Current classical computers are playing a critical role in advanced research such as in biology, climate analysis, economics, genomics, finance, etc. In many aspects, computing fuels the advances of our modern society. Yet, recent developments in artificial intelligence (AI) and machine learning will require even more powerful computing systems such as exascale computations per second due to an ever-increasing amount of data. But classical computing systems are hindered by the von-Neumann communication bottleneck, the physical separation between processor and memory. This offers the opportunity to explore a novel computing paradigm where the brain can serve as a computational model of how to deal with large amounts of (often fuzzy) information while being extremely dense, error-resilient and power efficient.