Just like digital information processing has revolutionized 20th century technology, quantum information processing and the second quantum revolution are shaping the 21st century. Yet, while classical computing is long set in the path of binary information, the future is still open for quantum information processing, and it would be fatal to force it into the same restrictive paradigm. The goal of this project is to break out of this artificial two-dimensional structure and tap into the large unused potential of high-dimensional quantum information processing. I have extensive expertise in the field of quantum information processing. During my PhD in photonics, I realized the highest fidelity state preparation and measurement of qudits reported to date, and recently I developed a full mathematical and experimental framework for the characterization of quantum coherence in multilevel systems. Building on this expertise, I will develop the first universal qudit quantum processor, using four electronic levels of trapped Ca ions, which are one of the most advanced platforms for quantum information processing. The hosting group of Prof. Rainer Blatt in Innsbruck is a world leader in trapped ion quantum information processing and pioneered all the necessary groundwork, such as laser cooling, coherent control, and large scale entanglement of ions to make this project possible. I will apply the newly developed qudit quantum processor to the quantum simulation of lattice gauge theories of critical interest in high energy physics. The development of this new technology also unlocks a wide range of open questions from quantum simulation to quantum communication and computation, which I and the host institution will be in a unique position to address. This fellowship will give me protected time to realise the proposed research and establish myself as an independent researcher in Europe and an expert in the new paradigm of qudit quantum information processing.