  Any unitary transformation of quantum computational networks is explicitly
decomposed, in an exact and unified form, into a sequence of a limited number
of one-qubit quantum gates and the two-qubit diagonal gates that have diagonal
unitary representation in usual computational basis. This decomposition may be
simplified greatly with the help of the properties of the finite-dimensional
multiple-quantum operator algebra spaces of a quantum system and the specific
properties of a given quantum algorithm. As elementary building blocks of
quantum computation, the two-qubit diagonal gates and one-qubit gates may be
constructed physically with one- and two-body interactions in a two-state
quantum system and hence could be conveniently realized experimentally. The
present work will be helpful for implementing generally any N-qubit quantum
computation in those feasible two-state quantum systems and determining
conveniently the time evolution of these systems in course of quantum
computation.
