The integration of symmetry into quantum models within geometric quantum machine learning has attracted increasing research attention. In this work, we introduce a symmetry-constrained quantum convolutional neural network framework tailored to few-shot learning in the noisy intermediate-scale quantum (NISQ) setting. By unifying equivariant data embeddings with symmetry-constrained quantum gate sets, our approach compresses the hypothesis space into group-invariant subspaces, enforcing geometric inductive biases that mitigate overfitting. Theoretically, we specialize existing generalization results for parameterized quantum circuits to our symmetry-constrained QCNN architecture and show that, under \(T \in \mathcal {O}(\log n)\) and \(M = \textrm{poly}(n)\) , the resulting bounds exhibit polylogarithmic scaling in the system size. This perspective complements more fine-grained, architecture-specific error decompositions by providing an alternative view that highlights how symmetry and parameter sharing compress the QCNN hypothesis space and influence the scaling behavior of existing theoretical results. To address NISQ hardware constraints, we implement a brick-layer circuit architecture with frequency collision avoidance, ensuring nearest neighbor connectivity and practical feasibility. Numerical simulations on binary MNIST and Fashion-MNIST tasks with additive Gaussian input noise ( \(\sigma = 0.2\) ) applied to the classical data and a noiseless statevector backend for all quantum models indicate that, for small-to-moderate training sets, the symmetric QCNN can reduce the generalization error by up to \(64\%\) relative to a generic QCNN and by up to \(74\%\) relative to a standard VQC under this input noise model. On the noisy MNIST task, the proposed framework attains up to \(93.9\%\) test accuracy with a stabilized loss around 0.28 in our simulations, while maintaining competitive performance against classical baselines such as SVMs and random forests, suggesting that symmetry-driven dimensionality reduction can improve generalization and robustness to input perturbations in quantum learning. Overall, our work presents a QCNN framework that combines symmetry preservation, generalization analysis based on existing theory, and NISQ-compatible architectural design within a single coherent model, and illustrates how these ingredients can be jointly exploited in geometric quantum machine learning.
