Suppression of decoherence due to classical noise by dynamical decoupling

We consider a pure dephasing model in the context of superconducting qubits. We show that the coherence time $T_2$ can be significantly increased by the application of a series of $\pi$ pulses. The most well known example, spin echo, a one pulse sequence, removes inhomogeneous broadening. However, $T_2$ can be further increased by applying more pulses. We discuss the experimental implications of various pulse sequences in the context of classical $1/f^{\alpha}$ noise in a Cooper-pair box qubit. We show that a recently proposed coherence-restoring pulse sequence [1, 2], discovered in the context of the spin-boson model, is optimal in certain regimes of parameter space. [1] G. S. Uhrig Phys. Rev. Lett. 98, 100504 (2007) \newline [2] B. Lee, W. M. Witzel, S. Das Sarma, arXiv:0710.1416 (2007).