  Ternary quantum processors offer significant computational advantages over
conventional qubit technologies, leveraging the encoding and processing of
quantum information in qutrits (three-level systems). To evaluate and compare
the performance of such emerging quantum hardware it is essential to have
robust benchmarking methods suitable for a higher-dimensional Hilbert space. We
demonstrate extensions of industry standard Randomized Benchmarking (RB)
protocols, developed and used extensively for qubits, suitable for ternary
quantum logic. Using a superconducting five-qutrit processor, we find a
single-qutrit gate infidelity as low as $2.38 \times 10^{-3}$. Through
interleaved RB, we find that this qutrit gate error is largely limited by the
native (qubit-like) gate fidelity, and employ simultaneous RB to fully
characterize cross-talk errors. Finally, we apply cycle benchmarking to a
two-qutrit CSUM gate and obtain a two-qutrit process fidelity of $0.82$. Our
results demonstrate a RB-based tool to characterize the obtain overall
performance of a qutrit processor, and a general approach to diagnose control
errors in future qudit hardware.
