Quantum computing with qudits

Recent progress in a development of quantum computing platforms operating with qudits ($d$-dimensional quantum particles with $d>2$) rises important questions of how such platforms can be used in the most efficient way for implementing known quantum algorithms. In my presentation, I will be discussing possible approaches for the implementation of qubit-based circuits using qudit-based hardware. These approaches include: (i) employing higher-level qudits to substitute ancillary qubits in the decomposition of multiqubit gates, (ii) embedding the computational space of multiple qubits into a single qudit, and (iii) combining approaches (i) and (ii). Special attention will be paid to the possible experimental implementation of the discussed approaches within the systems of superconducting qubits and trapped ion qudits.