In usual computer, there is an upper bound of computational speed because of irreversibility of logical gate.In order to avoid this demerit, Fredkin and Tof- foli [3] proposed a conservative logical gate.After that, Milburn [4] constructed a physical model of reversible quantum gate with beam splittings and a Kerr medium.This model is called FTM (Fredkin
− Toffoli
− Milburn gate) in this paper.This FTM gate was described by the quantum channel and the efficiency of information transmission of the FTM gate was discussed in [10].FTM gate is using a photon number state as an input state for control gate.The photon number state might be difficult to realize physically.In this paper, we introduced a new device on symmetric Fock space in order to avoid this difficulty.In Section 1, we briefly review noisy quantum channels and generalized beam splittings.In Section 2, we explain the quantum channel for FTM gate based on the notation of Section 1.In Section 3, we intruduced a new operator on symmetric Fock space and discuss the truth table for our new gate.