  We present a quantum SWAP gate valid for quantum systems of an arbitrary
dimension. The gate generalizes the CNOT implementation of the SWAP gate for
qubits and keeps its most important properties, like symmetry and simplicity.
We only use three copies of the same controlled qudit gate. This gate can be
built with two standard higher-dimensional operations, the Quantum Fourier
Transform and the d-dimensional version of the CZ gate.
