  If the interaction between qubits in a quantum computer has a non-diagonal
form (e.g. the Heisenberg interaction), then one must be able to "switch it
off" in order to prevent uncontrolled propagation of states. Therefore, such QC
schemes typically demand local control of the interaction strength between each
pair of neighboring qubits. Here we demonstrate that this degree of control is
not necessary: it suffices to switch the interaction collectively - something
that can in principle be achieved by global fields rather than with local
manipulations. This observation may offer a significant simplification for
various solid state, optical lattice and NMR implementations.
