  We consider the CNOT quantum gate as a physical action, i.e. as unitary in
time evolution of the two-qubit system. This points to the modeling of the
interaction Hamiltonian of the two-qubit system which would correspond to the
CNOT transformation; the analysis naturally generalizes to the Toffoli gate.
Despite nonuniqueness of the model of the interaction Hamiltonian, the analysis
distinguishes that the interaction Hamiltonian does not posses any global
(rotational) symmetry. This forces us to conclude that the direct
(non-mediated) interaction in the two-qubit system does not suffice for
implementing the CNOT gate. I.e., so as to be able succesfully to implement the
CNOT transformation, a mediator (i.e. an external physical system interacting
with both of the qubits) is required.
