Quantum Machine Learning for particle scattering entanglement classification

Entanglement is a key quantity for characterizing quantum correlations in particle scattering processes, but its direct evaluation is computationally demanding on quantum hardware. In this work, we investigate whether fermion density profiles, which are easier to access, can serve as proxies for entanglement by framing the problem as a classification task across multiple entanglement thresholds. Using the fermion scattering in the Thirring model as a test bed, we compare Quantum Convolutional Neural Networks (QCNNs) with classical CNNs of comparable parameter counts, and find that QCNNs achieve consistently competitive or superior accuracy with faster convergence and lower variance. Notably, we observe that increasing the model size does not improve the performance within the architectures studied here, and larger models appear to be more sensitive to the choice of encoding. Instead, a compact 4-qubits QCNN provides the best results, suggesting the importance of trainability and encoding choices over model scaling. These findings demonstrate the potential of quantum and quantum-inspired machine learning models for extracting nontrivial quantum information from accessible observables, with implications for high-energy physics and quantum many-body systems.