Quantum control of discrete noise in Josephson qubits

We develop a technique to study dynamical decoupling of a quantum system from a structured environment and apply it to non-Gaussian noise due to quantum bistable fluctuators and 1/f noise. We obtain analytic and numerical results for general operating points. For very large pulse frequency dynamic decoupling compensates decoherence and we found universal behavior. At intermediate frequencies noise can be compensated or enhanced, depending on the nature of the fluctuators and on the operating point. Results are interpreted in terms of quantum Zeno and inverse Zeno effect.