Optimal Dynamical Decoupling Sequence for Ohmic Spectrum

We investigate the optimal dynamical decoupling sequence for a qubit coupled to an ohmic environment. By analytically computing the derivatives of the decoherence function, the optimal pulse locations are found to satisfy a set of nonlinear equations which can be easily solved. These equations incorporates the environment information such as high-energy (UV) cutoff frequency \omega_c, giving a complete description of the decoupling process. The solutions explain previous experimental and theoretical results of locally optimized dynamical decoupling (LODD) sequence in high-frequency dominated environment, which were obtained by purely numerical computation and experimental feedback. As shown in numerical comparison, these solutions outperform the Uhrig dynamical decoupling (UDD) sequence by one or more orders of magnitude in the ohmic case.