A generalized two-qubit Hamiltonian has been developed for projective quantum feature maps, enabling a unified approach to encoding classical features through local Pauli fields and pairwise two-qubit Pauli interactions1. This advancement builds upon previous work on counterdiabatic Ising-glass and one-dimensional Heisenberg projective quantum feature maps. The introduction of this Hamiltonian-based framework provides a strategy for leveraging quantum processors as feature generators for classical machine-learning models. By harnessing the power of quantum computing, researchers can potentially create more efficient and powerful machine-learning models. The development of projective quantum feature maps has significant implications for the field of quantum computing, as it enables the creation of more sophisticated quantum-classical hybrids. This matters to practitioners because it has the potential to revolutionize the way classical machine-learning models are trained and deployed, particularly in fields where quantum computing can provide a significant advantage over classical computing methods.