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Adversarial learning represents a powerful technique for generating data statistics. Its successful implementation in quantum computational platforms is not straightforward due to limitations in connectivity, quantum operation fidelity, and limited access to the quantum processor for statistically relevant results. Constraining the number of quantum operations and providing a design with a low compilation cost, we propose a quantum generative adversarial network design that uses real Hilbert spaces as the framework for the generative model and a novel strategy to encode classical information into the quantum framework. We consider quantum generator and discriminator architectures based on a variational quantum circuit. We encode classical information by the stereographic projection, which allows us to use the entire classical domain without normalization procedures. For low-depth ansätze designs, we consider the real Hilbert space as the working space for the quantum adversarial game. This architecture improves state-of-the-art quantum generative adversarial performance while maintaining a shallow-depth quantum circuit and a reduced parameter set. We tested our design in a low resource regime, generating handwritten digits with the MNIST as the reference dataset. We could generate undetected data (digits) with just 15 epochs working in the real Hilbert space of 2, 3, and 4 qubits. Our design uses native quantum operations established in superconducting-based quantum processors and is compatible with ion-trapped-based architectures.