  We study the controllability of a closed control-affine quantum system driven
by two or more external fields. We provide a sufficient condition for
controllability in terms of existence of conical intersections between
eigenvalues of the Hamiltonian in dependence of the controls seen as
parameters. Such spectral condition is structurally stable in the case of three
controls or in the case of two controls when the Hamiltonian is real. The
spectral condition appears naturally in the adiabatic control framework and
yields approximate controllability in the infinite-dimensional case. In the
finite-dimensional case it implies that the system is Lie-bracket generating
when lifted to the group of unitary transformations, and in particular that it
is exactly controllable. Hence, Lie algebraic conditions are deduced from
purely spectral properties.
  We conclude the article by proving that approximate and exact controllability
are equivalent properties for general finite-dimensional quantum systems.
