Multi state logic in cluster state quantum computing

Quantum information processing (QIP) has made significant progress in recent years, but much of today's quantum hardware is artificially constrained to two-level information processing. Recent results have shown that current trapped-ion quantum hardware supports universal computation using a high-dimensional (qudit) encoding, allowing for increased computational complexity and more efficient quantum technologies. However, the qudit approach to quantum computation remains less developed than conventional qubit QIP frameworks, particularly in measurement-based quantum computing (MBQC). To remain competitive with binary-based approaches, it is essential to develop advanced capabilities such as MBQC and cluster states in systems using multi-state logic. The goal of this project is to elevate the MBQC framework and stabilizer formalism to quantum computers working with multi-state logic, enabling more efficient quantum technologies and enhancing Austria's leading role in the field of qudit QIP.