quant-phMar 9, 2026

Characterization and upgrade of a quantum graph neural network for charged particle tracking

Authors: Matteo Argenton, Laura Cappelli, Concezio Bozzi

Organizations: Department of Physics and Earth Science, University of Ferrara, Via Saragat 1, Ferrara, 44122, Italy · INFN Ferrara, Via Saragat 1, Ferrara, 44122, Italy

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Abstract

In the forthcoming years the LHC experiments are going to be upgraded to benefit from the substantial increase of the LHC instantaneous luminosity, which will lead to larger, denser events, and, consequently, greater complexity in reconstructing charged particle tracks, motivating frontier research in new technologies. Quantum machine learning models are being investigated as potential new approaches to high energy physics (HEP) tasks. We characterize and upgrade a quantum graph neural network (QGNN) architecture for charged particle track reconstruction on a simulated high luminosity dataset. The model operates on a set of event graphs, each built from the hits generated in tracking detector layers by particles produced in proton collisions, performing a classification of the possible hit connections between adjacent layers. In this approach the QGNN is designed as a hybrid architecture, interleaving classical feedforward networks with parametrized quantum circuits. We characterize the interplay between the classical and quantum components. We report on the principal upgrades to the original design, and present new evidence of improved training behavior, specifically in terms of convergence toward the final trained configuration.

Figures & tables

Figure 1: TrackML detector layout from [ 32 ] . The three different sub-detectors are shown on the left and with the associated colors in the z-r plane depiction on the right. Grey lines correspond to different pseudorapidity η\eta values.
Figure 2: Message passing algorithm. Information from node A is first propagated to its nearest neighbor D, and then propagated to the next to nearest neighbors C and E.
Figure 3: Block diagram of a graph neural network for edge classification. The iteration of Edge and Note Networks is responsible for the propagation of the information at different orders of proximity in the graph structure, as in Fig. 2 .
Figure 4: Structure of a generic hybrid sub-module in the QGNN, with encoding and readout layers to manage the dimensionality of the data, and a parametrized quantum circuit between classical networks. Arrows represent the data flow; no additional learnable parameters are present in-between different blocks, and the output of the previous block is directly taken as input to the next.
Figure 5: The 3-layers and 4-qubits parametrized quantum circuit used as foundation to the original hybrid classical-quantum layers of the QGNN. Information is encoded in the initial quantum state through angle encoding. RYRY gates perform YY -axis rotations, each parametrized by a trainable angle θi\theta_{i}
Figure 6: Original QGNN architecture accuracy, specificity, precision, and recall measured on the validation set, with four different dataset simulating different pileup values, μ=50,100,150,200\mu=50,100,150,200 .
Figure 7: The 3-layers and 6-qubits parametric quantum circuit used in the upgrade. The 64 features from the classical MLPs are encoded in the quantum state ∣ψ⟩\ket{\psi} through amplitude encoding; 64 output amplitudes are then extracted from the circuit.
Figure 8: Comparison of the learning metrics on the μ=200\mu=200 validation set. Blue lines represent data from the upgraded Quantum-GNN architecture, with [64,64] classical MLPs and 6-qubits quantum circuit with amplitude encoding. Orange lines correspond to data from the upgraded Classical-GNN, with [64,64] MLPs. Grey lines represent the original pre-upgrade architecture scores.
ModelAccuracyPrecisionRecallSpecificity
Upgraded QGNN0.960±0.0030.960\pm 0.0030.981±0.0030.981\pm 0.0030.946±0.0050.946\pm 0.0050.977±0.0040.977\pm 0.004
Upgraded CGNN0.964±0.0020.964\pm 0.0020.981±0.0050.981\pm 0.0050.952±0.0030.952\pm 0.0030.977±0.0070.977\pm 0.007
Original QGNN0.752±0.0130.752\pm 0.0130.990±0.0070.990\pm 0.0070.55±0.030.55\pm 0.030.993±0.0060.993\pm 0.006
Original CGNN0.790±0.0030.790\pm 0.0030.981±0.0040.981\pm 0.0040.612±0.0040.612\pm 0.0040.987±0.0030.987\pm 0.003
Table 1: Final-epoch kk -fold cross-validation performance of the upgraded and original reference models at μ=200\mu=200 .
Appendix figures & tables7 assets

Supplementary material from the paper’s appendix.

Appendix

Figure 9: Distribution of transverse momentum pTp_{T} in the 100-events sample dataset from [ 3 ] . The dashed black line represent the cut enforced at 1GeV.
Figure 10: Inference accuracy for different pileup datasets. The red line corresponds to the noiseless PennyLane statevector simulator; the blue line to the noisy Qiskit Aer simulator backend, with a noise model imported from the IBM Osaka device; the green line to the real remote IBM Osaka quantum hardware, accessed through PennyLane’s interface.
Figure 11: Original QGNN architecture accuracy, specificity, precision, and recall measured on the training set, with four different dataset simulating different pileup values, μ=50,100,150,200\mu=50,100,150,200 .
Figure 12: Comparison of the learning metrics on the μ=200\mu=200 training set. Blue lines represent data from the upgraded Quantum-GNN architecture, with [64,64] classical MLPs and 6-qubits quantum circuit with amplitude encoding. Orange lines correspond to data from the upgraded Classical-GNN, with [64,64] MLPs. Grey lines correspond to the original, pre-upgrade architectures.
Figure 13: Extended 12 qubits circuit with ∣ψ⟩=∣ψin⟩⊗∣ψin⟩\ket{\psi}=\ket{\psi_{\text{in}}}\otimes\ket{\psi_{\text{in}}} tested within the upgraded QGNN architecture for preliminary studies on expressivity enhancements.
Figure 14: Comparison of the training metrics between the Upgraded QGNN and the same architecture with the circuit in Fig. 13 , labeled Parallel QGNN.
Figure 15: Comparison of the validation metrics between the Upgraded QGNN and the same architecture with the circuit in Fig. 13 , labeled Parallel QGNN.

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