Subspace preserving quantum circuits are a class of quantum algorithms that, relying on some symmetries in the computation, can offer theoretical guarantees for their training. Those algorithms have gained extensive interest as they can offer polynomial speed-up and can be used to mimic classical machine learning algorithms. In this work, we propose a novel convolutional neural network architecture model based on Hamming weight preserving quantum circuits. In particular, we introduce convolutional layers, and measurement based pooling layers that preserve the symmetries of the quantum states while realizing non-linearity using gates that are not subspace preserving. Our proposal offers significant polynomial running time advantages over classical deep-learning architecture. We provide an open source simulation library for Hamming weight preserving quantum circuits that can simulate our techniques more efficiently with GPU-oriented libraries. Using this code, we provide examples of architectures that highlight great performances on complex image classification tasks with a limited number of qubits, and with fewer parameters than classical deep-learning architectures.