  We present a general method which expresses a unitary operator by the product
of operators allowed by the Hamiltonian of spin-1/2 systems. In this method,
the generator of an operator is found first, and then the generator is expanded
by the base operators of the product operator formalism. Finally, the base
operators disallowed by the Hamiltonian, including more than two-body
interaction operators, are replaced by allowed ones by the axes transformation
and coupling order reduction technique. This method directly provides pulse
sequences for the nuclear magnetic resonance quantum computer, and can be
generally applied to other systems.
