summary": "", "questions": "", "limitations": "", "rating": null, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "Yes", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "paper_topic_and_main_contributions": "", "excitement": null, "reproducibility": null, "ethical_concerns": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "summary_of_contributions": "The manuscript investigates quark-gluon jet classification in particle-level simulations through a hybrid quantum-classical architecture that embeds a variational quantum circuit into a rationale-aware graph contrastive learning framework. The authors propose a Quantum Rationale Generator (QRG) that replaces the classical rationale extraction stage in RGCL, claiming that this quantum module can more efficiently identify salient substructures within a jet graph. The approach combines quantum-based node scoring with a ParticleNet encoder and a contrastive objective augmented by rationale-aware and complement-pair losses. The work is original, technically competent, and clearly presented, with partial ablation studies. Results on Pythia8 quark-gluon jets indicate small improvements over classical and hybrid baselines, suggesting that the proposed quantum rationale mechanism can yield enhanced representations.\nWhile the contribution is conceptually interesting, several aspects require clarification before publication, particularly concerning the high energy physics realism of the simplified 7-particle jet representation, the absence of statistical uncertainty estimates, and the lack of concrete evidence for genuine quantum benefit or improved interpretability.\nLastly, I could not find any link to the code and trained models of the proposed architecture. Without public access to the codebase, the central claims of the paper remain impossible to verify or reproduce, which is a significant limitation for a methodological ML contribution.", "claims_and_evidence_yn": "Yes", "claims_explanation": "The manuscript reports improved performance for QRGCL when compared against classical models, although the evidence provided is limited. The performance gain is demonstrated almost exclusively through AUC, which is not the most informative or widely accepted metric for quark-gluon tagging in HEP and more relevant figures of merit such as background rejection at fixed signal efficiency are not presented. In addition the method is evaluated only on 7-10 nodes per jet, despite Figure 2 showing that realistic jets contain up to 120 constituents. This aggressive jet grooming might remove most of the physically relevant structure, raising concerns about whether the results would hold in realistic LHC scenarios.\nThe paper includes ablation studies (Appendix G), but these vary circuit hyperparameters rather than isolating the core contribution of the quantum rationale generator itself. There is no comparison against a classical rationale extractor, so the claimed benefit of the quantum component remains unverified. Claims of “rationale-awareness” are also unsupported by any interpretability analysis or physics-driven visualisation.", "audience_yn": "Yes", "audience_explanation": "The paper explores a hybrid quantum-classical architecture applied to graph contrastive learning, a topic that intersects several areas of active interest within the TMLR community. While the empirical evidence is not yet fully convincing, the methodological idea of integrating a quantum rationale generator into a contrastive learning pipeline is novel and would likely attract attention from researchers working on quantum-enhanced models, explainability, or ML for structured scientific data. The general framework could be of interest beyond high energy physics scenarios, provided the limitations and reproducibility issues are addressed.", "requested_changes": "There are a few points which should be addressed by the authors before consideration as an article in TMLR:\n\n- Dataset. The dataset description should be improved. It is unclear which jet dataset from reference [25] is used, and whether it includes c- and b-quark jets. If both are used, it should be clarified how these different jet classes enter the training. It should also be made explicit that these datasets are at Monte Carlo generator level and do not include any simulated reconstruction of an LHC detector.\n\n- Comparison between classes. The manuscript does not clearly discuss how the quark and gluon classes differ in the features used, nor does it present comparative plots that would allow the reader to understand the underlying class structure. In Figure 2 it is unclear which class is being shown, and the statement on page 3 claiming to “highlight the differences between the quark and gluon population” is not supported by the figure as presented. A clearer comparison between the two classes would help better understand the dataset.\n\n- Figure 3a is confusing, the azimuthal angle on the y-axis (\\psi in this article although it would be more correct to use \\phi) shows values above Pi. This should not happen as the particles should be within [-pi;pi] ( from https://energyflow.network/docs/datasets/#quark-and-gluon-jets, “Particles are ensured have to  \\phi values within \\pi  of the jet (i.e. no -periodicity issues).”). is the global \\phi of the jet shown here?\n\n- Graph directionality. On p. 4, the authors discuss edge direction and state: “The graphs are undirected, reflecting the bidirectional nature of interactions between particles.” This is not completely accurate, as the jet shower evolves from the interaction point outward. This directionality could potentially be exploited to further improve the model.\n\n- Number of active nodes. On p. 5, the choice of retaining only 7 active nodes should be better justified. Is this due to a technical limitation, or was an optimisation performed? This selection appears to remove more gluon jets than quark jets, which could lead to an unbalanced sample and also highlights the different particle-multiplicity distributions of the two populations. This should be explained and addressed.\n\n- Training protocols. The authors indicate that they trained for 50 epochs. Do the authors monitor for overfitting using a validation set and perform a final evaluation on a separate test set, as is standard ML practice? The authors should clarify whether stopping at 50 epochs affects training convergence.\n\n- Physics realism. The authors should address how well this model would perform in a realistic scenario in which jets are not studied at true generator level but reconstructed in an LHC experiment. Moreover, the jet grooming down to 7 components is very aggressive and might end up removing relevant physical features. Typical jets have O(50–100) constituents, as shown in Figure 2a. This item should be discussed. Addressing these points would improve transparency and reproducibility.\n\n- Evaluation metric. The authors should justify why AUC was selected as the primary figure of merit for jet classification. In high energy physics, AUC is often not the most informative metric, as it integrates over operating regions that are not relevant for practical analyses. A discussion of why AUC was chosen, and whether other metrics were considered, would improve the interpretability of the reported results.\n\n- Scalability limitations. The authors should explicitly discuss the scalability constraints of their approach. The 7-qubit restriction forces the model to operate on heavily truncated jets and therefore limits its physical realism. A subsection explaining how this constraint affects the applicability of the method, and how future quantum devices might overcome this bottleneck, would significantly improve the paper.\n\n\n- Minor editing. In some places, pseudo-rapidity (η) is confused with rapidity (y). This should be made consistent throughout the paper.", "broader_impact_concerns": "The work poses no direct ethical risks.", "additional_comments": "This is overall a conceptually innovative and methodologically solid paper that explores a new hybrid quantum-classical direction in graph contrastive learning applied to jet physics. Its main value lies in proof-of-concept novelty rather than in clear empirical quantum advantage. With the requested clarifications and a more tempered interpretation of results, it could become a valuable contribution.", "extra_scores": {}, "extra_text": {}}]

Author rebuttal:

Decision: Accept (poster)