  Any quantum computational network can be constructed with a sequence of the
two-qubit diagonal quantum gates and one-qubit gates in two-state quantum
systems. The universal construction of these quantum gates in the quantum
systems and of the quantum computational networks with these gates may be
achieved with the help of the operator algebra structure of Hamiltonians of the
systems and the properties of the multiple-quantum operator algebra subspaces
of the Liouville operator space and the specific properties of the quantum
algorithm corresponding to the quantum network. As an example, the two-qubit
diagonal gates are exactly prepared in detail in superconducting Josephson
junctions.
