The Quromorphic project will introduce human brain inspired hardware with quantum functionalities: It will build superconducting quantum neural networks to develop dedicated, neuromorphic quantum machine learning hardware, which can, in its next generation, outperform classical von Neumann architectures. This breakthrough will combine two cutting edge developments in information processing, machine learning and quantum computing, into a radically new technology. In contrast to established machine learning approaches that emulate neural function in software on conventional von Neumann hardware, neuromorphic quantum hardware can offer a significant advantage as it can b e trained on multiple batches of real world data in parallel. This feature is expected to lead to a quantum advantage. Moreover, our approach of implementing neuromorphic quantum hardware is very promising since there exist indications that a quantum advantage in machine learning can already be achieved with moderate fault tolerance. In a longer term perspective neuromorphic hardware architectures will become extremely important in both, classical and quantum computing, particularly for distributed and embedded computing tasks, where the vast scaling of existing architectures does not provide a long-term solution. Quromorphic aims to provide proof of concept demonstrations of this new technology and a roadmap for the path towards its exploitation. To achieve this breakthrough, we will implement two classes of quantum neural networks that have immediate applications in quantum machine learning, feed forward networks and non-equilibrium quantum annealers. This effort will be completed by the development of strategies for scaling the devices to the threshold where they will surpass the capabilities of existing machine learning technology and achieve quantum advantage. In preparation for future exploitation of this new technology, we will run simulations to explore its application to real world problems.