Quantum Fourier Transform with Qudits

We study the implementation of the quantum Fourier transform (QFT) over d-dimensional quantum systems (qudits). Specifically, we generalize the qubit algorithm to qudits and characterize its complexity with respect to gate sets appropriate for qudit-oscillator implementations (based on the Jaynes-Cummings Hamiltonians). We find that, for experimentally realizable interactions, highly efficient implementations of the qudit QFT are possible.