Quantum gates and degenerations

A three state Hamiltonian witha degenerate ground state is shown to exhibit the property of generating quantum gates for fixed values of the energy parameters just by using the ability of this quantum system to evolve in time yielding suitable sets of quantum probabilities. A method is presented, based on the conventional rules of quantum mechanics, for obtaining several gates without changing the system configuration, i.e. just by adjusting the times in which the interaction is switched on and off. The mathematical rules for generating such a set of gates are completely defined and described in this work. The corresponding physical implementation should involve fast Rabi pulses and very precise switches of the kind proposed in quantum geometric computation.