  Today's quantum computers operate with a binary encoding that is the quantum
analog of classical bits. Yet, the underlying quantum hardware consists of
information carriers that are not necessarily binary, but typically exhibit a
rich multilevel structure, which is artificially restricted to two dimensions.
A wide range of applications from quantum chemistry to quantum simulation, on
the other hand, would benefit from access to higher-dimensional Hilbert spaces,
which conventional quantum computers can only emulate. Here we demonstrate a
universal qudit quantum processor using trapped ions with a local Hilbert space
dimension of up to 7. With a performance similar to qubit quantum processors,
this approach enables native simulation of high-dimensional quantum systems, as
well as more efficient implementation of qubit-based algorithms.
