A sigle qubit Landau-Zener gate

We study the hamiltonian and dissipative dynamics of a system undergoing a sequence of level crossings. The resulting Landau-Zener effect makes a new implementation of a general single qubit gate possible. In the dissipative case, with a periodic bias, the level crossing counteracts the interlevel relaxation and drives the system toward a two dimensional attractor. This feature can in principle be used to implement quantum memory devices of new type.