Symmetry-constrained hybrid quantum-classical convolutional neural networks for rotation-robust face recognition

Face recognition systems struggle when faces appear at different orientations. Standard convolutional neural networks handle translation well but have no built-in way to deal with rotations or reflections. Quantum neural networks offer a different kind of expressiveness, but most existing designs ignore spatial symmetry altogether. This paper introduces Eq-MG-QCNN, a hybrid quantum-classical model that builds rotation symmetry directly into the quantum circuit. The quantum filter is designed to be exactly equivariant under the Klein four-group, which covers horizontal flips, vertical flips, and 180° rotations. This is done through two mechanisms: sharing rotation parameters across all qubits (as required by orbit analysis), and connecting all qubit pairs with symmetric CZ gates (forming a complete K₄ graph). The model is tested on the ORL and Yale face databases under four rotation angles (0°, 90°, 180°, 270°) and compared against a classical CNN, a classical equivariant CNN, and the MG-QCNN quantum baseline. All experiments use noiseless quantum simulation. Eq-MG-QCNN reaches 94.3% best accuracy on ORL and 89.9% on Yale with only six quantum parameters, two fewer than the baseline. The model also shows low rotational variation across all four test angles. These results suggest that embedding group symmetry into quantum circuits is a practical way to build orientation-stable feature extractors for face recognition.