  Given a unitary operator in a finite dimensional complex Hilbert space, its
unitary contraction to a subspace is defined. The application to quantum graphs
is discussed. It is shown how the contraction allows to generate the scattering
matrices of new quantum graphs from assembling of simpler graphs. The
contraction of quantum channels is also defined. The implementation of the
quantum gates corresponding to the contracted unitary operator is investigated,
although no explicit construction is presented. The situation is different for
the contraction of quantum channels for which explicit implementations are
given.
