  Qudit-based quantum computation offers unique advantages over qubit-based
systems in terms of noise mitigation capabilities as well as algorithmic
complexity improvements. However, the software ecosystem for multi-state
quantum systems is severely limited. In this paper, we highlight a quantum
workflow for describing and compiling qudit systems. We investigate the design
and implementation of a quantum compiler for qudit systems. We also explore
several key theoretical properties of qudit computing as well as efficient
optimization techniques. Finally, we provide demonstrations using physical
quantum computers as well as simulations of the proposed quantum toolchain.
