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We construct the exchange gate with small elementary gates on the space ofqudits, 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 wemeet with some different situation. However we can construct the exchange gateby 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 briefcomment on "imperfect clone".Comment: Latex File, 12 pages. I could solve the problems in Sec. 3 in the  preceding manuscript, so many corrections including the title were mad

Exchange gate on the qudit space and Fock space