  We use an n-spin system with permutation symmetric zz-interaction for
simulating arbitrary pair-interaction Hamiltonians. The calculation of the
required time overhead is mathematically equivalent to a separability problem
of n-qubit density matrices. We derive lower and upper bounds in terms of
chromatic index and the spectrum of the interaction graph. The complexity
measure defined by such a computational model is related to gate complexity and
a continuous complexity measure introduced in a former paper. We use
majorization of graph spectra for classifying Hamiltonians with respect to
their computational power.
