Quantum Rationale-Aware Graph Contrastive Learning for Jet Discrimination

TL;DR

The paper presents QRGCL, a hybrid quantum-classical graph contrastive learning framework for quark-gluon jet tagging. It introduces a Quantum Rationale Generator to identify salient subgraphs, integrating it with a ParticleNet encoder and a quantum-enhanced contrastive loss. On the quark-gluon jet dataset, QRGCL achieves an AUC of 77.53% with a compact 45-parameter quantum module, outperforming classical, quantum, and hybrid baselines. The work demonstrates that quantum rationales can guide data augmentation and representation learning under limited labels, with potential applicability to broader graph-based tasks in high-energy physics.

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. However, existing contrastive learning (CL) frameworks struggle to leverage rationale-aware augmentations effectively, often lacking supervision signals that guide the extraction of salient features 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 significantly enhances jet discrimination performance, reducing reliance on labeled data and capturing discriminative features. Evaluated on the quark-gluon jet dataset, QRGCL achieves an AUC score of $77.53\%$ while maintaining a compact architecture of only 45 QRG parameters, outperforming classical, quantum, and hybrid GCL and GNN benchmarks. These results highlight QRGCL's potential to advance jet tagging and other complex classification tasks in high-energy physics, where computational efficiency and feature extraction limitations persist.

Figures (5)

• Figure 1: QRGCL framework. The quantum rationale generator identifies a discriminative subset of nodes in the original graph. The rationale generator shared GNN-encoder and projection head is jointly optimized by minimizing the combined loss.
• Figure 2: Distribution of (a) number of particles in each jet, (b) transverse momentum, (c) total momenta, and (d) energy.
• Figure 3: Plot of (a) a sample jet shown in $(\psi, y)$ plane with each particle color-coded by its $p_{T,\alpha}^{(i)}$, (b) a sample of graph views used in our CL-based approach. Each graph represents a jet as a collection of nodes (particles) with associated physics-based features. The graphs are undirected, reflecting the bidirectional nature of interactions between particles.
• Figure 4: QRG circuit of the proposed QRGCL. The circuit operates on seven qubits, with each qubit corresponding to a node in the graph. The top portion shows the data encoding stage, where each qubit is initialized using an $H$ gate followed by $RX$-based angle encoding node features. $CRZ$ gates encode edge relationships between qubits. The bottom portion includes parameterized rotations ($RX$, $RY$, $RZ$) for adaptable representations and entanglement layers using $SWAP$ gates. Measurement results are obtained on a computational basis, with classical registers collecting the output.
• Figure 5: (a) Training and testing dynamics of QRGCL over 1000 epochs. The left graph illustrates loss curves, while the right graph presents accuracy curves. (b) ROC-AUC curve for all the benchmarked models

Theorems & Definitions (5)

• Theorem 1: Interpretation of RA and CP Losses
• proof : Proof Sketch
• Theorem 2: Role of Alignment and Uniformity
• proof : Proof Sketch
• Remark 1