  Multipartite entanglement is one of the core concepts in quantum information
science with broad applications that span from condensed matter physics to
quantum physics foundations tests. Although its most studied and tested forms
encompass two-dimensional systems, current quantum platforms technically allow
the manipulation of additional quantum levels. We report the experimental
demonstration and certification of a high-dimensional multipartite entangled
state in a superconducting quantum processor. We generate the three-qutrit
Greenberger-Horne-Zeilinger state by designing the necessary pulses to perform
high-dimensional quantum operations. We obtain the fidelity of $76\pm 1\%$,
proving the generation of a genuine three-partite and three-dimensional
entangled state. To this date, only photonic devices have been able to create
and certify the entanglement of these high-dimensional states. Our work
demonstrates that another platform, superconducting systems, is ready to
exploit genuine high-dimensional entanglement and that a programmable quantum
device accessed on the cloud can be used to design and execute experiments
beyond binary quantum computation.
