  We construct the exchange gate with small elementary gates on the space of
qudits, which consist of three controlled shift gates and three "reverse"
gates. This is a natural extension of the qubit case.
  We also consider a similar subject on the Fock space, but in this case we
meet with some different situation. However we can construct the exchange gate
by making use of generalized coherent operator based on the Lie algebra su(2)
which is a well--known method in Quantum Optics. We moreover make a brief
comment on "imperfect clone".
