Reaching a fundamental understanding of quantum many-body systems and fully harnessing their computational power for information processing is one of today’s greatest scientific challenges. To date, unprecedented research efforts are underway to build quantum devices, which would outperform the most powerful classical computers. At the same time, neural networks are currently revolutionising the handling of large amounts of data, with enormous success in pattern and speech recognition, machine learning, the analysis of ‘big data’ and ‘deep learning’. Driven by the hope of combining massive parallel information processing in neural networks with quantum advantages like computational speedup, there have been various efforts to develop quantum neural networks – without satisfactory answers to date. The overarching goal of this theoretical research programme is to tackle this enormous challenge from a fresh perspective: we will establish and explore a conceptual framework for quantum neural networks and identify quantum optical physical building blocks, based on concepts in the domain of open many-body quantum systems. This ambitious aim will be achieved by interlinking a multitude of scientific areas ranging from atomic physics, quantum optics, quantum engineering and condensed matter physics to quantum information and computer science. This research will not only generate a genuine step change in our fundamental understanding of the ways nature allows for quantum information processing. It will also lay the foundation for quantum neuromorphic engineering of a new generation of quantum neural hardware in state-of-the-art and newly emerging experimental systems of ultra-cold atoms and trapped ions. With my interdisciplinary background in quantum information and quantum engineering, quantum optics and atomic physics, I am in a unique position to successfully realise this research. I will also strongly benefit from the vital scientific environment at Swansea University.