  The quantum Fourier transform (QFT) is a key ingredient of several quantum
algorithms and a qudit-specific implementation of the QFT is hence an important
step toward the realization of qudit-based quantum computers. This work
develops a circuit decomposition of the QFT for hybrid qudits based on
generalized Hadamard and generalized controlled-phase gates, which can be
implemented using selective rotations in NMR. We experimentally implement the
hybrid qudit QFT on an NMR quantum emulator, which uses four qubits to emulate
a single qutrit coupled to two qubits.
