  Qudit is a multi-level computational unit alternative to the conventional
2-level qubit. Compared to qubit, qudit provides a larger state space to store
and process information, and thus can provide reduction of the circuit
complexity, simplification of the experimental setup and enhancement of the
algorithm efficiency. This review provides an overview of qudit-based quantum
computing covering a variety of topics ranging from circuit building, algorithm
design, to experimental methods. We first discuss the qudit gate universality
and a variety of qudit gates including the pi/8 gate, the SWAP gate, and the
multi-level-controlled gate. We then present the qudit version of several
representative quantum algorithms including the Deutsch-Jozsa algorithm, the
quantum Fourier transform, and the phase estimation algorithm. Finally we
discuss various physical realizations for qudit computation such as the
photonic platform, iron trap, and nuclear magnetic resonance.
