  Recent developments in qudit-based quantum computing, in particular with
trapped ions, open interesting possibilities for scaling quantum processors
without increasing the number of physical information carriers. In this work,
we propose a method for compiling quantum circuits in the case, where qubits
are embedded into qudits of experimentally relevant dimensionalities,
$d=3,\ldots,8$, for the trapped-ion platform. In particular, we demonstrate how
single-qubit, two-qubit, and multiqubit gates can be realized using
single-qudit operations and the Molmer-Sorensen (MS) gate as a basic
two-particle operation. We expect that our findings are directly applicable to
trapped-ion-based qudit processors.
