  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 first experimental
demonstration 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 $78\pm 1\%$,
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 manipulate these high-dimensional states. Our work demonstrates that
another platform, superconducting systems, is ready to exploit high-dimensional
physics phenomena and that a programmable quantum device accessed on the cloud
can be used to design and execute experiments beyond binary quantum
computation.
