Quantum computers are extremely promising emerging technologies with inter-disciplinary teams around the globe working on their development and implementation. Yet, progress is hampered by fundamental difficulties in scalability, end-user friendliness, certification of components and algorithms, and limited application scope to real-world problems. To overcome these urgent challenges, NeQST leverages an extended quantum information processing paradigm based on multi-level carriers of quantum information—qudits. Both the quantum hardware at the fundamental level, and many problems of scientific and technological relevance, are expressed in terms of multi-level systems, making this approach the most efficient choice to unlock the full potential of quantum computers and simulators. NeQST will generate foundational breakthroughs in the full value chain of qudit quantum information processing. These include qudit based firmware with scalable characterization and automatized design tools harnessing a larger Hilbert space; an end-user friendly high-level control and simulation software, enabling non-specialists to utilize the qudit hardware; the efficient simulation of quantum models of scientific relevance, such as gauge theories; the solution of optimization problems in academia and industry naturally phrased in terms of multi-level variables; and certification tools specifically designed for multi-level quantum information, enabling a device-independent validation of data. NeQST results will therefore elucidate the role of dimension in quantum physics and its use as a resource for quantum information processing. To achieve its ambitious goals, NeQST has assembled an inter-disciplinary team of leading academic and industry partners, and has developed a well-rounded work plan, as well as detailed dissemination and exploitation strategies.