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Taking advantage of quantum mechanics for executing computational tasks faster than classical computers or performing measurements with precision exceeding the classical limit^, requires the generation of specific large and complex quantum states. In this context, cluster states are particularly interesting because they can enable the realization of universal quantum computers by means of a ‘one-way’ scheme, where processing is performed through measurements. The generation of cluster states based on sub-systems that have more than two dimensions, d-level cluster states, provides increased quantum resources while keeping the number of parties constant, and also enables novel algorithms. Here, we experimentally realize, characterize and test the noise sensitivity of three-level, four-partite cluster states formed by two photons in the time and frequency domain, confirming genuine multi-partite …