In the last years, artificial intelligence (AI) has driven critical advancements in sectors like healthcare, autonomous vehicles, entertainment, and finance, transforming science, technology, and our daily lives. Deep-learning neural networks (NNs) are central to many of these AI systems due to their ability to learn complex patterns, largely owing to their nonlinear activation function. However, NNs are typically built on traditional von Neumann architectures, where separate memory and processing units result in inefficiencies, leading to high costs and energy consumption as AI models grow more complex. This has boosted great interest in unconventional computing architectures, like neuromorphic computing, which mimics the brain's design for more sustainable and scalable AI systems. Photonics presents a promising solution here, offering unmatched speed, parallel processing, and energy efficiency that outperform traditional electronic chips. Despite this potential, realizing all-optical NNs presents considerable technical challenges. Key obstacles include weak nonlinear optical interactions, which are essential for creating complex input-output relations in NNs via nonlinear activation functions. In turn, plasmonic systems can provide stronger nonlinearities, but ohmic losses hinder their application. Q-MIND aims pioneer a radically-new nanometer-scale, ultrafast and energy-efficient technology to address current limitations in neuromorphic computing. Specifically, it will integrate phonon-polaritons—quantum hybrids of light and lattice vibrations—in 2D materials, which can guide light at the nanoscale with minimal energy loss, and heavily doped semiconductors, which will provide tunability and dynamic control of nonlinear interactions. Both materials' nonlocal behavior will be key to unlocking novel nanoscale nonlinear processes at the heart of Q-MIND's vision. Q-MIND aligns with EU and UN priorities on sustainable development and AI and quantum technologies.