  We show how the quantum Zeno effect can be exploited to control quantum
many-body dynamics for quantum information and computation purposes. In
particular, we consider a one dimensional array of three level systems
interacting via a nearest-neighbour interaction. By encoding the qubit on two
levels and using simple projective frequent measurements yielding the quantum
Zeno effect, we demonstrate how to implement a well defined quantum register,
quantum state transfer on demand, universal two-qubit gates and two-qubit
parity measurements. Thus, we argue that the main ingredients for universal
quantum computation can be achieved in a spin chain with an always-on and
constant many-body Hamiltonian. We also show some possible modifications of the
initially assumed dynamics in order to create maximally entangled qubit pairs
and single qubit gates.
