Hybrid Quantum-Classical Representation Learning for Dark Matter Substructure Classification

This proposal presents a plan to develop hybrid quantum-classical models for classifying dark matter substructure from strong gravitational lensing images, as part of the ML4SCI DeepLense project. The classification task involves three classes: no substructure, CDM subhalo substructure, and vortex substructure from axion/fuzzy dark matter. I propose two complementary approaches: Projected Quantum Kernels (PQK), which encode CNN-extracted image features into quantum states and ompute kernel matrices for SVM classification, and Quantum Convolutional Neural Networks (QCNN), which use parameterized quantum circuits as trainable convolutional filters in a hybrid pipeline. Both methods will be benchmarked against classical baselines on the DeepLense Model I/II/III datasets and evaluated under realistic NISQ noise conditions using depolarizing and devicecalibrated noise models, with error mitigation techniques such as ZNE and PEC. Beyond the standard implementations, I also propose using a GPT-2-based autoregressive Transformer to automatically generate task-optimized quantum circuits for both PQK feature maps and QCNN layers, replacing hand-designed circuit templates. Additional experiments include data-efficiency analysis on small training subsets, hybrid kernel fusion combining classical RBF with PQK, and transfer learning evaluation across different dark matter model datasets.