  Construction of explicit quantum circuits follows the notion of the "standard
circuit model" introduced in the solid and profound analysis of elementary
gates providing quantum computation. Nevertheless the model is not always
optimal (e.g. concerning the number of computational steps) and it neglects
physical systems which cannot follow the "standard circuit model" analysis. We
propose a computational scheme which overcomes the notion of the transposition
from classical circuits providing a computation scheme with the least possible
number of Hamiltonians in order to minimize the physical resources needed to
perform quantum computation and to succeed a minimization of the computational
procedure (minimizing the number of computational steps needed to perform an
arbitrary unitary transformation). It is a general scheme of construction,
independent of the specific system used for the implementation of the quantum
computer. The open problem of controllability in Lie groups is directly related
and rises to prominence in an effort to perform universal quantum computation.
