Dissipative effects in Josephson qubits

Recent experiments with Josephson junctions have demonstrated long coherence times, a property crucial for their use in quantum information processing. Motivated by these experiments, we analyze the effect of the low-frequency noise with a singular power spectrum (e.g., the 1/f noise) on the coherence of Josephson qubits. We pay special attention to higher-order contributions of the noise to the dissipative effects in the qubits' dynamics