Brain research and quantum technology are at the focus of 21st century science. Although theoretical and experimental studies have provided some insights regarding the mechanisms of how the brain acquires, represents and stores information, a comprehensive theory of the brain and the underlying neural information processing is still missing. Experimental techniques to study brain processes on different levels of description, notably the sub-neuron (synaptic, dendritic and axonal), single neuron and neural network level, are therefore of fundamental importance for brain research. Recently, a new promising technique in solid state physics has emerged for measuring electric and magnetic fields at the nanometer scale with unprecedented spatiotemporal resolution (sub-micron and sub-ms range). The nitrogen-vacancy (NV) defect in diamond is a unique ultra-sensitive quantum device that can sense external magnetic and electrical fields via its spin states, which can be read-out optically using electron spin resonances. The NEURONQ project aims towards the development of an NV centre based neuroimaging system for real-time recording of neural activity on the sub-neuron, neuron and neuron network level under ambient conditions. The NEURONQ projects combines both disciplines, brain research and quantum technology, into an exciting multidisciplinary research effort by combining expertise from physicists, neuroscientists and nanoengineers. The NEURONQ project is expected to have impact of paramount importance for basic neuroscience research and neurotechnology, and thus, will significantly contribute to European scientific and technological competitiveness and excellency.